3rd Grade - Gateway 2

The materials reviewed for STEMscopes Math Grade 3 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 4: Multiplication Models, Explore 1: Equal Groups, Procedure and Facilitation Points, students develop conceptual understanding as they reason about how a model represents products as the number of groups multiplied by the number in a group. “Begin by projecting counters in a few groups with an equal number of counters in each group (Example: four groups of three counters). DOK-1 Ask students to talk to their shoulder partners about what they see and what they think it means… Student answers will vary but may include the following: We see four groups. Each group has three counters. All groups are equal. If we add all the counters together, we can get 12 counters. …Ask students to write a sentence that describes what they see. … Ask students to share how they described the groups on the screen. Ask students to share their sentences and emphasize how each time a group is added, the total increases by the same number. DOK-1 Ask students if they know what mathematical operation that sentence represents. Follow the students’ lead and write a multiplication symbol down. Pose the question, ‘What does this symbol represent?’ It represents “times,” “multiplied by,” “multiplication,” “repeated addition,” and “equal groups of.” Take a marker and under the × symbol write “groups of.” Explain that another way we can think of this multiplication symbol is “groups of.” DOK -2 Have students look back at the model. Ask students, ‘How could you describe the model using the phrase groups of?’ Have students share their ideas. Write down what they say. You should emphasize the student response that means “Three groups of four.” Show how three groups of four can be written as 3\times4. Repeat this three more times with different equal groups. For each new group of counters, ask students to write the following on their desk using the dry-erase marker:Sketch the model of equal groups on the screen.Write it in word form, using groups of (Example: two groups of three). Translate that into a multiplication sentence (Example: 2\times3). Distribute paper plates and counters to each group,and a copy of the Student Journal to each student. Tell students that at each station they will read a scenario, make a model of the problem with plates and counters, write a descriptive sentence, and practice writing multiplication sentences. Break students into groups and have them rotate around the room through the different scenarios. Monitor students as they work, asking them guiding questions: DOK-1 How many equal groups are there? How many are in each group? DOK-1 How can you say it using groups of? After the Explore, invite the class to a Math Chat to share their observations and learning.” (3.OA.1)

• Scope 7: Multiply by Multiples of 10, Explore, Skill Basics-Repeated Addition of Multiples of 10, Procedure and Facilitation Points, students develop conceptual understanding of multiplication by multiples of 10 by working with repeated addition. “1. Distribute the base-ten rods to each group. 2. Have groups draw one Multiple of 10 Cards from their bags. 3. Instruct groups to work together using the base-ten rods to make an array that matches their chosen number. Ask the following questions: a. How many base-ten rods did you use to represent your number? Answers will vary depending on the number. b. What does repeated addition mean? Repeated addition means adding the same number over and over. c. What repeated addition sentence do your base-ten rods show that represents your chosen number? Answers will vary depending on the number. 4. Have students write their chosen number and the repeated addition sentence their base-ten rods represent on their Multiples of 10 Work Mats. 5. Repeat steps 2–4 two more times as demonstrated in the following example work mat:, 6. When students have three numbers and addition sentences on their Multiples of 10 Work Mats, ask the following questions: a. How did you form your arrays? Answers will vary. We knew the rods were worth 10, so we put four rods together to make 40. b. What do you notice about your number sentences? They all add 10s. c. How are the number chosen and the number sentence related? The 10s are added the same number of times as the digit in the tens place of the chosen number. 7. Distribute the Student Handouts. Have students use repeated addition sentences to represent numbers that are multiples of 10 and identify multiples of 10 using repeated addition sentences.” (3.NBT.3)

