The materials reviewed for STEMscopes Math Grade 5 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

STEMscopes materials develop conceptual understanding throughout the grade level. In the Teacher Toolbox, STEMscopes Math Philosophy, Elementary, Conceptual Understanding and Number Sense, STEMscopes Math Elements, this is demonstrated.  “In order to reason mathematically, students must understand why different representations and processes work.” Examples include:

• Scope 6: Model the Four Operations with Decimals, Explore 1–Adding Decimals, Procedure and Facilitation Points, students develop conceptual understanding of adding whole numbers and decimals to the hundredths place. “1. Read the following scenario: a. Mr. Hunley makes wooden signs for friends and family. He has decided that he wants to build other things too! Help Mr. Huntley figure out the total amount of wood needed for his different projects. 2. Pass out a set of bases ten blocks, Scenario Cards, and 2 complete Place Value Mats to each group. Distribute a Student Journal to each student. 3. Students should begin by reading the first Scenario Card and discussing with their group members what is happening in the problem. 4. Explain to students that we are going to change our whole. Instead of the unit cube as a value of 1, we are going to use the 100 flat as the value of 1. 5. Have the students work together to discuss and solve the following questions. Allow time for students to discuss and then share. a. DOK-1 If the 100 flat has a value of 1, what is the value of the rod? b. DOK-1 If the rod has a value of 0.1 or $\frac{1}{10}$, what is the value of the unit? 6. Next ask students to discuss and then share how they use place value when adding whole numbers. Listen and guide students as they talk within their groups before sharing. Students must have the following understanding: a. Digits 0-9 have a different value depending on the position in a number. b. Add whole numbers with like units, such as the digits in the ones place are added, the digits in the tens place are added, the digits in the hundreds place are added, etc. c. Regrouping or renaming numbers to add.$$79+8$$ -add 9 ones and 8 ones and regroup to have 1 ten and 7 ones to make 87. Students may rename 7 tens to make 79 ones to add 8 ones. Emphasize the same units that must be added. 7. Explain to students that adding decimals is the same as when they add with whole numbers. a. Digits have different values depending on the position in a number. b. Decimals use the base ten format the same as our whole numbers. c. Add the same units such as ones added with ones, tenths added with tenths, and hundredths added with hundredths. d. Flexible thinking by decomposing your digits and then composing your numbers to combine the values. 8. Students should use the base ten blocks to model the numbers being added on their Place Value Mats. Each number should be modeled on its own Place Value Mat before they are added together. 9. Ask students before they begin adding the decimals to refer back to the scenario. a. DOK-2 About how many feet do you think Mr. Henley will need for his project? Students should estimate the sum for 2.8 and 1.48. Listen to students’ understanding of place value and estimation. 10. Students will then combine the amounts and record the totals. If needed, students should regroup 10 of a place value for one of the next-highest place values or rename to add the values. 11. As students are working, circulate around the room and discuss the following: a. DOK-2 What did you have to do if there were 10 or more in one place value? b. DOK-2 Why do you think the Place Value Mat has the place values lined up? 12. Ask students if their estimations were close to their solutions. Discuss why or why not. 13. Representing the number that was built with base ten blocks, students should shade in grids and record as equations on their Student Journals. Students should repeat this process for each Scenario Card. 14. After the Explore, invite the class to a Math Chat to share their observations and learning. 15. When students are done, have them complete the Exit Ticket to formatively assess their understanding of the concept.” (5.NBT.7)

• Scope 9: Add and Subtract Fractions, Engage, Foundation Builder, Solve and Justify, Part 2, develops students’ conceptual understanding as they reason about different representations for fractions. “Continue to project the slideshow for student reference. Place students in small groups. Provide each group with a student handout and preview the instructions. Provide students access to fraction towers and explain that this visual tool can be used while solving a problem. Provide each group access to materials for making a visual display. Discuss the components of a visual display: It should be written in large bold writing. All work should be shown in an organized fashion. Colors may be used to emphasize key steps, but they should not be distracting or used for decorative purposes. Any combination of visual models, words, numbers, and equations are included to communicate thinking. Discuss how to prepare an explanation for the visual display: Determine who will speak and in what order, and practice the explanation several times. Have students work together to solve each problem. Find as many different strategies as possible, approve student work, and have each group make one visual display. Try to include an example of each type of each visual fraction model used in the class. Have each group post their visual display for the whole class to see. Allow groups to visit one another’s displays as they think about how each solution is similar or different from one another. Bring the whole class together. Invite students to share their visual displays and to explain their thinking. Highlight any additional visual fraction models that were not previously demonstrated on the slideshow. Discussion points: When you add or subtract fractions, what is the denominator of the solution? Explain why. The denominator is the same as that of the fractions you were adding together or subtracting. The denominator shows the size of the pieces, so it doesn’t change if you add on or take away some of the pieces. How do you find the numerator of the sum or difference? You add or subtract the numerators of the fractions. How does a number line help you add or subtract fractions? You can see how many tick marks to add or subtract to see what the total is. Each fraction you are adding or subtracting can be a jump on a number line. Once you put all the jumps together, you will land on the final solution. You jump to the right to model addition and jump to the left to model subtraction. How do fraction towers or tape diagrams help you add or subtract fractions? You can see how many fractional parts make up a whole. Each fraction part is the same size within the model. You can shade in or build on parts that are added on or remove parts that are taken away.” (5.NF.1)

• Scope 17: Volume in Cubic Units, Explore 1–Cubic Units, Procedure and Facilitation Points, students develop conceptual understanding of a cube with a side length of one as a unit cube and understand that the volume of a three-dimensional figure is the number of unit cubes packed within the space without gaps or overlaps. “Part 1: Boxing Hats, 1. Read the following scenario: a. The Jolly Elf hat Factory just got a big order for elf hats at the North Pole, and they have hired you to pack shipping boxes with the elf hats! It is your job to fit as many elf hats into each shipping box as you can. Each centimeter cube contains one elf hat. The boxes will have lids, so the elf-hat boxes cannot go over the top of the shipping box. 2. Give each student a Student Journal. Give each group Shipping Box 1, a centimeter ruler, and a centimeter cubes. Ask questions such as the following: a. DOK-1 How can you pack the boxes so that you can fit as many elf hats into Shipping Box 1 as possible? 3. Explain that students should record how many elf hats fit the length, width, and height of Shipping Box 1 on their Student Journals. 4. Allow students to pack the boxes and write their cube totals.  5. After they have packed their boxes with cubes, students should measure the length, width, and height of the shipping box and the elf-hat boxes using the centimeter ruler. Students should record these measurements on their Student Journals. Ask questions such as the following: a. DOK-1 What are the dimensions of the elf-hat boxes that you measured? 6. Explain that this is called a cubic centimeter. Have students refer to the cubic foot and cubic yard or meter that was built. . Discuss with students how each of these are called cubic units because their length, width, and height are each 1 unit of measure. For this activity, students will be working with cubic centimeters. For the “Missing boxes” part of this lesson, students will be using cubic centimeters and cubic inches. a. DOK-1 How many elf hats could you fit into a shipping box with dimensions of 5 cm long, 4 cm wide, and 3 cm tall?  7. Explain that the word for the amount of space objects or substances take up is volume. 8. Explain that because the cubes fit together side by side, we use cubic units to measure the space, or volume, inside an object like the shipping box. Ask questions such as the following: a. DOK-2 What is the volume of Shipping Box 1? 9. Students should write the volume of Shipping Box 1 on their Student Journals. 10. Give students Shipping Box 2. Ask questions such as the following: a. DOK-2  Compare Box 1 and Box 2. Which box do you think will hold more elf hats? b. DOK-1 How will you find the volume of this box? 11. Have students complete the information for Shipping Box 2 on their Student Journals. As students are working, monitor and check for understanding. Ask questions such as the following: a. DOK-1 How many eld-hat boxes could you fit into Shipping Box 2? b. DOK-1 What is the volume of Shipping Box 2? Part ll:nMissing Boxes 1. Tell students the Jolly Elf Hat Factory didn’t get their shipment of new boxes in yet, but they still need to figure out how many elf-hat boxes will fit into each shipping box when they do arrive. The factory knows many eld-hat boxes will fit in the length, the width, and the height of each box. a. Questions 3 and 4 are in cubic centimeters and 5 and 6 are in cubic inches. Be sure to emphasize that students need to be mindful when answering questions, using manipulatives, and labeling correctly. 2. Tell students that even though they don’t have the shipping boxes, they can still use the centimeter cubes to build the box shape and determine the volume of the shipping box. 3. Have students work on building the boxes using the information on the Student Journal and centimeter and inch cubes. Students should complete the information on their Student Journals. 4. As students are working, monitor and check for understanding. Ask questions such as the following: a. DOK-2 How did you know many centimeters the length of Shipping Box 3 was? b. DOK-1 What are the dimensions of the bottom, or base, of Shipping Box 4? 5. After students have found the volume of Shipping Boxes 3 - 6, have them meet with another group and review their answers. If there are discrepancies with the answers, have them rebuild the boxes using the centimeter or inch cubes and reach an agreement on the volume of the boxes. 6. Students should complete the reflection question on their Student Journals. 7. After the Explore, invite the class to a Math Chat to share their observations and learning.  8. When students are done, have them complete the Exit Ticket to formatively assess their understanding of the concept. 9. Return to the Hook, and instruct students to use their newly acquired skills to successfully complete the activity.” (5.MD.3) 

The materials provide opportunities for students to independently demonstrate conceptual understanding throughout the grade level. Examples include:

• Scope 7: Multiply Multi-Digit Whole Numbers, Elaborate, Fluency Builder-Multiplication Baseball, Procedure and Facilitation Points, students use the algorithm to multiply multi-digit whole numbers. The game cards used provide three by two multiplication problems for students to solve. “1. Demonstrate how to play a few rounds with another student. Students will need to become familiar with the basic skills of baseball. 2. Stack the game cards facedown in the center of the game board. 3. Roll a die to see who is at bat first. The player who rolls the greater number is the batter. The other player is the pitcher. 4. The batter should line up his or her four counters behind home plate. 5. The pitcher will draw a card from the pile without showing the batter and read it aloud. 6. The batter will solve the problem on scratch paper. The pitcher will check the batter’s work. The correct answer to each problem is in blue at the bottom of each card. 7. If the batter answers correctly, he or she will roll the die to see where to move his or her first counter. a. Roll a 1 or 3: Move to first base. b. Roll a 2 or 4: Move to second base. c. Roll a 5: Move to third base. d. Roll a 6: Home run! 8. If the batter answers incorrectly, it is an out. The pitcher should use the dry-erase marker to put a tally mark in the Outs section of the game board, 9. The pitcher places the game card in a separate pile. Game cards will only be used once each game. 10. The pitcher draws and reads a new equation card to the batter. The batter again answers and follows the rules in steps 7 and 8 of these instructions. Note: You should show students how to move multiple counters that are in play. For example, if the batter’s first counter is on second base and the batter rolls a 5 on his or her next turn, the batter will move the first counter home, and the second counter will go to third base. Model how to keep track of runs. 11. The batter will keep track of his or her runs by using the dry-erase marker to put tally marks in the Runs section of the game board. 12. Repeat steps 4-10 of these instructions until the batter has either gotten three outs or moved all his or her counters home. When either of these things happens, players will switch roles and begin a new inning. 13. Play four innings and count up the runs to determine the winner. 14. Students will work to complete the student recording sheet. They will be creating multiplication equations on their own and trade papers with their partner. Their partner will have to solve in the Work Space column on the recording sheet. a. Remind students to use a three-digit number multiplied by a two-digit number for their multiplication equation.” (5.NBT.5)

• Scope 9: Add and Subtract Fractions, Explain, Show What You Know-Part 1: Addition with Unlike Denominators Using Equivalent Fractions, students use pictorial models to find common denominators to add fractions. Students should individually complete the Show What You Know activity that correlates with the Explore activity they just completed. Each Show What You Know piece correlates with the same number Explore. For example, Show What You Know Part 1 will allow students to practice the skills they developed in Explore 1. “Find the common denominator and use equivalent fractions to solve. Complete the missing values within each row. $\frac{3}{4}+\frac{1}{5}$ Visual Model ___ Equations ___   $\frac{1}{2}+\frac{1}{3}$ Visual Model ___ Equations ___” (5.NF.1)

• Scope 10: Model Fraction Multiplication, Evaluate, Skills Quiz, engages students in conceptual understanding as they connect fraction equations with models. “Match the fraction equation to the fraction model it represents, and solve below.” Questions 1-5 listed below have models showing each fraction that must be matched to the correct fraction equation. Question 1: "$\frac{1}{3\times5}$" Question 2: $\frac{3}{4}\times\frac{2}{3}$, Question 3: $\frac{4}{5}\times3$ Question 4: $\frac{1}{5}\times\frac{3}{4}$ Question 5: $\frac{3}{6}\times4$. (5.NF.4a) 