• Scope 16: Compose and Decompose Fractions into Units, Engage, Foundation Builder, Part II, students develop conceptual understanding as they demonstrate that a fraction of \frac{a}{b} represents the quantity formed by parts of size \frac{1}{b}. “Distribute the Student Handout to each student. Challenge students to complete the first part (partitioning a shape) in question one independently. Ask them to move around the room and find another student who partitioned their rectangle differently. Have them sketch this way on their Student Handout. Challenge students to complete question two independently. Ask students to use crayons or colored pencils provided.Invite them to compare their answers with their group. Discussion points: How did you shade in one half of a circle if it was divided into fourths? Shading in two fourths is the same as shading in one half of the shape.How would you describe a whole that is divided into two equal pieces? Two halves”. (3.NF.1)

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

• Scope 5: Division Models, Show What You Know–Part 1: Equal Groups and Shares, Student Handout, students engage in conceptual understanding as they interpret division problems. “Part 1: Equal Groups and Shares Draw a model and fill in the blanks.” Question One: “Clay has 36 pieces of gum that he wants to share with his 9 friends. How many pieces will each of his friends get? Numbers: ___ ÷ ___ = ___ “ listed under the equation stems: “Words: ___ ___ ___.” Question Two: “Camille works at a dog pound that has 24 dogs that need to be walked. There are 5 other workers who are going to help Camille. How many dogs do the workers each have to walk if they are going to share the job equally? Numbers: ___ ÷ ___ = ___” Listed under the equation stems: “Words: ___ ___ ___” (3.OA.2)

• Scope 12: Apply the Area Formula, Elaborate, Fluency Builder-Area Battle, Procedure and Facilitation Points, students play a game (in pairs) to measure area using the formula. “1. Gather students together on a rug or large-group teaching area. 2. Model how to play the game for a few rounds with a student volunteer or volunteers. a. Players shuffle the Area Battle cards and deal them evenly facedown in a pile in front of each player. b. Both players flip over their top card at the same time. c. Players find the area shown on their cards and write their answers on the student recording sheet with the number sentence used to find it. d. The player with the larger area card wins both cards and puts them faceup in a stack next to his or her pile of unplayed cards. e. If there’s a tie, each player keeps the card he or she played and adds it to the faceup stack of claimed cards. f. Continue playing until all cards have been claimed. The player with the most cards after all the cards are claimed is the winner. 3. Divide students into pairs. Mixing students by ability is recommended. 4. Monitor students as they play, and clarify directions for any pair who needs help. 5. Ask students the following questions: a. What is the area shown on your card? b. What is the area shown on your partner’s card? c. How do you know who has the card with the greater area? d. Can you think of another way to find the area shown on this card? e. What operation or operations were you using to find the area? 6. Remind students to record the number sentence and area on their student recording sheet as they play. 7. Students may play more than one round if time allows.” (3.MD.7b)

• Scope 18:  Compare Fractions, Evaluate, Skills Quiz, students engage in conceptual understanding as they compare fractions by reasoning about their size. Models for the following fractions are given and students asked to complete the inequality: Question one: "\frac{3}{8}___ \frac{3}{4}" Question two: "\frac{6}{8}___ \frac{4}{8}”, Question 3: "\frac{2}{6}___ \frac{3}{6}". Questions 4-6 ask students to “Write the appropriate comparison symbol (<, >, =) and the correct fractions for each set of models. Question four: models given for \frac{1}{4} and \frac{1}{8}, Question five: models given for \frac{2}{6}  and \frac{2}{3} , Question six: models given for \frac{2}{4}  and \frac{4}{8}.” (3.NF.3)

The materials reviewed for STEMscopes Math Grade 3 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: Third Grade, Activities, Daily Numeracy–Solve It, Procedure and Facilitation Points, and Slideshow, engages students in adding 2-digit numbers using various strategies. Slide 1, "43+98" “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.” … “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…?” (3.NBT.2)

• Scope 2: Addition and Subtraction Fluency, Explore, Explore 1–Adding Using Base Ten Strategies, Procedure and Facilitation Points, engages students in procedural fluency with teacher support as they add 3-digit numbers. “3. Read the following scenario: ‘A group of friends goes to a flea market to buy used baseball cards and football cards. When the group arrives home, they want to determine which friend bought the most cards. You need to help them figure out who bought the most cards by adding up the total number of cards for each friend.’ Students are given cards with the information about how many baseball cards and football cards each friend bought. 13. After the Explore, invite the class to a Math Chat to share their observations and learning. Question: DOK-3 What do you notice when you look at the value of a number in each place compared to the digit? DOK-3 How did you use each part of a number to combine the two amounts?” (3.NBT.2)

• Scope 6: Multiplication and Division Strategies, Explore, Explore 4–Missing Factors and Quotients, Procedure and Facilitation Points, engages students in procedural fluency with teacher support as they use strategies to find cards that represent the relationship between multiplication and division. “Questions: DOK-2 How did you determine the quotient of the division sentence? DOK-2 What did you notice about the matching cards? DOK-3 How did that help you solve the other card?” (3.OA.7) 

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

• Scope 2: Addition and Subtraction Fluency, Explain, Show What You Know–Part 4: Subtracting Using Number Line Strategies, Student Handout, engages students in procedural fluency as they subtract within 1,000. “Model each expression on a numberline and record the difference.” Question one and two, the column labeled “Expression” shows the following expressions: "328-124" and "745-428". Two columns are provided after each expression and labeled “Number Line Model” and “Difference”. Questions 3 and 4 have nothing in the column labeled “Expressions” and have two number line models in the columns labeled “Number Line Model”. The number line for question 3 begins with 125 then shows a jump of 300 to the point 425 followed by a jump of 75 to point 500 then 9 to an unlabeled point. Students are expected to enter the difference in the column labeled “Difference”. The number line for question 4 begins with 230 then shows a jump of 600 to 830 then a jump of 50 to point 880 then a jump of 8 to an unlabeled point. (3.NBT.2)

• Scope 6: Multiplication and Division Strategies, Elaborate, Fluency Builder–Products: 1, 2, 3, Procedure and Facilitation Points, engages students in procedural fluency as they play a game determining factors and products of a multiplication equation. “4. The first player places a coin within a circle under a one-digit factor. 5. The second player places the other coin within a circle under a different one-digit factor. Once two coins are on the game board, the first player finds the product of the two marked factors and shades this product on the game board. 6. The second player moves one coin under a one-digit factor to another one-digit factor. The other coin remains where it is. The second player determines the product of the two marked numbers and shades the product on the game board.” (3.OA.7)

• Scope 7: Multiply by Multiples of 10, Explore 1-Multiply by Multiples of 10 Using Base Ten Blocks, Exit Ticket, students demonstrate procedural skill and fluency as they multiply a number by a multiple of ten. “Multiply by Multiples of 10 Exit Ticket, Mohammad and Drew created snack bags after their parents went to the grocery store. Help Mohammad and Drew figure out how many snacks their parents bought for them. Complete each number sentence based on the model representation. 1. Drew noticed a box that comes with 30 packages of plain potato chips. His mom bought 3 boxes. How many plain potato chips are there? There are ___ groups of ___ tens = ___ tens,  ___ \times ___ = ___  2. Mohammad noticed a box of crackers that contained 6 packages with 40 crackers in each package. How many crackers are there in all? There are ___ groups of ___ tens = ___ tens,  ___ \times ___ = ___  3. Mohammad and Drew’s mom bought 3 cases of water. There are 40 water bottles in each case. How many water bottles did their mom buy? There are ___ groups of ___ tens = ____ tens, ___ \times ___ = ___.” (3.NBT.3)