The materials reviewed for STEMscopes Math Grade 5 meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

STEMscopes materials develop procedural skills and fluency throughout the grade level. In the Teacher Toolbox, STEMscopes Math Philosophy, Elementary, Computational Fluency, STEMscopes Math Elements, these are demonstrated. “In each practice opportunity, students have the flexibility to use different processes and strategies to reach a solution. Students will develop fluency as they become more efficient and accurate in solving problems.” Examples include:

• Daily Numeracy: Fifth Grade, Activities, Daily Numeracy–Solve It, Procedure and Facilitation Points and Slideshow, students demonstrate procedural skill and fluency as they solve whole number multiplication problems using the standard algorithm. Slide 7, "$482\times45$" “2. Display the slideshow prompt of the day, and ask students to silently think and solve. Instruct students to give hand signals when they are ready to answer. 3. Call on students to give out answers only. Record student answers on chart paper.” (5.NBT.5)

• Scope 7: Multiply Multi-Digit Whole Numbers, Explore, Explore 1–Standard Algorithm, Math Chat, students engage in procedural fluency with teacher support as they multiply multi-digit numbers using the standard algorithm. “Questions: DOK-2 How is multiplying three-digit numbers by two-digit numbers similar to multiplying three-digit numbers by one-digit numbers? DOK-1 Which place values do you use from each number to find partial products?” (5.NBT.5)

• Scope 14: Numerical Expressions, Explore, Explore 1–Order Matters, Procedure and Facilitation Points, students learn the value of a standard order of operations and how failing to follow the order of operations can change the value of an expression. “1. Share the following scenario with the class: a. Tran volunteers at the animal shelter on the weekends. His job is to feed the dogs. There are 5 big dogs, 6 medium-sized dogs, and 10 puppies. Each of the big dogs eats 3 cups of dog food, each of the medium-sized dogs eats 2 cups of dog food, and 1 cup of dog food is divided equally between two puppies. How much dog food does Tran need each time he feeds the dogs at the animal shelter? 2. Distribute 75 centimeter cubes or snap cubes to each pair. 3. Encourage pairs to use the cubes to solve the problem. 4. As students are working, monitor and check for understanding. Ask questions such as the following: a. DOK-1 How can you figure out how much dog food Tran needs for the big dogs? b. DOK-1 How can you figure how much dog food Tran needs for the puppies? d. DOK-1 how can you find out how much food Tran needs? 5. Tell students to use the whiteboard (or paper) to write an expression that would represent the entire problem and write their solution to the problem (32 cups of food). 6. Have each student pair share their expression with another student pair and discuss their thinking. 7. Write the expression $5\times3+6\times2+10\div2$ on the board. Ask questions such as the following: a. DOK-1 What is the root word of evaluate? b. DOK-1 Why do you think we call this process “evaluating” an expression? c. DOK-1 How could we evaluate this expression? 8. Work from left to right evaluating this expression: $5\times3=15$, $15+6=21$, $21\times2=42$, $42+10=52$, $52\div2=26$, Ask questions such as the following: a. DOK-1 What value did you get initially? b. DOK-2 Why is that value different from the value I just got? 9. Explain to students that sometimes certain parts of expressions need to be grouped together and evaluated first, rather than just necessary to do operations in a certain order other than simply left to right. There are symbols we can use to organize these steps. 10. Write the original expression with parentheses this time: $(5\times3)+(6\times2)+(10\div2)$. 11. DOK-2 Ask students to turn and talk to a partner about what the addition of parentheses does for this expression and how this new version relates to the original problem. 12. Explain to students that there are also rules we can use to organize the steps when solving expressions. These rules make up a standard procedure used in mathematics called the order of operations. 13. Tell students that the first thing to do in the order of operations is to solve what is in parentheses. Ask students the following: a. DOK-1 How are multiplication and division related? 14. Explain that since division is the opposite, or inverse, of multiplication, they create related equations, as in $8\times4=32$ and $32\div4=8$. Therefore, multiplication and division expressions are done first in the order in which they appear, working left to right. 15. Emphasize that neither is more important than the other, so they are performed in order from left to right. 16. DOK-1 How are addition and subtraction related? 17. Explain that since subtraction is the opposite, or inverse, of addition, they create equivalent equations. In other words, $3+4=7$ and $7-4=3$. Therefore, addition and subtraction expressions are done next in the order in which they appear, working left to right. Neither one is more important than the other, so they are performed in the order they occur in the expression from left to right. 18. Distribute a Student Journal to each student. 19. Tell students that there is a problem that needs to be solved at each station. Their task is to solve the problem by first using the manipulatives and to then create an expression that represents the problem, using parentheses when needed to get the correct solution. 20. Explain that once they have written their expression, they should evaluate it using the correct order of operations. They should be on the lookout for times when parentheses must be used to ensure the correct order of operations is performed. 21. Assign student pairs to stations. As students are working, monitor and check for understanding. Ask questions such as the following: DOK-1 What expression did you write that represents the problem? DOK-2 Why did you put parentheses around 3 x $9.50? DOK-2 What process did you use to evaluate the expression? b. Station 2: DOK-1 How many bouncy balls does Sam have? DOK-2 What process did you use to find the solution? c. Station 3: DOK-2 How many action figures did the boys get? How do you know? DOK-3 Why did you use parentheses around the first 3 numbers? DOK-1 Were the parentheses necessary? d. DOK-2 Were parentheses necessary? Why or why not? 22. When students have finished, give each pair the two Task Cards. Have them use the 75 centimeter cubes or snap cubes to determine the expression that fits the scenario. Students should then evaluate the expression. 23. As students are working, monitor and check for understanding. Ask questions such as the following: a. DOK-1 How did you decide which expression matched the Cookin’ Up Something Sweet problem? b. DOK-1 How did you decide which expression matched the Extreme Chew problem? 24. After the Explore, invite the class to a Math Chat to share their observations and learning. 25. When students are done, have them complete the Exit ticket to formatively assess their understanding of the concept.” (5.OA.1)

The materials provide opportunities for students to independently demonstrate procedural skills and fluency throughout the grade level. Examples include:

• Scope 7: Multiply Multi-Digit Whole Numbers. Explain, Show What you Know Part 1–Using the Standard Algorithm, students demonstrate procedural skill and fluency of multiplying multi-digit whole numbers using the standard algorithm. “Students should individually complete the Show What You Know activity that correlates with the Explore activity they just completed. Each Show What You Know piece correlates with the same number Explore. For example, Show What You Know Part 1 will allow students to practice the skills they developed in Explore 1. Use the standard algorithm to solve each problem. $386\times34$, $634\times62$, $219\times87$, $427\times51$, $588\times44$, $187\times73$. (5.NBT.5)

• Scope 14: Numerical Expressions, Evaluate, Skills Quiz, Student Handout, Questions 1 and 11, students solve problems involving multiple operations. “Solve the expressions. 1. $7\times(32\div4)-8=$ ___, Write the statements as numerical equations with symbols. 11. Find 4 more than the quotient of 49 divided by 7.” (5.OA.1)

• Scope 19: Apply Volume Formulas, Explain, Show What You Know-Part 2: Volume of Rectangular Prisms, Student Handout, students find the volume of a rectangular prisms using the volume formula. “The local pet store provides a doggy-boarding service. Each dog that is boarded has a room in the shape of a rectangular prism, and each room has a volume of 160 cubic feet. In the boxes below, construct 2 different doggy rooms with a volume of 160 cubic feet. Include a drawing of each room and label the dimensions. Then choose the one you think has the best design. Explain your reasoning. Doggy Room #1, length = ___ feet, width = ___ feet, height = ___ feet,  volume = ___ cubic feet Doggy Room #2, length = ___ feet, width = ___ feet, height = ___ feet, volume = ___ cubic feet, Which doggy room (rectangular prism) did you choose? Explain your reasoning. ___, How did you figure out the volume of each doggy room so it was equivalent to 160 cubic feet? Explain your reasoning. ___” (5.MD.5b)

The materials reviewed for STEMscopes Math Grade 5 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of mathematics.

STEMscopes materials include multiple routine and non-routine applications of mathematics throughout the grade level, both with teacher support and independently. Within the Teacher Toolbox, under STEMscopes Math Philosophy, Elementary, Computational Fluency, Research Summaries and Excerpt, it states, “One of the major issues within mathematics classrooms is the disconnect between performing procedural skills and knowing when to use them in everyday situations. Students should develop a deeper understanding of mathematics in order to reason through a situation, collect the necessary information, and use the mechanics of math to develop a reasonable answer. Providing multiple experiences within real-world contexts can help students see when certain skills are useful.”  

This Math Story activity includes both routine and non-routine examples of engaging applications of mathematics. For example:

• Scope 10: Model Fraction Multiplication, Elaborate, Math Story–Firefighters’ Pancake Supper, students solve both routine and non-routine problems with teacher support. “Read the passage and answer the questions that follow. 2. How much money did the first nine diners pay in all? 4. Based on the passage, how long did the pancake supper last? A. 2 hours and 45 minutes, B. 3 hours and 15 minutes, C. 3 hours and 30 minutes, D. 4 hours and 15 minutes, 5. Captain Addams kept a record of the orders so he would know how many supplies they needed for next year’s supper. Of the 25 families served, $\frac{2}{5}$ bought the all-you-can-eat ticket. All the families who came are listed in the chart. How many families ordered the all-you-can-eat tickets? A 15, B 25, C 35, D 10” (5.NF.4a)

Engaging routine applications of mathematics include:

• Scope 5: Compare Decimals, Engage, Hook–Photo Finish, Procedure and Facilitation Points, students develop application of comparing two decimals with teacher support on routine problems. “Part II: Post-Explore, 1. After students have completed the Explore activities for this topic, show the phenomena video again and repeat the situation. 2. Review the problem and allow students to solve it. 3. Split the class into 6 small groups. Each group needs a resealable bag with the cards from Photo Finish! 4. Tell the students that the riders’ finishing times, in the close group of first finishers, were a little over 54 minutes. They were so close that we have times to the thousandths. They will pull out two times at a time and compare them by placing the correct comparison sign between them. They will also decide who the faster rider would be between the two. 5. Discuss the following:  a. DOK-1 Which place do you look at first when you’re comparing decimals? b. DOK-1 What does a 0 in the thousandths place mean? c. DOK-2 When you were deciding which rider was faster, what did you look at?” (5.NBT.3b)

• Scope 9: Add and Subtract Fractions, Explore, Explore 1–Adding with Unlike Denominators Using Equivalent Fractions, Procedure and Facilitation Points, students develop application with routine problems with teacher support as they use pictorial models to find common denominators to add fractions. “1. Read the following scenario: Your aunt and uncle have a big farm where they grow crops. You enjoy being on their farm, so you have offered to help your uncle and aunt with the chores during the weekends. They have divided their farmland into several different sections. They need your help in determining what fraction of the land is being used for some crops. Can you help? 2. Distribute the copies of the Student Journal to each student, and materials to each group. 3. Invite students to read Scenario 1 together. 4. Explain that your uncle and aunt have divided up an area of land for his corn crop. Ask the following questions: a. DOK-1 What does it mean that $\frac{3}{8}$ of the field is being planted with corn? 5. Have students look at the area planned for planting wheat. 6. Explain that he has divided up an area of land for his wheat crop. Ask the following questions: a. DOK-1 What does it mean that $\frac{1}{4}$ of the field is being planted with wheat? 7. Ask students to discuss in their groups: How can $\frac{3}{8}$ and $\frac{1}{4}$ be added together? 8. DOK-2 Invite students to share what was discussed among groups. 9. Explain to students that they will use manipulatives to come up with equivalent fractions for each fraction in order to create common denominators. 10. Invite them to draw the model and to use a colored pencil to indicate each crop. Ask them to use models to answer the questions in their Student Journal...” (5.NF.1)

Engaging non-routine applications of mathematics include:

• Scope 11: Multiplication Problem Solving Using Fractions, Explain, Show What You Know: Part 1, Area with Fractional Side Lengths engages students in independently solving non-routine problems involving multiplication of fractions. “Problem 3, Emmanuela wants to use half of the wrapping paper to wrap her brother's birthday gift. The dimensions of the wrapping paper are $3\frac{2}{4}$ inches by 7 inches. Once Emmanuela wraps the gift, what is the area size of the remaining piece of wrapping paper?“ (5.NF.6)

• Scope 20: Graph on a coordinate Plane, Explore 2 - Plotting Shapes, Procedure and Facilitation Points, students develop applications with non-routine problems with teacher support as they plot shapes on a coordinate plane in the first quadrant. “1. Distribute a Student Journal to each student. 2. Distribute a Blueprint and a Furniture Shapes handout to each pair. 3. Read the following scenario: a. Michaela is deciding how to arrange the furniture in her living room. She decides to use graph paper to create a blueprint of the room. She then cuts out shapes, to represent the furniture in her room. This way, she can experiment with different layouts without having to actually move the furniture. With your partner, cut out the shapes, and help Michaela find an arrangement for her furniture. 4. Invite students to discuss the following with their partners before sharing with the class: a. DOK-1 How can Michaela use a grid to help her determine the arrangement of her furniture? b. How can coordinate pairs relate to the furniture position? c. What are some things Michaela needs to take into consideration as she is plotting her furniture position? 5. Have students work with their partners to place the furniture on the Blueprint by cutting out the shapes and looking at the coordinates for each shape. Have them record the coordinates of each corner on the Blueprint. 6. As students collaborate, walk around to  monitor student understanding. 7. Have students complete the activity on their Student Journals. 8. After the Explore, INvite the class to a Math Chat to share their observations and learning. 9. When students are done, have them complete the Exit Ticket to formatively assess their understanding of the concept.” (5.G.2) 

The materials reviewed for STEMscopes Math Grade 5 meet expectations in that the three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade.