The materials reviewed for STEMscopes Math Grade 3 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: Problem Solve Using the Four Operations, Elaborate, Math Story - Crafts, Sweets, and Goodies . . . Oh My!, students solve both routine and non-routine problems with teacher support. Non-Routine: “Read the passage and answer the questions that follow. 7. In the community center, there are 22 booths. Most of the booths have two people working at all times, but a few only have one person. What is a reasonable estimate of how many people are working in the booths? A. About 40 people (22\times2=44), B. About 44 people (22\times2=44), C. About 20 people (22\times1=22), D. About 30 people (22\times1=22); Routine: 8. On Monday, A&M Cupcakes sold 24 vanilla cupcakes. On Tuesday, they sold 48 vanilla cupcakes. On Wednesday, they sold 30 more cupcakes than they did on Monday. Which equation could be used to find c, the number of cupcakes they sold in all three days? A. c=24+48+30, B. c=24+48+24+30, C. c=24+24+30, D. c=24+30, 9. At the end of the week, Michael wanted to know the total number of cupcakes they sold. He created this chart to help him. Michael wants to find the total number of cupcakes they sold. Show below any strategy or model that he could use to solve, and write a corresponding equation.” (3.OA.8)

Engaging routine applications of mathematics include:

• Scope 6: Multiplication and Division Strategies, Engage, Hook–Appetizers and Toothpicks, Procedure and Facilitation Points, students develop application through a routine problem with teacher support as they use the associative property of multiplication to demonstrate that a multiplication problem can be solved in more that one way and the order in which numbers are grouped does not affect the product. “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. Your parents are throwing a party. They want you and your sister to make layered desserts. There will be 2 trays, each holding 7 desserts. Each dessert needs 5 ingredients to construct the five layers. Your dad asks you and your sister to construct the desserts in the following way from bottom to top: cookie, marshmallow, chocolate, orange, and a cherry on the top–held together with a toothpick. Your mom asks how many total ingredients you will need to construct the desserts. Your sister says you should multiply the number of trays by the number of desserts per tray and then multiply that product by the number of ingredients per dessert. You argue that you should multiply the number of ingredients per dessert by the number of deserts per tray. Then multiply that product by the number of trays. How many total pieces of ingredients do you need to make the desserts? Who had the correct strategy? Make models to discover who is correct. 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. 4. Discuss the following: a. DOK-3 How will making a model of the desserts help us find how many ingredient pieces are needed to make the desserts? b. DOK-3 How will making a model of the desserts help us determine who had the correct strategy for finding the number? c. DOK-1 What is the associative property of multiplication? 5. Move on to complete the Explore activities. 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. Put students in small groups of 4. Give each group of students two pieces of half-sheet-sized graph paper, a box of toothpicks, a bottle of liquid glue, a box of crayons or colored pencils, a piece of lined paper, and a pencil. 4. Instruct students that they need to make models of the desserts. Tell them that each half sheet of graph paper represents the two trays that will be holding the desserts. They will color in squares in certain colors to represent each ingredient in the desserts. Write the colors to represent each ingredient on the board. They are as follows: a. cookie = yellow b. marshmallow = pink c. chocolate = brown d. orange = orange e. cherry = red 5. Students should follow the instructions to start at the bottom and color squares in a vertical line in the following order: cookie, marshmallow, chocolate, orange, and cherry. They can then use liquid glue to glue a toothpick on top of the squares colored on their tray (graph paper) to represent one dessert on the tray. 6. Students should make 7 desserts to go on each serving tray (graph paper). Tell them the desserts should be spaced apart on the tray like they would be at the party. 7. Give students about 10 minutes to create the two trays of desserts and determine how many pieces of ingredients were used to create the desserts. 8. Students should try out both strategies. Instruct students that they can work the problem in their heads if they are fluent in their multiplication facts or they can use the pencil and notebook to figure out the solutions. a. Sister’s strategy: number of trays multiplied by the number of desserts per tray and then that product multiplied by the number of pieces of ingredients per dessert. b. Your strategy: number of pieces of ingredients per dessert multiplied by the number of desserts per tray and then that product multiplied by the number of trays. 9. Students should then count the number of pieces of ingredients to check their answers. Hint: students can count by 5’s. 10. Instruct each small group to tell the class which strategy was right - yours or your sister’s. Did everyone in the class agree? 11. Discuss the following: a. DOK-2 What was the solution for the sister’s strategy? b. DOK-2 What was the solution for your strategy? c. DOK-1 What was the solution you found when you used the model and counted the number of pieces of ingredients needed to make the correct number of desserts? d. DOK-1 Do either of the strategies result in the same solution you got when you counted the number of pieces of ingredients needed to make the desserts? e. DOK-3 Why did both strategies work and result in the same solution? f. DOK-1 Who was correct, your sister or you? g. DOK-1 Is there another way the numbers could be grouped/ordered that would also result in the same solution? h. DOK-2 Is any one of the ways grouped in a way that makes it easier to find the solution?” (3.OA.5) 