All three aspects of rigor are present independently throughout the grade. Examples where instructional materials attend to conceptual understanding, procedural skill and fluency, and application include:

• Daily Numeracy: Fifth Grade, Activities, Daily Numeracy-Solve It, Slide 3 and Procedure and Facilitation Points, students demonstrate procedural fluency of subtracting decimal numbers. Slide 3, "$431.4-31.43$" Procedure and Facilitation Points, “1. Gather students in a group with a piece of chart paper and a marker. Students should not have anything with them for this activity. 2. Display the slideshow prompt of the day, and ask students to silently think and solve. Instruct students to give hand signals when they are ready to answer. 3. Call on students to give out answers only. Record student answers on chart paper. 4. Ask students to volunteer and to explain the strategies they used to get answers. For numberless word problems, students discuss the actions that occur in the problem. Numbers can be inserted after discussion, and students can solve the problem. 5. As students share strategies, ask the class if they agree or disagree, and provide sentence stems for their responses. a. I agree because . . ., b. I disagree because . . ., c. Can you explain why you . . . ? d. I noticed that . . ., e. Could you . . . ?” (5.NBT.7)

• Scope 9: Add and Subtract Fractions, Engage, Hook–Pizza Portions, Procedure and Facilitation Points, students develop conceptual understanding of addition and subtraction of fractions with unlike denominators. “Part I: Pre-Explore, 1. Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. 2. Explain the situation while showing the video behind you: a. Lane’s family has decided to have pizza for dinner. Lane can eat $\frac{1}{2}$ of a pizza. His sister McKenna can eat $\frac{3}{4}$ of a pizza. His dad usually eats $\frac{3}{4}$ of a pizza, and his mom usually eats $\frac{5}{8}$ of a pizza. The pizzas are divided into 8 pieces. How many pizzas should they order? (Hint: It is okay if they have pieces left over for lunch the next day, but they want to be sure they have enough pieces so everyone can eat what he or she usually does.) 3. Ask students, ‘What do you notice? What do you wonder? Where can you see math in this situation?’ Allow students to share all ideas. Student answers will vary. Sample student responses: I see that fractions are math. I can tell that we will be adding fractions. I can see that some of the fractions have like denominators and some of the fractions have unlike denominators. I wonder if it will be easy to find a common denominator. I wonder if there will be pieces of pizza left over. 4. Show students a copy of the Student Handout. Explain that this will be a multi-step process. Then discuss the following: a. DOK-1 What information do we have and what do we know? b. DOK-2 What steps will need to be taken to solve the problem? …” (5.NF.1)

• Scope 11: Multiplication Problem Solving Using Fractions, Explore 2–Fraction Multiplication Problem Solving, Procedure and Facilitation Points, students develop application of fraction multiplication as they solve real-world problems involving whole numbers, mixed numbers, and fractions using visuals and equations. “1. Introduce the following scenario to students. a. Today is Field Day for the fifth grade! Everyone can feel the excitement. Before the day begins this year, the coaches want all fifth graders to be part of the planning process. They need your help to make sure the event is a success! 2. Distribute the Student Journal and Grid to each student. 3. Explain to students that at each station, the coaches have a problem they need help solving. 4. Encourage groups to collaborate and discuss multiple strategies to solve each problem. Let them know that there are manipulatives available if needed. 5. Instruct students to model their strategies and solutions on their Student Journals. In addition, they will write the equation and solution statement for each problem. 6. Explain that if they create a grid model for a station, they will need to cut it out and glue it onto the Student Journal. 7. As students are working, monitor their work and discussions. Look for understanding and misconceptions. Ask guiding questions as they are working. a. What are you solving for in this question? b. What are you multiplying? How do you know? c. How can you show that? d. What does the answer mean? 8. After the Explore, invite the class to a Math Chat to share their observations and learning. 9. When students are done, have them complete the Exit Ticket to formatively assess their understanding of the concept. 10. Return to the Hook, and instruct students to use their newly acquired skills to successfully complete the activity.” (5.NF.6)

Multiple aspects of rigor are engaged simultaneously throughout the materials in order to develop students’ mathematical understanding of a single unit of study or topic. Examples include:

• Scope: 5: Compare Decimals, Explain, Show What You Know–Part 1: Equal Number of Decimal Places, students demonstrate application of knowledge of decimal place value alongside conceptual understanding as they compare decimals using an equal number of decimal places up to thousandths using base ten blocks and grid models. “Compare using <, >, or =. Rewrite the decimals in the place value chart. Circle the place value that proves your choice. 1.387 ___ 1.837  The decimal ___ is ___ than ___ because ___.” 5.NBT.3b)

• Scope 10: Model Fraction Multiplication, Explain, Show What You Know–Part 1: Multiply Fractions by Whole Numbers, students demonstrate conceptual understanding alongside application by modeling multiplication of a fraction by a whole number and whole number by a fraction. Students should individually complete the Show What You Know activity that correlates with the Explore activity they just completed. Each Show What You Know piece correlates with the same number Explore. For example, Show What You now Part 1 will allot students to practice the skills they developed in Explore 1. “Sarah’s sister Margo invited Sarah to a tea party. Sarah poured herself, Margo, and Margo’s teddy bear each a $\frac{2}{3}$cup serving of tea. How many total cups of tea did Sarah pour? Model ___, Solution: ___, Write the multiplication equation that corresponds with the model you created. Explain your reasoning about the product value–is the product value greater or less than the value of the factors and why?” (5.NF.4a)

• Scope 13: Divide Unit Fractions, Evaluate, Skills Quiz, engages students in conceptual understanding alongside application of division strategies to solve word problems using division of a whole number and unit fractions. “Solve the word problems below by using visual fraction models. 1. Mary is making 5 cakes. Each cake will be divided into fourths. How many pieces of cake will there be when Mary cuts all the cakes? 2. A seamstress is using ___ of a $\frac{1}{2}$yard of fabric to make dresses for 3 girls. How much fabric will the seamstress use for each dress? 3. Ms. Davis is refilling her glue bottles for her art classes. She has ___ of a $\frac{1}{3}$ gallon of glue to refill 6 glue bottles. How much glue from the gallon will go into the glue bottles? 4. George is making peanut butter and jelly sandwiches for himself and 4 siblings. George cuts each sandwich into halves. How many sandwich pieces will there be when all the sandwiches are cut?” (5.NF.7b)

The materials reviewed for STEMscopes Math Grade 5 meet expectations for supporting the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

Students have opportunities to engage with the Math Practices across the year and are identified for teachers within the Standards of Mathematical Practice within the Explore sections of the scopes. MP1 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students make sense of problems and persevere in solving them as they work with the support of the teacher and independently throughout the scopes. Examples include:

• Scope 7: Multiply Multi-Digit Whole Numbers, Explore, Explore 1–Standard Algorithm, Standards of Mathematical Practice, “MP.1 Make sense of problems and persevere in solving them: Students make sense of quantities and their relationships when they use place value disks, base ten blocks, and other representational methods, to understand and solve multiplication problems.” Exit Ticket, students determine the different amount of money collected to a football game according to the type of ticket that was bought. “Tickets to the high school football game cost $21 for an adult, $14 for a student, and $55 for a family four pack. At Friday night’s game, 269 adult tickets, 387 student tickets, and 415 four packs were sold. Find how much money was collected from each type of ticket. Uses the standard algorithm to solve each problem.” 

• Scope 14: Numerical Expressions, Explore, Explore 2–Grouping Symbols, Standards of Mathematical Practice, “MP.1 Make sense of problems and persevere in solving them: Students understand and solve problems by applying their knowledge of operations with whole numbers and their understanding of the order of operations.” Exit Ticket: “Catie’s Catering charges $18.25 per person for an entree. For an additional $5, the person can have dessert too. Catie receives a dinner order for 16 people. Of those, 10 will have both an entree and a dessert. The other 6 will just have an entree (no dessert). How much will the meal cost? Write an expression that represents this problem. Then evaluate the expression.”

• Scope 20: Graph on a Coordinate Plane, Explore, Explore 3–Graphing Real World Problems, Standards of Mathematical Practice, “MP.1 Make sense of problems and persevere in solving them: Students make sense of coordinate values within the context of a problem, and they look for efficient ways to navigate their way along the coordinate plane.” Procedure and Facilitation Points: “Distribute a Student Journal to each student.Read the following scenario: You and your business partners own a company that sells shirts. As with any business, there are many tasks that need to be completed for the business to run smoothly and to make money. Today, you and your business partners will be collecting and documenting data on a coordinate plane. It is important that your group works together to help your company run a successful business. Display the Coordinate Plane Anchor Chart to review important vocabulary from past Explores. Invite students to discuss the following questions with their groups before sharing with the class: DOK-1 What does the picture on the anchor chart represent? DOK-1 What is a coordinate plane? DOK-2 How do you think a coordinate plane can help us document our business data? DOK-1 What does the vertical number line represent? DOK-1 What does the horizontal number line represent? DOK-1 What do the numbers (3, 4) represent when using a coordinate plane? DOK-1 What is an ordered pair? DOK-1 What does the first number represent in an ordered pair? DOK-1 What does the second number represent in an ordered pair? DOK-1 What does the point where the x-axis and y-axis meet represent? DOK-1 What is the origin? DOK-1 How would we plot the ordered pair (3, 4) on our coordinate plane? Explain to the class that they will be using their knowledge of coordinate planes to represent their business scenarios. They will read each station card as a group and then use the coordinate plane and dry-erase markers to represent the data from each scenario. Explain to students that they will need to rotate the job of placing ordered pairs on their coordinate plane. After each student has placed a point on the coordinate plane, they must write the ordered pair and their name on the Who Marked the Spot card. After the group has agreed that the points are representing the ordered pairs correctly, they will then record their data on their Student Journals. Place each group at a station, and monitor student collaboration as they work together as a group. Ask the following questions to assess their understanding: DOK-2 After reading the scenario, what do you think the x-coordinate represents? DOK-2 After reading the scenario, what do you think the y-coordinate represents? DOK-2 What information in the scenario can help you figure out the relationship for the ordered pairs that are being represented on the coordinate plane? DOK-1 Is each number line on the coordinate plane counting by the same amount? DOK-1 What should you do if your ordered pair doesn’t fall exactly on a line? …”

MP2 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students reason abstractly and quantitatively as they work with the support of the teacher and independently throughout the scopes. Examples include:

• Scope 3: Read and Write Decimals, Explore, Explore 2 - Decimals in Expanded Form, Standards of Mathematical Practice, “MP.2 Reason abstractly and quantitatively: Students understand decimals represent a specific quantity. They are able to connect the written decimal to a specific quantity and can read and write it accurately.” Part II “1. Distribute a Student Journal to each student. 2. Explain to students that they are going to use their understanding of expanded form to help them with the following scenario. 3. Distribute a set of Baseball Cards and a set of place value disks to each group. 4. Read the following scenario: a. A brand-new coed baseball team is finishing its first season. The Sunny City Cyclones are made up of men and women of all ages. Your task is to analyze some of the players’ batting averages. 5. Explain to students that they will be using decimal numbers with varying digits in each place and that they work with their groups to represent this decimal in various forms, including expanded form. 6. Explain that students will be looking at each player’s baseball card. They will focus on the player’s batting average. They will write this decimal in numerals on their Student Journals. Then they will use base ten blocks and place value disks to model each decimal. 7. The Place Value Mats are provided for students to practice drawing their models of the base ten blocks and place value disks with their partners before drawing them on their Student Journals. a. Note: Encourage students who may want to accurately draw each base ten block that their drawings don’t have to be perfect. Encourage them to represent the base ten blocks by drawing boxes for ones, dots for thousandths, lines or sticks for hundredths, and squares for tenths. This will allow students to draw their models more quickly. 8. Two Place Value Mats and dry-erase markers are given to each group in case some students are more comfortable using one manipulatives over the other. Students within the group can work on different Place Value Mats and explain their work to each other. 9. Once students have completed their work on their Place Value Mats and discussed their findings, they will then write an expression to show the value of each digit in the decimal and use these values to write the number in expanded form…” 

• Scope 6: Model the Four Operations with Decimals, Explore, Explore 2–Subtracting Decimals, Standards of Mathematical Practice, “MP.2 Reason abstractly and quantitatively: Students will represent decimals, focused on their values, with any of the four operations using concrete models or strategies. They connect the models/strategies to a written method with the ability to explain their reasoning. Estimation is used before solving as students concentrate on the quantities and operation involved.” Scenario Cards: Card One: “Mr. Huntley is making a small sandbox for the Sullivans’ one-year-old son, Beckham. He needs 14.03 liters of waterproof weather treatment for the sandbox. He only has 5.15 liters in his workshop! Can you help Mr. Huntley figure out how many more liters he needs to buy to complete the project? ‘Mr. Huntley is making a small sandbox for the Sullivans’ one-year-old son, Beckham. He needs 14.03 liters of waterproof weather treatment for the sandbox. He only has 5.15 liters in his workshop! Can you help Mr. Huntley figure out how many more liters he needs to buy to complete the project?’” Card two: “The town’s recreation center asked Mr. Huntley to help it build a welcome board out of painted pinewood. He needs 8 feet of pinewood for the sign, but he only has 1.61 feet in his workshop. 1 Help him determine how much more pinewood he needs.” Card three: “Mr. Jeff is surprising his wife with a beautiful natural wood dining table. The main plank of wood that Mr. Huntley is using is 11.5 feet, but according to the email, it only needs to be 8.32 feet. How much does Mr. Huntley need to cut off?”

• Scope 10: Model Fraction Multiplication, Explore, Explore 1–Multiply Fractions by Whole Numbers, Standards of Mathematical Practice, “MP.2 Reason abstractly and quantitatively: Students recognize that fractions represent specific quantities and their quantities change when multiplied. Students observe that when multiplying a fraction greater than one the number increases, and when multiplying a fraction less than one the number decreases.” Procedure and Facilitation Points: “There should be two sets of the three stations. Assign a station where each group will begin. Explain the following scenario: Today, you will be the production manager for the Fresh Sips Beverage Company. A production manager has quite a few responsibilities. As you go through the factory, it is your responsibility that everything runs smoothly, and you may come across some problems that you have to solve. In room 1, also known as Station 1, you will be helping the Sassy Strawberry-Lemon Punch workers follow the proper ingredients to fill the order. In room 2, or Station 2, the supply room workers need help solving the problem for the supplies needed for the big birthday order. Finally, in room 3, or Station 3, you will have to solve some problems that the accountants are having with the weekly production totals. Discuss with students the different models found in each station. In Station 1, students will use fraction tiles to model. In Station 2, they will use fraction circles to model. Finally, in Station 3, students will use number lines. Ask students to review the Station Card at their station and determine what units they are modeling. DOK-1 Discuss with students that when you solve problems that people solve in everyday life, they are not always dealing with only whole numbers. Ask for examples. An example is $\frac{2}{5}$ of a gallon of lemon juice, $\frac{3}{4}$ of a box. Have students discuss with their groups how they can model the scenarios and work together within their stations using the materials provided to model and solve the problems. …Note for Station 3: Fresh Sips Production Instruct students to each use three of the strips of manila paper and tape them together along the short ends to make a longer strip. Next, have students use the ruler to draw an unlabeled number line in the middle of the strip, along the full length of the strip.Then have them place a mark near the left side of the line for 0. Have them use the whole fraction tile to mark the whole-number intervals on the line by laying the 1 whole tile under the number line, starting at 0 and using the other end to mark 1. … DOK-1 Ask them what they notice about the product of a fraction and the whole number factor. DOK-2 Why would that be? DOK-3 How can you prove it? DOK-1 Ask the students what they notice about the product and factor that is a fraction. DOK-2 Why would that be? DOK-3 How can you prove it? DOK-2 Before you even start modeling or multiplying, how can you estimate the product to be when multiplying a fraction by a whole number?...”

The materials reviewed for STEMscopes Math Grade 5 meet expectations for supporting the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials provide opportunities for student engagement with MP3 that are both connected to the mathematical content of the grade level and fully developed across the grade level. Mathematical practices are identified for teachers within the Standards of Mathematical Practice within the Explore sections of the Scopes. Students construct viable arguments and critique the reasoning of others, in connection to grade-level content, as they work with support of the teacher and independently throughout the Scopes. Examples include:

• Scope 6: Model the Four Operations with Decimals, Explore, Explore 4, Multiply Decimals: Arrays and Area Models, Exit Ticket, Student Handout, Standards for Mathematical Practice: “MP.3 Construct viable arguments and critique the reasoning of others: Students will make conjectures and explore their solutions, looking for evidence of proof as they determine the concrete model or strategy needed to solve a decimal problem. Students listen to others asking clarifying questions and expecting feedback. They may provide counterexamples to justify conclusions.” Exit Ticket: “You had been begging your parents to let you have a dog. They finally gave in, and now you are getting a new dog! You need to have a place for the dog to stay at night, so you do some research on the size of doghouse your dog will need. According to the experts, your dog needs a house with an area of at least 8 square feet on the bottom. You find a doghouse on sale with the following dimensions:” An image of a dog house with a floor labeled with a width of 2.52 feet and length of 3.75 feet. “Is this dog house big enough for your new dog? Use an area model to find out! The area of the floor of the doghouse is ___ square feet. Is the house big enough for your new dog? Explain.”

• Scope 10: Model Fraction Multiplication, Evaluate, Decide and Defend, Student Handout, Standards for Mathematical Practice: “MP.3 Construct viable arguments and critique the reasoning of others: Students explain calculations based upon models and properties of operations. They participate in mathematical conversations to share strategies and to make sense of alternative reasoning of others.” Evaluate: Decide and Defend: Multiply It! “James’s teacher asked him to label each scenario below using one of the following descriptions: Description 1: This scenario would end with a product that is less than the first factor being multiplied. Description 2: This scenario would end with a product that is greater than the first factor being multiplied” A model of 3 circles and a multiplication sign and $\frac{1}{2}$ is shown. “Which scenario would you use to describe what would happen in the expression above? Why do you think this? What is the product of the problem above? ___. Which scenario would you use to describe what would happen in the expression above? Why do you think this? What is the product of the problem above? ___. ”

• Scope 11: Multiplication Problem Solving Using Fractions, Explore, Explore 2–Fraction Multiplication Problem Solving, Standards for Mathematical Practice, Procedure and Facilitation Points, students build experiences with MP3. In the Standards for Mathematical Practice, the program notes the work with MP3. “MP.3 Construct viable arguments and critique the reasoning of others: Students explain calculations based upon models and properties of operations. They participate in mathematical conversations to share strategies and to make sense of alternative reasoning of others.” In Procedure and Facilitation Points, “1. Introduce the following scenario to students. a. Today is Field Day for the fifth grade! Everyone can feel the excitement. Before the day begins this year, the coaches want all fifth grades to be part of the planning process. They need your help to make sure the event is a success!. 2. Distribute the Student Journal and Grid to each student. 3. Explain to students that at each station, the coaches have a problem they need help solving. 4. Encourage groups to collaborate and discuss multiple strategies to solve each problem. Let them know that there are manipulatives available if needed. 5. Instruct students to model their strategies and solutions on their Student Journals. In addition, they will write the equation and solution statement for each problem. 6. Explain that if they create a grid model for a station, they will need to cut it out and glue it into the Student Journal. 7. As students are working, monitor their work and discussions. Look for understanding and misconceptions. Ask guiding questions as they are working: a. What are you solving for in this question? b. What are you multiplying? How do you know? c. How can you show that? d. What does the answer mean? 8. After the Explore, invite the class to a Math Chat to share their observations and learning. Math Chat: DOK-2 What are the different ways that you could have chosen to solve each problem? DOK-2 What observations did you have about multiplying with mixed numbers? DOK-3 What connections did you make while doing this Explore activity? DOK-2 Find someone who used a different strategy than you for the same card. Compare the two strategies.”

• Scope 15: Classify Two-Dimensional Figures, Elaborate, Fluency Builder–Name that Shape, Instruction Sheet, engages students as they listen to the arguments of others and decide if they make sense. “Play this game in a group of three to four. You Will Need: 1 Set of secret shape cards (per group); 1 Set of shape cards (per group); 1 Passes Inspection mat (per group); 1 Does Not Pass Inspection mat (per group); 1 Student recording sheet (per player). How to Play: 1. Pick a person to be the Shape Inspector. The Shape Inspector shuffles all the secret shape cards and places them facedown in a pile. 2. Lay out the shape cards in even rows, faceup, for all players to see. 3. The Shape Inspector draws a secret shape card from the stack and holds this card so the other players can’t see it. 4. On the first turn, each player takes a turn by pointing to one card and asking the Shape Inspector, “Will this pass inspection?” The Shape Inspector checks the card and tells the player yes or no. (Each secret attribute card has an answer key indicating all the cards that pass inspection— that is, all the cards with shapes that fit into the classification on the secret card.) 5. If the card passes, the player places the card faceup on the Passes Inspection mat. If it does not pass, the card is placed faceup on the Does Not Pass Inspection mat. 6. After all players have placed one card on either mat, each player asks the Shape Inspector if a new card meets inspection. The player has the option to make one guess to name the mystery shape. 7. The first player to correctly name that shape wins the round and becomes the Shape Inspector for the next round. 8. Between each round, pause to complete the student recording sheet. 9. After eight rounds, or when time runs out, the game ends. The player who won the most rounds wins the game.”

The materials reviewed for STEMscopes Math Grade 5 meet expectations for supporting the intentional development of MP4: Model with mathematics; and MP5: Use appropriate tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

Students have opportunities to engage with the Math Practices across the year and are identified for teachers within the Standards of Mathematical Practice within the Explore sections of the Scopes. MP4 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students model with mathematics as they work with the support of the teacher and independently throughout the Scopes. Examples include:

• Scope 3: Read and Write Decimals, Explore, Explore1–Read and Write Decimals, Print Files, Exit Ticket engages students in MP4 as they accurately model each value as a numeral, base ten block model and number name. “Read each scenario, and correctly represent each value as a numeral, a base ten block model, and with a number name. Wally World needs 2.034 pounds of spaghetti placed into a prepared meal container. Represent this weight in the space below.” Below this description are columns labeled: “Numeral: Base Ten Block: Number Name:” The second question is set up the same with columns and directions for the following question: “Wally World needs four hundred eight thousandths of a pound of sliced ham placed into a prepared meal container. Represent this weight in the space below.”

• Scope 8: Divide Multi-Digit Whole Numbers, Explore, Explore 1–Rectangular Arrays, Print Files, Scenario Cards engage students in MP4 as they model the situation with an appropriate representation. Students use base ten models to represent the division problems necessary to answer the questions. “Scenario 1—Dealership 1 Fred’s Fine Motors is about to have their grand opening. They just received shipments totaling 1,560 cars. They want to park the cars in 24 rows. Plan how the cars will be arranged on the dealership’s parking lot to determine how many cars will be parked in each row. Scenario 2—Dealership 2 All-Star Auto needs to park 864 used cars in 18 rows on their lot. Plan how the cars will be arranged in the dealership’s parking lot to determine how many cars will be parked in each row. Scenario 3—Dealership 3 Drive Away Happy is moving to a new location. They need to park their 1,176 cars on the new lot. They want each row to have 56 cars. Plan how the cars will be arranged on the dealership’s parking lot to determine how many rows of cars will be on their lot. Scenario 4—Dealership 4 Carl’s Cruisers is the largest dealership in the state. They have 4,212 cars on their lot. They need your help in arranging each row on their lot to have spaces for 36 cars. Plan how the cars will be arranged on the dealership’s parking lot to determine how many rows of parking spaces are needed. Scenario 5—Dealership 5 Speedy Cars is having their annual clearance sale. They have 1,462 cars on sale. They want to park these cars in 17 rows. Plan how the cars will be arranged in the dealership’s parking lot to determine how many cars will be parked on each row.”

• Scope 11: Multiplication Problem Solving Using Fractions, Explore, Explore 2–Fraction Multiplication and Problem Solving, Procedure and Facilitation Points, engages students in MP4 as they model different situations at each station. The students ask students to explain their reasoning as to what they are multiplying as well as asking them to show their reasoning. “Introduce the following scenario to students. Today is Field Day for the fifth grade! Everyone can feel the excitement. Before the day begins this year, the coaches want all fifth graders to be part of the planning process. They need your help to make sure the event is a success! Distribute the Student Journal and Grid to each student. Explain to students that at each station, the coaches have a problem they need help solving. Encourage groups to collaborate and discuss multiple strategies to solve each problem. Let them know that there are manipulatives available if needed. Instruct students to model their strategies and solutions on their Student Journals. In addition, they will write the equation and solution statement for each problem. Explain that if they create a grid model for a station, they will need to cut it out and glue it onto the Student Journal. As students are working, monitor their work and discussions. Look for understanding and misconceptions. Ask guiding questions as they are working: What are you solving for in this question? What are you multiplying? How do you know? How can you show that? What does the answer mean? After the Explore, invite the class to a Math Chat to share their observations and learning.”