• Scope 8: Multiplication and Division Problem Solving, Explore, Explore 1: Model and Solve One-Step Word Problems, Exit Ticket, students apply multiplication strategies independently to solve a routine problem. “As a way to thank you for your help with the lunchtime orders, the principal is treating 18 people in your class to a field trip! You are excited to be going, but now sack lunches need to be ordered as soon as possible. Your job is to make sure each sack lunch includes three mini cookies for each student. How many cookies do you need to order? Create a model and an equation using a symbol for the unknown that represents the diagram. Then use any strategy to solve the problem.” (3.OA.3)

Engaging non-routine applications of mathematics include:

• Scope 4: Multiplication Models, Explore 4–Number Lines and Skip Counting, Procedure and Facilitation Points, students develop application through non-routine problems with teacher support as they determine the total number of objects they have packed for their camping trip by representing multiplication problems using number lines and multiples. “Part I: Counting Equal Groups 1. DOK-1 Begin by asking students to take a minute to look around the class. Ask them to find equal groups of something. 2. Give students 1 or 2 minutes to discuss among themselves and then share with the class. 3. Choose one of the students’ ideas to expand upon. The example below will focus on the number of shoes per student. Distribute a dry-erase marker, eraser, and a meterstick covered by clear tape to each group. 4. DOK-2 Ask students to draw a model of the number of shoes on four people. They can draw the model using a dry-erase marker on their desk (or a small dry-erase board). 5. Allow students to share how they modeled the problem. 6. DOK-1 Ask students to write down a multiplication number sentence for this problem and explain what the equation means. Share with the class: 4\times2=8 7. Divide the class in half and have each half stand in a line across from each other. 8. Have students figure out how many shoes there are on the other side of the classroom. Listen for different strategies students used to figure out the total number of shoes. Listen specifically for skip counting. 9. DOK-1 Allow a few students to share how they found the total number of shoes. a. DOK-1 What numbers would you say when you count by twos? b. DOK-1 How many times did you count a group of two? Explain. c. DOK-1 How many shoes are there? d. When we count by a certain number, that is called skip counting! 10. Have students return to their groups and look at the meterstick. Tell students that the meterstick can be used as a number line. 11. Have students practice skip counting by twos as if they were counting groups of students with two shoes. Students should use the dry-erase marker to circle each number they say when they skip sound by twos. 12. Introduce that the numbers circled are called multiples. Since they skip counted by two, each number they said was a multiple of two.  Part II: Camping Trip 1. Tell students that they are preparing for a big camping trip and that each group has begun packing a bag (show envelopes). 2. Explain that since they will be staying for several days, they’ve gone shopping for some essentials, and those come in packs.  3. Challenge students to use the meter stick as a tool to find the total number of different types of items.  4. Distribute the camping bag envelopes to each group. 5. Monitor students as they work, asking them guiding questions. a. DOK-1 How many packs are there. How many are in each pack? b. DOK-2 How did you use the number line (meter stick) to model the packs of items? 6. After the Explore, invite the class to a Math Chat to share their observations and learning. 7. When students are done, have them complete the Exit Ticket to assess their understanding of the concept. 8. Return to the Hook and instruct students to use their newly acquired skills to successfully complete the activity. (3.OA.1) 