MP5 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students use appropriate tools strategically as they work with the support of the teacher and independently throughout the Scopes. Examples include:

• Scope 5: Comparing Decimals, Elaborate, Problem-Based Task-Batter Up! students build experience with MP5 as they use technological-based tools and different websites to research baseball players to “build” a team. “Every year in June, baseball teams have what’s called a draft. During the draft, the 30 Major League clubs will take turns selecting players to play on their team. Once you enter the league and start playing games, a player will earn a batting average for how well they can hit the ball. The batting average is defined by the number of hits divided by at bats. It is usually reported to three decimal places. Baseball coaches want players on their team who have a batting average of .300 or greater. This means that the baseball player can usually hit the ball and get on base 1 out of 3 at bats.Your Task: You and a partner are coaches of MLB teams. Research baseball players and their batting averages, and draft your top 10 baseball players. Compare each player chosen from each round. The greater the number, the better the player. The catch is that one partner can only draft players between the years 1990-2000, and the other partner can only draft players between 2001-2011. Decide which person will draft from which set of years, and then complete your draft picks on the Make Your Picks page. Make sure you don’t choose the same player from another year since baseball players can play baseball for many years in a row. Decide on your team name and what years you will be drafting from and write them below. Then, using the internet, research baseball player batting averages and decide which 10 players you would like to draft. Record their names and their batting averages in the table.”

• Scope 12: Fractions as Division, Explore, Evaluate, Decide and Defend, Print Resources, Student Handout, engage students in MP5: Use appropriate tools strategically. “During Teacher Appreciation Week, Kyle’s mom brought in 3 pies for the teachers to share. The only problem is that there were 4 teachers. The math teacher told them not to worry. $3\div4$ is the same thing so each teacher will get a pie. This didn’t make any sense to the other teachers. Use the circles below to show the situation and explain how the math teacher got her answer.” Below this scenario are three equal-size circles presented as tools for students to use to solve the problem. 

• Scope 20: Graph on a Coordinate Plane, Evaluate, Decide and Defend, Print Files, Student Handout, engages students in MP5 as students use a coordinate grid to determine the location of a treasure. “Buried Treasure: Will’s mom sent him on a treasure hunt around the neighborhood. Their neighborhood map was set up just like a coordinate grid. She told Will that their house was the origin. His mom gave him his first clue and a map. At each location there will be another clue. Buried Treasure Will says that it’s not possible to find the treasure because he doesn’t have enough information. Is he correct? Track Will’s treasure hunt on the coordinate plane. Label each stop including Will’s house. Prove Will right or wrong. Graph on a Coordinate Plane 1 ___ The first stop will be at (2, 3). At the first stop, Will’s clue will take him to go to (0, 6) At the second stop, Will’s last clue says, “Walk 8 blocks east and 2 blocks south to find the treasure.” Below is a grid with the x and y axis labeled from 0-8 on each axis.

The materials reviewed for STEMscopes Math Grade 5 meet expectations for supporting the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

Students have opportunities to engage with the Math Practices across the year and are identified for teachers within the Standards of Mathematical Practice within the Explore sections of the Scopes. MP6 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students attend to precision as they work with the support of the teacher and independently throughout the Scopes. Examples include:

• Scope 8: Divide Multiple Digit Whole Numbers, Explore, Explore 3–Partial Quotients, Exit Ticket, students attend to precision as they decompose the dividend into base-ten units and find the quotient starting with the highest place value. “Use partial quotients to solve the problems below. Show your work in the space provided. The toy store sold 32 electric trains for a total cost of $4,928. How much did each train cost? Answer ___  The game store sold video games for $64 each. If they sold a total of $9,088 worth of video games, how many games did they sell? Answer ___” 

• Scope 14: Numerical Expression, Explore, Explore 1–Order Matters, Print Files, Exit Ticket engages students in attending to precision and using the specialized language of mathematics. “Create an expression that represents the word problem below, evaluate it, and then describe the process you used to evaluate it. Lilly hired 3 teens to mow her grass and rake the leaves. She paid them $75 to mow and $30 to rake, and the boys split the money equally. Since the boys also swept her sidewalk, she paid each of them an extra $5 as well. Write an expression that shows how much money each teen received.” Space is provided for “Expression, Evaluate, Process-Description, Solution”. “Circle the expression that matches the word problem below. Then explain your reasoning. Mauri received a gift card for $100. He went to the movies 3 times with that card. Each time he spent $10 on a ticket, $1.50 on a drink, and $1.50 each for 2 boxes of candy. One time he bought popcorn for $3.50. Which expression below can be used to determine the amount he had left on his card? $100-3\times10+(1.5+2)\times1.5-3.5$; $100-3(10+1.5+2\times1.5)-3.5$ Reasoning:___”

• Scope 17: Represent Measurement with Line Plots, Explore, Explore 1–Problem Solving with Measurement on a Line Plot, Print Files, Student Journal page 1 and Scenario Card 1 engage students in MP6: Attend to precision. “Use the space below to draw a line plot for the data from each Scenario Card. Answer the questions.” Below this prompt, a space to create the plot where a line is provided and labeled “Mr. Lyon’s Science Investigation” followed by this prompt: “Mr. Lyons wanted to reuse the water from the previous investigation. He combined all the water from the beakers and then equally redistributed it among the 8 beakers. How much total water did he have? How much water did each beaker receive?”This is followed by a space for students to provide “Equation(s)” and show “Work:” and write a “Solution Statement”. Students will use the data on the Scenario Card 1 lto complete. Scenario Car 1: “Mr. Lyons is preparing for a science investigation in his classroom. He takes 8 beakers from the cabinet and fills them with the amounts of water shown below.” the following measurements in Liters are given: "$\frac{1}{8}$; $\frac{1}{8}$; $\frac{1}{4}$; $\frac{1}{2}$, $\frac{1}{8}$; $\frac{1}{2}$; $\frac{1}{4}$; $\frac{1}{8}$ Create a line plot to show this data.”

The materials reviewed for STEMscopes Math Grade 5 meet expectations for supporting the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

Students have opportunities to engage with the Math Practices across the year and are identified for teachers within the Standards of Mathematical Practice within the Explore sections of the Scopes. MP7 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students look for and make use of structure as they work with the support of the teacher and independently throughout the Scopes. Examples include:

• Scope 3: Read and Write Decimals, Explore, Explore 1–Read and Write Decimals, Procedure and Facilitation Points, students build experience with MP7 as they look for the multiplicative pattern within the structure of the base-ten system. “Part I 1. Distribute a Student Journal to each student and the bag of base ten blocks to each group. 2. Explain to students that sometimes we can use the same shape but look at it differently. For example, right now the unit block represents the value of 1. 3. Have the students work together to discuss and solve the following questions. Allow the groups time to work together and discuss their answers before sharing with the class. a. DOK-1 What is the value of the rod? b. DOK-1 What is the value of the flat? c. DOK-1 What is the value of the cube? d. DOK-1 What are the number names that we give these values? e. DOK-2 How did you figure out the value of each model? 4. Explain to students that now we are going to change the whole. The thousand cube is not going to have the value of 1. 5. Have the students work together to discuss and solve the following questions. Allow the groups time to work together to discuss their answers before sharing with the class. a. DOK-1 What is the value of the flat? b. DOK-1 What is the value of the rod? c. DOK-1 What is the value of the unit? d. DOK-1 What are the number names that we give these values? e. DOK-2 How did you figure out the value of each model?… 7. Explain to the students that they will be working with decimals today. A decimal represents a value that is part of the whole. We use decimals when we need to be more accurate than what a whole number can provide. 8. Have the students discuss as a group where they have seen decimals in the world around them… 10. After students have had enough time to discuss, gather the class together for a quick Math Chat. Part II: Preparing Meals 1. Read the following scenario to the class: a. Today you are working for Wally World grocery store and helping it prepare meal kits for customers. Each meal kit needs to be a specific weight and have a label placed on the container so customers know the food inside and its weight. Help the grocery store place the correct weight inside each container using base ten blocks, and write the correct weight on the label using the numeral form and number name. 2. Explain to students that around the room are 5 stations of meal kits that need to be prepared to the proper weight. Some of the weights are written as a numeral, and some are written with a number name. 3. Explain that when writing a number name, we will write the word and to represent the decimal just like when we say and to represent a decimal in money. We must also include the name of the place value spot of the last digit in our numeral. a. DOK-1 What would be the number name if my decimal went one place after the decimal? b. DOK-1 What would be the number name if my decimal went two places after the decimal? c. DOK-1 What would be the number name if my decimal went three places after the decimal? 4. Explain that the students job is to represent each weight using the least number of base ten blocks on their Place Value Mats… 6. Monitor students as they work together, and ask the following questions to check for understanding: a. DOK-1 What does the cube represent? b. DOK-1 What does the flat represent? c. DOK-1 What does the rod represent? d. DOK-1 What does the unit represent. e. DOK-1 What word do we use to represent the decimal in a number name? f. DOK-2 How do we know whether to put tenths, hundredths, or thousandths at the end of the number name? g. DOK-2 how can we use the numeral to help us represent a model? h. DOK-2 How can we use the number name to help us represent a model?”

• Scope 6: Model the Four Operations with Decimals, Explore, Explore 3–Multiply Decimals - Place Value, Procedure and Facilitation Points, students build experience with MP7 as they look closely to discern how to best represent a decimal problem. “1. Discuss the different ways we can think about base ten blocks. a. DOK-1 If a flat is equal to one whole, what is the value of a rod? A unit? 2. Read the following scenario to students: a. Welcome to the Crazy Cake Factory! We specialize in creating the tastiest 10-by-10-inch sheet cake. Our customers love them! However, our customers don’t always want the whole sheet cake. Sometimes they order just a part of a cake or parts of many different flavors of cake! To charge them the right price, we need to figure out how much cake is being ordered each time! Each flat represents one 10-by-10-inch cake or one whole cake. … 5. As students are working, circulate around the room and discuss the following: a. DOK-2 What patterns do you notice? b. DOK-2 How do you find one group of one-tenth? c. DOK-2 How do you find one-tenth of one-tenth? 6. Have students continue on to the next set of orders. Students should find the total amount of cake for the first two orders without using the base ten blocks since they involve only whole numbers. The rest of the orders should be modeled using the base ten blocks. 7. As students continue working through the orders, circulate around the room and discuss the following: a. DOK-1 As you move through the orders, what changed about the digit 5? b. DOK-2 How did changing the place value of the digit 5 affect the place value of the product?” 

• Scope 10: Model Fraction Multiplication, Explore, Explore 2–Multiply Fractions by Fractions,  Procedure and Facilitation Points, students build experience with MP7 as they explore a variety of visual models in reasoning about multiplication with fractions, and they interpret the structure of multiplication as scaling. “1. Explain the following scenario to the class: a. You and your friends want to hike some of the local trails this summer. Since there are so many, the group of you decided to hike a part of the trails your first week. Then later in the summer, the group of you will pick your favorite ones to hike the entire trail length. 2. Explain that the first four trails have been placed in stations around the room, and students must determine the distance they hiked on the trail. 3. Encourage them to sketch a model to help find the distance. a. In Scenarios 1 and 3: Invite students to create an area model with their dry-erase markers on the desk. The model will help them determine the common denominator and the distance they traveled in their problem before they sketch it on their Student Journals. b. In Scenarios 2 and 4: Invite students to use the strips of manila paper and draw a number line to create a model for the problem. … c. In addition to each model, the group will develop a multiplication equation for the hiking trail scenario. d. Challenge the groups to observe and compare the total distance hiked (product) to the length of the total trail, and the fraction they hiked. Together reason why the product results in what it does…a. DOK-1 Scenario 2 starts with ¼ mile; how much did you hike? b. DOK-1 What fraction do you need to separate each of the ¼ intervals? c. Have students separate each ¼ interval into sixths. d. DOK-2 How many fractional sections are there now? … 7. Then have them talk about separating the length of the trail into equal intervals based on what they are multiplying by. a. DOK-1 Scenario 4 starts with $\frac{3}{5}$ mile; how much did you hike? b. DOK-1 What fraction do you need to separate each of the $\frac{1}{5}$ intervals? c. Have students separate each $\frac{3}{5}$ interval into fourths. d. DOK-2 How many fractional sections are there now? e. DOK-2 How many 20ths are there in $\frac{3}{5}$? How big is $\frac{1}{4}$ of $\frac{3}{5}$?”