• Scope 13: Perimeter, Engage, Hook–2 Gardens and Their Perimeters, Procedure and Facilitation Points, students develop application of area and perimeter on non-routine problems with teacher support. “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. Put each student in a small group and give each group of students a resealable bag with toothpicks. 4. Instruct students that they need to figure out how many feet of fencing their grandma needs to purchase for each of the two gardens. Students should also determine whether the gardens have equivalent perimeters. Remind students that each toothpick in the resealable bag they were given represents a linear foot of distance. a. Tell students that they must use the dimensions of the gardens given in the scenario when constructing their toothpick models. b. Give students about 10 minutes to create the gardens by building each garden perimeter out of toothpicks.  Then students should determine the perimeters of both gardens. c. Instruct each group to tell the class how many feet of fencing each of their gardens required or the perimeters of their gardens.  Were the perimeters equivalent for both gardens?” (3.MD.8)

The materials reviewed for STEMscopes Math Grade 3 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:

• Fact Fluency: Multiplication and Division, 9s, Fact Fluency–Station 1, Procedure and Facilitation Points, students develop procedural fluency with multiplication facts. “1. Students will follow the prompt to create a 5\times10 array using counters. Students will answer the following questions on their Student Journal: a. What multiplication sentence does this show? 5\times10, b. What is the product of 5\times10? 50, 2. Next, students will remove one counter from each group of 10. Students can show this on their Student Journal by circling the counters they removed. Students will answer the following questions on their Student Journal: a.  How many counters were removed? 5, b. What is the new total? 45, c. What multiplication sentence does this show now? 9\times5,  3. Repeat the activity modeling an array for 3\times10. 4. Students will then fill in the table to show their \times9 and \times10 facts and respond to the following reflection question: How can you use the \times10-1 set strategy to help solve the nines facts? I can use the \times10-1 set strategy to figure out the nines by doing the × 10 fact first, then subtracting one group. Like 8\times9, do 8\times10 first, which is 80, then subtract one group of 8 and that’s 72. So, 8\times9=72.” (3.OA.7)

• Scope 2: Addition and Subtraction Fluency, Explain, Show What You Know–Pat 1, students demonstrate application through a routine problem as they solve three-digit addition problems. “Peri baked cookies for her sleepover. She baked 124 chocolate chip cookies and 110 peanut butter cookies. How many cookies does Peri have for her sleepover?” (3.NBT.2)

• Scope 15: Fractions on a Number Line, Explore 1–Unit Fractions on a Number Line, Procedure and Facilitation Points, students develop conceptual understanding when they represent a fraction as a number on a number line and define the interval units shown on the number line. “1. Have the students find their one-half tile and make observations about it. 2. Invite students to discuss the following questions with the students around them and share out to class: a. DOK-1 What do you notice about this piece? b. DOK-1 What do you think this piece represents? c. DOK-1 How do you know? d. DOK-1 Do both of these parts represent the same thing? Explain. 3. Explain that each individual equal piece is called a unit, and when we refer to each equal fractions part, it is called a unit fraction. 4. Present the following scenario to the class: a. The Bright Idea Light Company needs your help! As a lighting designer, you are creating different lighting options for your clients. To do this, it is important to know how many unit pieces of electrical wires you need to connect individual bulbs and how the string of lights will be partitioned. Let’s get to lighting it up! 5. Explain that, to light designers, it is important that each light bulb is equally spaced to create an attractive design.  6. Ask students to take out their yarn and line it up above the unit fraction for \frac{1}{2}. 7. Challenge them to discuss the following questions with their group while exploring the yarn and fraction tiles. Have a discussion with the class: a. DOK-2 What do the unit fractions represent for the lighting design? b. DOK-1 How do you know? c. DOK-1 How is the string of lights partitioned? d. DOK-1 How many unit pieces of electrical wire will the whole string be partitioned into? 8. Emphasize that one-half is not the center point but the distance from the start of the line to the end of the first unit, or partition. 9. Encourage students to use the yarn and/or tiles to help determine how this light design can be represented on the number line on their Student Journal. 10. Monitor collaborative groups as they line their tiles and/or strings to the number line provided in the first box of their Student Journal. 11. Access understanding as you are monitoring by using the following questions: a. DOK-2 How do the string/tiles relate to the number line? b. DOK-2 How do you know? c. DOK-2 I see numbers on the tiles. Looking at the models, what do you think they represent? d. DOK-1 How can you draw this light design on a number line? e. DOK-1 What does the space between each tick mark represent? f. DOK-1 How many equal unit pieces of electrical wire will I need for this design? 12. Discuss findings of the first box as a class. 13. Challenge students to create more light designs using the strings and/or tiles and using the number line in their Student Journal to represent their model. 14. Monitor collaborative groups as they complete the rest of the light designs. Use guiding questions above to assess their understanding. 15. After the Explore, invite the class to a Math Chat to share their observations and learning. 16. When students are done, have them complete the Exit Ticket to formatively assess their understanding of the concept.” (3.NF.2)