MP8 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students look for and express regularity in repeated reasoning as they work with the support of the teacher and independently throughout the Scopes. Examples include:

• Scope 2: Place Value Relationships, Explore, Explore 2–Powers of 10, Procedure and Facilitation Points, students build experience with MP8 as they utilize repeated reasoning and regularity to explain patterns in the placement of the decimal point and in the number of zeros at the end of a product when multiplying or dividing by powers of 10. “Part I 1. Distribute a Student Journal to each student and a set of Business Cards and place value disks to each group. 2. Have the students organize the place value disks based on place value and order from greatest place value to least place value. 3. Ask students the following questions about what they notice with the place value disks, and have them turn and talk with their groups about their observations: a. How many disks are needed before you get to the next place value? b. DOK-1 What relationship do the place value disk represent between each place value? c. DOK-1 How do we determine which place value is greater than another place value? 4. After discussing these questions with the class, read the following scenario: a. There are many businesses in the city where you live and around the world. A business must earn money to stay open, but it also must pay employees and help customers. Each business has different needs, and some have hired you and your group to help it figure out its earnings, how to pay employees, or help its customers. 5. Explain to students that they will be reading each Business Card scenario with their groups and working together to represent each scenario as a model with their place value disks, as an expression, and then with a value. 6. As students are working, monitor the groups, and ask the following questions to check for understanding: a. DOK-1 How can you tell when we need to multiply to find our answer? b. DOK-1 How can you tell when we need to divide to find our answer? c. DOK-2 What pattern do you notice happening over and over again? d. DOK-2 What do you notice about the whole numbers when I either multiply 10 or divide by 10? 7. Groups will record their work and observations on their Student Journals as they complete each scenario card.  Part II 1. Explain to students that they will continue to work with multiplying and dividing by 10 in Part 2 of their Explore; however, now they will be working with decimal numbers. 2. Review with students briefly the following questions: a. DOK-2 What pattern did you notice occurred when you would multiply a whole number by 10 or multiple 10s? b. DOK-2 What pattern did you notice occurred when you would divide a whole number by 10 or multiple 10s? c. DOK-2 Do you think when I multiply or divide a decimal by a 10 or multiple 10s that it will have the same outcome? 3. Read the following scenario to the class: a. Banks deal with all kinds of different coins, and they must place them in rolls so that they are easier to organize. Banks must also undo these rolls and distribute these coins to bank customers. The bank needs your help in organizing and distributing these coins. 4. Explain to students that there are Coin Cards with the appropriate coins at each station around the room. Their group’s job is to read each scenario card and model that scenario using their coins.  They will then write an expression and a value for each part of their scenario on their Student Journals. … 6. As students are working at each station, monitor for understanding by asking the following questions: a. DOK-1 How can you tell when we need to multiply to find our answer? b. DOK-1 How can you tell when we need to divide to find our answer? c. DOK-1 How can I use the coins to help me represent the scenario? d. DOK-2 What pattern do you notice when we are multiplying a decimal by 10? Can I simply add a zero to the end of my product? e. DOK-2 What pattern do you notice when we are dividing a decimal by 10? Can I simply take a zero away from the end of my quotient?”

• Scope 16: Unit Conversions, Explore, Explore 1–Convert Units of Length, Standards for Mathematical Practice, Procedure and Facilitation Points, students build experience with MP8 as they find relationships between units and between different-sized converted units. “1. Read the following scenario: a. An urban planner begins to create a design for improvements to a small town that is quickly growing. The planner will use existing buildings and add new places and structures to prepare for the growing population. There are many limitations and regulations that she must follow. … 4. Explain that their job is to use the measurement tools and given information to answer each question and make sure that the planner’s measurements are accurate. … 6. As students are working, monitor and check for understanding. Ask questions such as the following: a. DOK How did you convert meters to centimeters? b. DOK-1 How did you convert inches to yards? c. DOK-1 Do you notice a pattern when you need to convert a measurement unit to the next-smallest measurement unit? d. DOK-1 Do you notice a pattern when you need to convert a measurement unit to the next-largest unit? 7. When students have completed the conversions at all six stations, have them meet with another group and share their answers. If there are any discrepancies between answers, both groups should return to that station and resolve the problem.” 

• Scope 21: Generate and Graph Numerical Patterns, Explore, Explore 2–Generate and Graph Two Numerical Patterns, Procedure and Facilitation Points, students build experience with MP8 as they examine numerical patterns with the same starting number for two different rules and identify relationships between corresponding terms. “1. Introduce the scenario to the students: a. It’s Carnival time! There is always so much to do at a carnival. We can ride the rides, play so many games, and eat a ton of yummy food. Everything is so much fun, but the contests are always the most popular attractions. Each of the stations represents a different contest. Work together to determine how much you can win! 2. Explain that when they are trying different numbers that represent a change in a scenario or context, that is called a variable and is usually represented by a letter like x or y. a. DOK-1 How can you represent the scenario numerically with a variable? b. DOK-1 How can we represent this pattern continuing with different numbers? c. DOK-2 How would the graph compare to the numbers on the table? 3. As the students are working in groups, monitor discussions, and look for misconceptions. 5. Students should record the rules, define what the variables mean, and describe the rule in their own words on their Student Journals. 6. Students should then use the rules to complete the tables showing the numerical patterns. 7. For each contest there are two rules. Be sure to record both tables on the same graph. … 9. Ensure that students do the following with each graph: a. Give the graph a title and label each axis. They can reference what each variable represents. b. Students should then look at the values for z and the values for y to decide what scale to use on each axis. c. Have students write the number values along each axis. d. DOK-1 Guide students in finding the line that represents x = 0. Zero is found where the x-axis and y-axis intersect. What is that called? e. DOK-1 When x = 0, what is the value of y? f. Find the value of x on the x-axis and the value of y on the y-axis. Where they intersect, place a point. Have students repeat the same process for each value listed in the table. 10. Continue to monitor, asking the following guiding questions to assess understanding. a. DOK-1 For the x-axis, should we count by ones, twos, fives or 10s? b. DOK-1 For the y-axis, what should we count by? c. DOK-1 What is the first value we have the x in our table? d. DOK-1 Both rules are related to each other. What do you notice about the two tables? e. DOK-2 What do you notice about the two lines when you graph them? When it is a multiplying rule, they get further apart. Any ideas why? f. DOK-2 How can you discover how the two rules are related to each other?”

The materials reviewed for STEMScopes Math Grade 5 meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.

Materials provide comprehensive guidance that will assist teachers in presenting the student and ancillary materials. Within each Scope, there is a Home dropdown menu, where the teacher will find several sections for guidance about the Scope. Under this menu, the Scope Overview has the teacher guide which leads the teacher through the Scope’s fundamental activities while providing facilitation tips, guidance, reminders, and a place to record notes on the various elements within the Scope. Content Support includes Background Knowledge; Misconceptions and Obstacles, which identifies potential student misunderstandings; Current Scope, listing the main points of the lesson, as well as the terms to know. There is also a section that gives examples of the problems that the students will see in this Scope, and the last section is the Coming Attractions which will describe what the students will be doing in the next grade level. Content Unwrapped provides teacher guidance for developing the lesson, dissecting the standards, including verbs that the students should be doing and nouns that the students should know, as well as information on vertical alignment. Also with each Explore, there is a Preparation list for the teacher with instructions for preparing the lesson and Procedure and Facilitation Points which lists step-by-step guidance for the lesson. Examples include:

• Scope 5: Compare Decimals, Explore, Explore 2–Unequal Number of Decimal Places, Procedure and Facilitation Points. Teachers follow these steps:  “1. Ask students if they have ever seen a horse race. Allow them to share their experiences. 2. Prepare pictures or a video clip of the Kentucky Derby so students may have a visual picture of what a horse race is. 3. Explain that a famous race called the Kentucky Derby is run every year on a track called Churchill Downs in Louisville, Kentucky. The length of the track is 1.25 miles. Well-prepared horses race for the finish line so they can be called the champion of the Kentucky Derby! 4. Tell students they will be comparing the times it took champion horses from different years to run the track at the Kentucky Derby. Of the two horses racing, the one with the faster time would be the champion. 5. Ask students to discuss in their groups what it means to have a faster time in a race. Will the number be the greatest or least, and why?”

• Scope 12: Fractions as Division, Explore, Skill Basics–Reason with Benchmark Fractions, Procedure and Facilitation Points. Teachers will follow these instructions:  “1. Give a Student Work Mat, dry-erase marker, and dry-erase eraser to each student. 2. Tell students they will be given some fractional parts. With partners, they will decide if the fractional parts are less than, greater than, or equal to the benchmark fraction on one whole. 3. Give bag 1 to each pair. Instruct them to remove the two trapezoids and fraction card from the bag. 4. Instruct students to draw two trapezoids under Fraction Model on the Student Work Mat. 5. As you discuss the following questions, have students write the information on the Student Work Mat: a. What does the fraction card say? Write “halves” on the Student Work Mat. b. If these trapezoids represent halves, what does each trapezoid, or part, represent? Write “one-half” on the Student Work Mat. c. How many one-halves, or parts, are in a whole? Write “2” on the Student Work mat. D. How many trapezoids, or parts, are there? Write “2” on the Student Work Mat. e. What fraction do these trapezoids, or parts, represent? Write "$\frac{2}{2}$" on the Student Work Mat. f. Are these trapezoids, or parts, less than, equal to, or greater than one whole? Write "$\frac{2}{2}=1$ whole” on the Student Mat.” 

• Scope 19: Apply Volume Formulas, Explore, Skill Basics–Differentiate Square Units from Cubic Units, Procedure and Facilitation Points. Teachers perform the following steps:  “1. Project the first slide of the Square Units and Cubic Units Slideshow. 2. Distribute a Square and Cubic Units Graphic Organizer to each student. 3. Discuss the following question: a. What do you notice about these shapes? I. If students don’t mention it, lead them to understand that these unit squares are two-dimensional figures. 4. Instruct students to draw a model of a square unit in the Square Unit Model section of their Square and Cubic units Graphic Organizers. Ask the following question: a. What are the dimensions of a square unit? 5. Instruct students to write “1 unit long by 1 unit wide” in the Square Unit Dimensions section of their Square and Cubic Units Graphic Organizers. Ask the following questions: a. What does the area of a figure represent? B. How can we use these square units to find the area of a figure? C. How are the words square and area related? 6. Instruct students to remove their inch tiles from the bag and find the area of the Square Units section on the Square Units and Cubic Units Work Mat. 7 Ask the following questions: a. How many inch tiles were you able to place in the section? B. What is the area of this section? C. What are some other things you could measure using square units?”

The materials reviewed for STEMScopes Math Grade 5 meet expectations for containing adult-level explanations and examples of the more complex grade/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.

Each Scope has a Content Overview with a Teacher Guide. Within the Teacher Guide, information is given about the current Scope and its skills and concepts. Additionally, each Scope has a Content Support which includes sections entitled: Misconceptions and Obstacles, Current Scope, and Coming Attractions. These resources provide explanations and guidance for teachers. Examples include:

• Scope 5: Compare Decimals, Home, Content Overview, Teacher Guide, Vertical Alignment, Future Expectations. It states, “As students reach sixth grade, they are expected to fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm. The use of the algebraic system of rational numbers is extended to include negative numbers. Additionally, decimals are used when reasoning and solving one variable equations and inequalities.”

• Scope 10: Model Fraction Multiplication, Home, Content Support, Current Scope. It states, “Students use area models, tape diagrams, and number lines to make sense of the process for multiplying two fractions or for multiplying a fraction by a whole number. Students create story contexts that represent the multiplication of fractions, and they write equations to represent the solutions. Students interpret multiplication as scaling or resizing. Students reason about how numbers change when they are multiplied by fractions by considering the size of a product in relation to the sizes of each factor. Students recognize that when multiplying a fraction greater than one the number increases, and when multiplying by a number less than one the number decreases.”

• Scope 15: Classify Two-Dimensional Figures, Home, Content Support, Misconception and Obstacles. It states,  “Students might think that a 2D shape can only fit into one category. For example, they may not realize that a square can also be called a quadrilateral, parallelogram, and rectangle. Using visual graphic organizers, such as Venn diagrams or T-charts can help students organize shapes into hierarchies and varying subcategories.”

• Scope 20: Graph on a Coordinate Plane, Home, Content Support, Coming Attractions. It states,  “In grade six, students use all four quadrants of the coordinate system to plot polygons and to reason about their attributes. In grades six and seven, students analyze proportional relationships by making tables of equivalent ratios and graphing them on a coordinate plane. In grade eight, students observe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Eighth-grade students describe the functional relationship between two quantities by using the coordinate system to graph and analyze functions. Students have used tables to represent and compare values since the fourth grade, but in grade eight, the domain Functions is introduced. In eighth grade, functions are formally worked with as an algorithm for slope; students define, evaluate, and compare linear functions.”

The materials reviewed for STEMScopes Math Grade 5 meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series.

Correlation information is present for the mathematics standards addressed throughout the grade level and can be found in several places including a drop-down Standards link on the main home page, within teacher resources, and within each Scope. Explanations of the role and progressions of the grade-level mathematics are present. Examples include:

• In each Scope, the Scope Overview, Scope Content, and Content Unwrapped provides opportunities for teachers to view content correlation in regards to the standards for the grade level as well as the math practices practiced within the Scope. The Scope Overview has a section entitled Student Expectations listing the standards covered in the Scope. It also provides a Scope Summary. In the Scope Content, the standards are listed at the beginning. This section also identifies math practices covered within the Scope. Misconceptions and Obstacles, Current Scope, and Background Knowledge make connections between the work done by students within the Scope as well as strategies and concepts covered within the Scope. Content Unwrapped again identifies the standards covered in the Scope as well as a section entitled, Dissecting the Standard. This section provides ideas of what the students are doing in the Scope as well as the important words they need to know to be successful.

• Teacher Toolbox, Essentials, Vertical Alignment Charts, Vertical Alignment Chart Grade K-5, provides the following information:  “How are the Standards organized? Standards that are vertically aligned show what students learn one grade level to prepare them for the next level. The standards in grades K-5 are organized around six domains. A domain is a larger group of related standards spanning multiple grade levels shown in the colored strip below: Counting and Cardinality, Operations and Algebraic Thinking, Number and Operations in Base Ten, Number and Operations–Fractions, Measurement and Data, Geometry.” Tables are provided showing the vertical alignment of standards across grade levels.

• Scope 12: Fractions as Division, Home, Content Unwrapped, Implications for Instruction, states, “Implications for Instruction in previous grade levels, students have experience with number lines and evenly partitioning sections for fractions. In this grade level, students expand this knowledge to divide fractional parts evenly. Students should understand that a fraction is equivalent to the numerator divided by the denominator. For example, 12 is the same as one whole divided into two parts or 1 divided by 2. Students should understand word problems involving a whole number divided by a whole number that equals a fraction. Some answers are mixed numbers instead of just fractions or whole numbers. Students should also be able to express between what two whole numbers an answer exists. For example, $\frac{3}{2}=1\frac{1}{2}$ which lies between the whole numbers 1 and 2 on a number line.”

• Scope 14: Numerical Expressions, Engage, Accessing Prior Knowledge, Procedure and Facilitation Points, standard 5.OA.2, states, “Read the first bullet with students, and ask students to convert the words into a number sentence, i.e., an equation. Invite students to share their equations with the class. Ask students if there is exactly one way to represent this number sentence. Repeat the process explained above with the other three bulleted word problems. Ask the students if there are any similarities among all of the word problems. Ask the students if there are any differences. Before concluding the conversation, extend student thinking to explain what operation these equations are related to and explain why. If students are struggling to complete this task, move on to the Foundation Builder to fill this gap in prior knowledge before moving on to other parts of the Scope.”

The materials reviewed for STEMscopes Math Grade 5 meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies. 

The Teacher Toolbox contains an Elementary STEMscopes Math Philosophy document that provides relevant research as it relates to components for the program. Examples include:

• Teacher Toolbox, Essentials, STEMscopes Math Philosophy, Elementary, Learning within Real-World, Relevant Context, Research Summaries and Excerpts, states, “One of the major issues within mathematics classrooms is the disconnect between performing procedural skills and knowing when to use them in everyday situations. Students should develop a deeper understanding of the mathematics in order to reason through a situation, collect the necessary information, and use the mechanics of math to develop a reasonable answer. Providing multiple experiences within real-world contexts can help students see when certain skills are useful. “If the problem context makes sense to students and they know what they might do to start on a solution, they will be able to engage in problem solving.” (Carpenter, Fennema, Loef Franke, Levi, and Empson, 2015).

• Teacher Toolbox, Essentials, STEMscopes Math Philosophy, Elementary, CRA Approach, Research Summaries and Excerpts, states, “CRA stands for Concrete–Representational –Abstract. When first learning a new skill, students should use carefully selected concrete materials to develop their understanding of the new concept or skill. As students gain understanding with the physical models, they start to draw a variety of pictorial representations that mirror their work with the concrete objects. Students are then taught to translate these models into abstract representations using symbols and algorithms. “The overarching purpose of the CRA instructional approach is to ensure students develop a tangible understanding of the math concepts/skills they learn.” (Special Connections, 2005) “Using their concrete level of understanding of mathematics concepts and skills, students are able to later use this foundation and add/link their conceptual understanding to abstract problems and learning. Having students go through these three steps provides students with a deeper understanding of mathematical concepts and ideas and provides an excellent foundational strategy for problem solving in other areas in the future.” (Special Connections, 2005).” STEMscopes Math Elements states, “As students progress through the Explore activities, they will transition from hands-on experiences with concrete objects to representational, pictorial models, and ultimately arrive at symbolic representations, using only numbers, notations, and mathematical symbols. If students begin to struggle after transitioning to pictorial or abstract, more hands-on experience with concrete objects is included in the Small Group Intervention activities.”

• Teacher Toolbox, Essentials, STEMscopes Math Philosophy, Elementary, Collaborative Exploration, Research Summaries and Excerpts, states, “Our curriculum allows students to work together and learn from each other, with the teacher as the facilitator of their learning. As students work together, they begin to reason mathematically as they discuss their ideas and debate about what will or will not work to solve a problem. Listening to the thinking and reasoning of others allows students to see multiple ways a problem can be solved. In order for students to communicate their own ideas, they must be able to reflect on their knowledge and learn how to communicate this knowledge. Working collaboratively is more reflective of the real-world situations that students will experience outside of school. Incorporate communication into mathematics instruction to help students organize and consolidate their thinking, communicate coherently and clearly, analyze and evaluate the thinking and strategies of others, and use the language of mathematics.” (NCTM, 2000)

• Teacher Toolbox, Essentials, STEMscopes Math Philosophy, Elementary, Promoting Equity, Research Summaries and Excerpts, states, “Teachers are encouraged throughout our curriculum to allow students to work together as they make sense of mathematics concepts. Allowing groups of students to work together to solve real-world tasks creates a sense of community and sets a common goal for learning for all students. Curriculum tasks are accessible to students of all ability levels, while giving all students opportunities to explore more complex mathematics. They remove the polar separation of being a math person or not, and give opportunities for all students to engage in math and make sense of it. “Teachers can build equity within the classroom community by employing complex instruction, which uses the following practices (Boaler and Staples, 2008): Modifying expectations of success/failure through the use of tasks requiring different abilities, Assigning group roles so students are responsible for each other and contribute equally to tasks, Using group assessments to encourage students' responsibility for each other's learning and appreciation of diversity” “A clear way of improving achievement and promoting equity is to broaden the number of students who are given high-level opportunities.” (Boaler, 2016) “All students should have the opportunity to receive high-quality mathematics instruction, learn challenging grade-level content, and receive the support necessary to be successful. Much of what has been typically referred to as the "achievement gap" in mathematics is a function of differential instructional opportunities.” (NCTM, 2012).” STEMscopes Math Elements states,“Implementing STEMscopes Math in the classroom provides access to high quality, challenging learning opportunities for every student. The activities within the program are scaffolded and differentiated so that all students find the content accessible and challenging. The emphasis on collaborative learning within the STEMscopes program promotes a sense of community in the classroom where students can learn from each other.”

The materials reviewed for STEMScopes Math Grade 5 meet expectations for providing a comprehensive list of supplies needed to support instructional activities. 

The Teacher Toolbox provides an Elementary Materials List that provides a spreadsheet with tabs for each grade level, K-5. Each tab lists the materials needed for each activity. Within each Scope, the Home Tab also provides a material list for all activities. It allows the teacher to input the number of students, groups, and stations, and then calculates how many of each item is needed. Finally, each activity within a Scope has a list of any materials that are needed for that activity. Examples include:

• Scope 4: Round Decimals, Elaborate, Fluency Builder–Rounding Decimal Bingo, Materials, “Printed, 1 Instruction Sheet (per pair), 1 Set of Bingo Cards (per class), 1 Set of Rule Cards (per bingo caller), 1 Student Recording Sheet (per student), Reusable, 50 Translucent counters (per pair)”

• Scope 12: Fractions as Division, Explore, Explore 1–Fractions as Division with No Remainders, Materials, “1 Student Journal (per student), 1 Set of Ice Cream Cards (per group), 1 Exit Ticket (per student), Reusable, 4 Sets of fraction tiles (per group) OR 4 Sets of fraction circles (per group), Colored pencils or markers or crayons (per student)”

• Scope 16: Unit Conversions, Explore, Explore 4–Convert Units of Time, Materials, “Printed, 1 Student Journal (per student), 1 Task Cards (per class), 1 Exit Ticket (per student), Reusable, 1 Geared practice clock (per group), 1 Timer (per group)”

The materials reviewed for STEMScopes Math Grade 5 meet expectations for including an assessment system that provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up. 

In Grade 5, each Scope has an activity called Decide and Defend, an assessment that requires students to show their mathematical reasoning and provide evidence to support their claim. A rubric is provided to score Understanding, Computation, and Reasoning. Answer keys are provided for all assessments including Skills Quizzes and Technology-Enhanced Questions. Standards-Based Assessment answer keys provide answers, potential student responses to short answer questions, and identifies the Depth Of Knowledge (DOK) for each question. 

After students complete assessments, the teacher can utilize the Intervention Tab to review concepts presented within the Scopes’ Explore lessons. There are Small-Group Intervention activities that the teacher can use with small groups or all students. Within the Intervention, the lesson is broken into parts that coincide with the number of Explores within the Scope. The teacher can provide targeted instruction in areas where students, or the class, need additional practice. The program also provides a document in the Teacher Guide for each Scope to help group students based on their understanding of the concepts covered in the Scope. The teacher can use this visual aide to make sure to meet the needs of each student. Examples include:

• Scope 5: Compare Decimals, Evaluate, Standards-Based Assessment, Answer Key, Question 3, Part B, provides a possible way a student might complete the problem. “Which beetle was the longest? Which beetle was the shortest? Explain your reasoning. (DOK-3) Beetle C is the longest beetle, and beetle B is the shortest beetle. Sample reasoning: All of the beetles are over 3 cm long. To determine the longest length, I compared the decimal digits from left to right. Beetles A and C both have the digit 6 in the tenths place. Beetle A has a 4 in the hundredths place, and Beetle C has a 7 in the hundredths place. Since 7 hundredths is greater than 4 hundredths, I knew that beetle C was the longest. Likewise, to find the shortest length, I saw that beetles B and D both have the smallest digit in the tenths place, but Beetle B has a 3 in the hundredths place, and Beetle D has a 4 in the hundredths place. Since 3 hundredths is less than 4 hundredths, Beetle B has the shortest length. (5.NBT.3b)

• Scope 16: Unit Conversions, Evaluate, Standards-Based Assessment, Answer Key, Question 7, Part A, provides a possible solution a student might provide. “Shawn made a large batch of punch. He used 128 fluid ounces of water. Part A How many cups were used? Explain your reasoning. (DOK-3) 8. Makayla’s dad designed a building that is 2,808 inches tall. What is the building’s height in yards? (DOK-2) A, 78 yards B, 234 yards C, 936 yards D, 8,424 yards There are 16 cups in 128 fluid ounces. Sample reasoning: There are 8 ounces in a cup. I divided 128 by 8. $128\div8=16$” (5.MD.1)

• Scope 20: Graph on Coordinate Plane, Intervention, Small-Group Intervention, Procedure and Facilitation Points states,“Part II: Finding Coordinates, 1. Refer to the large coordinate plane. 2. Draw a large T-chart. Label the left side x, and the right side y. This is where you will write practice coordinates for the students to find. 3. Ask for student volunteers to do the following: (They can do this with a game piece or their finger if they are using a coordinate on a chart paper.) a. Jump three times on the origin. b. Walk on your tiptoes along the x-axis. c. Walk on your tiptoes along the y-axis. d. Walk to the location of (2, 3). e. Walk to the location of (4, 4). f. Walk to the location of (0, 1). g. Walk to the location of (5, 0).”

The materials reviewed for STEMscopes Math Grade 5 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series. 

Assessment opportunities are included in the Exit Tickets, Show What You Know, Skills Quiz, Technology-Enhanced Questions, Standards-Based Assessment, and Decide and Defend situations. Assessments regularly demonstrate the full intent of grade-level content and practice standards through a variety of item types, including multiple choice, multiple response, and short answer. While the MPs are not identified within the assessments, MPs are described within the Explore sections in relation to the Scope. Examples include:

• Scope 3: Read and Write Decimal Numbers, Evaluate, Standards-Based Assessment, Question 5, provides opportunities for students to demonstrate the full intent of MP6, Attend to precision, as they attend to precision when reading and comparing decimal numbers, paying close attention to the place values used. “List the following numbers in order from least to greatest. Write your answer in the box. 16.2, 16.102, 16.021” 

• Scope 11: Multiplication Problem Solving Using Fractions, Evaluate, Decide and Defend, Print Files, Student Handout and Explore, Explore 2, Print Files, Exit Ticket provide opportunities for students to demonstrate the full intent of the standard 5.NF.6, “Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.” “Franklin was doing a project on eye color. He was trying to figure out what fraction of the class was represented by brown-eyed girls. His teacher showed him the picture below to help him, but he didn’t understand it. Explain to Franklin how to use the model to find the fraction of girls with brown eyes in his class.” Below the prompt are three circles. The first is divided into fifths with three pieces shaded, the second is divided into fourths with three pieces shaded. There is a multiplication sign between these two models. Following the second model is an equal sign and a circle divided into twentieths with nine shaded pieces. “Write the equation that goes with the picture.” ”For the big field day finale, the whole class must work together to win. To win, the class must use a sponge to fill a bucket of water. The team with the most water in the bucket after every teammate has finished wins. This year, the winning team filled their gallon bucket. How much water was in the winning bucket?” This is followed by a box for a model, then a line for solution statement and equation. 

• Scope 12: Fractions as Division, Evaluate, Skills Quiz, Print Files, Student Handout, Questions 1 and 2, provide opportunities for students to demonstrate the full intent of the standard 5.NF.3, Interpret a fraction as division of the numerator by the denominator $(\frac{1}{b}=a\div b)$. Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem…) “Read the word problems and solve. 1. There are 3 siblings that want to equally share 5 cookies. How much of the cookies does each sibling get? 2. The Lowells have some land that they want to divide among their 4 grandchildren. If the grandparents have 13 acres, how much land does each grandchild get?” Below question two is a bar model divided into four equal boxes with 13 on top of the model.

The materials reviewed for STEMscopes Grade 5 meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level mathematics.

Within the Teacher Toolbox, under Interventions, materials regularly provide strategies, supports, and resources for students in special populations to help them access grade-level mathematics. Within each Explore section of the Scopes there are Instructional Supports and Language Acquisition Strategy suggestions specific to the Explore activity. Additionally, each Scope has an Intervention tab that provides support specific to the Scope. Examples include:

• Teacher Toolbox, Interventions, Interventions–Adaptive Development, Generalizes Information between Situations, supplies teachers with teaching strategies to support students with difficulty generalizing information. “Unable to Generalize: Alike and different–Ask students to make a list of similarities and differences between two concrete objects. Move to abstract ideas once students have mastered this process. Analogies–Play analogy games related to the scope with students. This will help create relationships between words and their application. Different setting–Call attention to vocabulary or concepts that are seen in various settings. For example, highlight vocabulary used in a math problem. Ask students why that word was used in that setting. Multiple modalities - Present concepts in a variety of ways to provide more opportunities for processing. Include a visual or hands-on component with any verbal information.”

• Scope 4: Round Decimals, Home, Content Support, Misconceptions and Obstacles states, “Students may think as you move to the left of the decimal point, the number increases in value. Using visual models can help students understand the magnitude between powers of ten. Students may think that the longer the number is the greater its value is, but a decimal with one decimal place may actually be greater than a number with two or three decimal places. Students should be given ample experience to reason about the size of decimal numbers.”

• Scope 14: Numerical Expressions, Explore, Explore 3–Interpreting Expressions, Instructional Supports states, “1. Review key words for all operations, including sum. Difference, product, quotient, less than, more than, double, triple, decreases, etc. 2. If students are struggling with how to set up each expression, it may be helpful to review the order of operations and when it would be necessary to use parentheses in the problem. 3. If students continue to struggle, provide them with more simplistic situations to model until they gain confidence with the process.”

The materials reviewed for STEMscopes Math Grade 5 meet expectations for providing extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity.

Within each Scope, Scope Overview, Teacher Guide, a STEMscopes Tip is provided. It states,  “The acceleration section of each Scope, located along the Scope menu, provides resources for students who have mastered the concepts from the Scope to extend their mathematical knowledge. The Acceleration section offers real-world activities to help students further explore concepts, reinforce their learning, and demonstrate math concepts creatively.” Examples include:

• Scope 10: Model Fraction Multiplication, Acceleration, Math Today–A Home for Bees, Question 1 states, “Holes will be drilled into the thin side of the house for the bees to enter and exit. What is the area of this side? Use a model and write an expression to solve.” Question 2, “What is the area of the front of the house? Use a model and write an expression to solve.” 

• Scope 13: Divide Unit Fractions, Acceleration, Math Today–Natural Energy, Question 1 states, “People took shifts riding the 20 bicycles throughout the movie. The movie was 3 hours long, and each bicycle rider rode for $\frac{1}{4}$ of an hour. How many shifts were there throughout the movie? Show the answer using the model below.” Question 2, “The bicycle riders were so thirsty after they finished their shift! The Brazil bicycle cinema organizers had 50 liters of water. If each rider drank $\frac{1}{2}$ liter of water, how many riders were able to drink water throughout the night?” Question 3, “The generator still needs to be $\frac{1}{5}$ filled. 7 people are going to share the responsibility of riding the bicycle to generate the power. What fraction will each rider generate?” 

• Scope 19: Apply Volume Formulas, Acceleration, Math Today–Fighting Forest Fires, Question 1 states, “The smallest air tanker is the Single Engine Airtanker (SEAT). Below is a rectangular prism that can hold the same amount of water as a SEAT. What is the amount of water that can be sprayed from this air tanker?” Question 2, “The Lockheed EC-130Q Hercules is a medium-sized fixed-wing tanker airplane. It can hold more water or retardant than the SEATs. If the base of the container has an area of 83.5 square feet and a height of 6 feet, what is the volume?”

The materials reviewed for STEMscopes Math Grade 5 meet expectations for providing strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics. 

Within the Teacher Toolbox, the program provides resources to assist MLLs when using the materials. The materials state, “In the curriculum, we have integrated resources to support teachers and families. Below are a few features and elements that can be used to support students at their level and provide an opportunity for families and caregivers to engage in student learning.” Examples include but are not limited to:

• “Proficiency Levels by Domain – In this section, you will find a snapshot of language application across domains at different proficiency levels. Teachers can use this tool to help identify a student’s English proficiency level by analyzing how students are able to interpret and produce language.”  

• “Working on Words – This open-ended activity allows students to take agency and accountability for their growing vocabulary. This activity also encourages making relevant, personal connections to new terms in different ways, such as identifying cognates.” 

• “Sentence Stems/Frames – Students are able to practice engaging in purposeful discussion. These sentence stems and sentence frames can be used for different intents, such as asking for clarification, defending their thinking, and explaining their responses.” 

• “Integrated Accessibility Features – Across the curriculum, we have embedded tools that allow students to listen to text being read, find the definition of words in the moment, make notes, and highlight words and phrases.” 

• “Parent Letters – Each scope includes a letter tailored to caregivers in which the content of a scope, including its vocabulary, is explained in simplified terms. Within the Parent Letters, we have included an activities section called Tic-Tac-Toe–Try This at Home that students can engage in along with their families. This letter is written in two languages.” 

• “Tiered Supports – Within each Explore lesson, we have included tiered supports and strategies that can be applied during the lesson for students at each proficiency level. These range in focus across all domains.” 

• “Language Connections – Every scope has three Language Connection activities, one at each proficiency level. Language Connections meets the students at their proficiency level by providing teachers with prompts to support students in demonstrating their understanding in each language domain.” 

• “Virtual Manipulatives – Students are able to use these across the curriculum to help them justify their answers when expressive language may be limited. These can also be used as tools for creating meaningful connections to vocabulary terms and skills.” 

• “Visual Glossary/Picture Vocabulary – Students are able to combine visual representations and mathematical terms using student-friendly language.” 

• “Distance Learning Videos – Major skills and concepts are broken down in these student- facing videos. Students and caregivers alike can engage in the activities at home at their own pace and incorporate familiar objects. In this way, students can apply their own language to math.” 

• “My Math Thoughts/Math Story – These literary elements give students the opportunity to practice reading and writing about math. Students can apply reading strategies to aid with comprehension and practice not just math vocabulary, but situational vocabulary as well.”

Guidance is also provided throughout the scopes to guide the teacher. Examples include:

• Scope 16: Unit Conversions, Explore, Explore 1–Convert Units of Length, Print Files, Student Journal (Spanish) provides  support for students who read, write, speak a different language than English to engage in the content. The print files contain the lesson’s task cards in Spanish.

• Scope 19: Apply Volume Formula, Explore, Explore 2–Using Three Dimensions to Measure Volume, Language Acquisition Strategy Language Acquisition Strategy provides support for students who read, write, speak a different language than English to engage in the content. “The following Language Acquisition Strategy is supported in this Explore activity. See below for ways to support a student's English language development. Students practice using formal and informal spoken language at appropriate times. Students may speak formally or informally while working in their groups. Give each group a chance to present a solution to the rest of the class. Formal language should be used when presenting to the class. Allow them time to write a formal explanation on an index card before they present.”

• Scope 21: Generate and Graph Numerical Patterns, Explore, Explore 2–Generate and Graph Numerical Patterns, Language Acquisition Strategy, provides support for students who read, write, speak a different language than English to engage in the content. “The following Language Acquisition Strategy is supported in this Explore activity. See below for ways to support a student's English language development. Students use prior experiences to understand academic concepts in math.Check for understanding of the terms rule, graph, multiplicative, additive, and numerical pattern. Working with the class, have students create a definition for each—keep this word bank in an easily accessible place. Add the following sentence strands to the Student Journal page: In an additive rule, a value is being ___ to the x-value to get the y-value. In a multiplicative rule, a value is being ___ to the x-value to get the y-value. In an additive graph, when the x-value is 0, the y-value is ___. In a multiplicative graph, when the x-value is 0, the y-value is ___.”

The materials reviewed for STEMscopes Math Grade 5 meet expectations for providing manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods. Examples include:

• Scope 5: Compare Decimals, Intervention, Small Group Intervention, Procedure and Facilitation Points, Part I provides for students’ active participation in content through the use of manipulatives. “Does the length of the decimal or amount of digits within the decimal determine its value? Provide an example to demonstrate your thinking. Not necessarily. It is more important to compare the values of each place value position. For example, 0.2 has fewer digits than 0.123, but it has a greater value, because two-hundredths is greater than one-hundredth and also greater than one hundred twenty-three-thousandths. Provide each pair with a Student Handout, and a zip-top bag containing a set of Number Cards, a Spinner, and a paper clip. Prompt students to generate decimal numbers to the thousandths. Each student will place the decimal point card on the table. Then, they use a paper clip anchored with a pencil to spin a number. Explain that this number indicates the amount of digit cards to draw. Draw the corresponding number of digits and place them in order after the decimal point on the table. Once the students have generated a number, they will use place value disks to represent the number on the first page of the Student Handout. Once both students have built a number, students write the word form of the decimal and compare both decimals (using two comparison statements) on the second page of the Student Handout. Students may need prompting to swap the placement of each number and to reverse the inequality sign. Invite a few pairs of students to share their results with the group. Provide each student with a sticky note and invite them to write the value of each digit of their decimal. Repeat the process as needed.Invite pairs to talk about their comparisons and how they used place value to find the greater number. Afterward, allow time for students to complete the Checkup individually.”

• Scope 8: Multiplication Problem Solving Using Fractions, Explore, Virtual Manipulative–Fraction Tiles provides for students’ active participation in content through the use of virtual manipulatives. Manipulatives may be assigned to students through the online platform and used to engage in lessons from Scope 8. 

• Scope 15: Classify Two-Dimensional Figures, Procedure and Facilitation Points, provides for students’ active participation in content through the use of manipulatives. “Distribute the geoboard, rubber band, and Geoboards handout to each student. Instruct students to use the rubber band to make a square on their geoboards. Ask the following questions: What do you notice about the sides of the square? All four side lengths are congruent. The opposite sides are parallel to each other. The sides are perpendicular to each other. What do you notice about the angles in the square? The angles are all congruent. They are all right angles formed by perpendicular sides.Instruct students to draw the square from their geoboards in the upper left geoboard on the Geoboards handout. Remind students that we use tick mark symbols to identify when attributes of a figure are congruent. Explain that arrow symbols identify sides of figures that are parallel. Ask the following question: On which sides should we draw arrows to distinguish them as being parallel? We should draw them on the top and bottom sides and the left and right sides. Remind students that the number of tick marks on congruent sides and angles must be the same. Explain the same is true for distinguishing parallel sides. If there is more than one pair of parallel sides in a figure, we draw additional arrows on the other pairs of parallel sides. Model and instruct students to draw one arrow in the middle of each of the top and bottom sides on the square and two arrows in the middle of each of the left and right sides on the square.”