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 4, Multiplication Models,  Explore 1–Equal Groups, Exit Ticket, students apply understanding of arrays and multiplication alongside conceptual understanding as they determine the total number of objects in a scenario by using equal groups. “Look around your classroom. Equal groups are all around you! Sketch two examples of equal groups. Include a real-world problem to go with each sketch, a “groups of” statement, and a multiplication sentence.” (3.OA.1) 

• Scope 8: Multiplication and Division Problem Solving, Explain, Show What You Know, Part 2: Model and solve two-step Word Problems, students apply their understanding of multiplication strategies alongside procedural fluency to solve a word problem. “Solve each problem: Explain your reasoning using a model or strategy. Write an equation with a variable to represent the problem. Write a solution statement. Multiplication and Division Problem Solving, Part 2, Kelly had a sleepover. She invited 5 friends and made chocolate chip cookies. Each of the 6 girls ate 6 cookies. At the end of the night, there were 11 cookies left. How many chocolate chip cookies did Kelly make for her sleepover?” (3.OA.3)

• Scope 19: Time, Explain, Show What You Know–Part 2: Problem Solving with Time on a Number Line, students show conceptual understanding alongside application as students practice problem solving with time using a number line. 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. The problem shows a chart with start time, end time, number line and duration. “The table shows the duration of time students spent in the library last Saturday. Complete the missing information within each row. Start Time: 1:53 p.m., End Time 2:20 p.m., Number Line, Duration___.” (3.MD.1) 

The materials reviewed for STEMscopes Math Grade 3 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 4: Multiplication Models, Explore, Explore 3–Multiplication with Tape Diagrams, Standards of Mathematical Practice, “MP.1 Make sense of problems and persevere in solving them: As students persist in providing a context to different multiplication problems, clear explanations and justifications of their contexts will be required.” Procedure and Facilitation Points, “Part I 1. Introduce the scenario to the class. On your way to school this morning, you counted 9 houses on your neighborhood street. You noticed that every single house has exactly 6 windows. You started to think that you could probably make some money washing windows in your neighborhood. You wished you could figure out a way to see how many windows there are in all without having to count them individually. 2. Challenge students to turn and talk to a partner to describe different ways they can represent the total number of windows that could be washed… 5. Distribute linking cubes to each pair of students. 6. Ask students the following questions: a. DOK-1 What do you need to find? 7. Instruct students to take our 9 linking cubes. Tell them that these represent the houses. 8. DOK-2 Challenge students to turn to their elbow partner and discuss what else we need to do to represent the problem and what we could do to model that. Share  9. Encourage students to find a way to represent this information using the manipulatives. 10. DOK-2 Invite students to share their solutions. 11. Challenge pairs to draw their model and discuss observations. 12. DOK-2 Invite students to turn to a partner to discuss what observations they can make about their model. 13. Explain that the models covered are called tape diagrams. 14. How does a tape diagram represent an equation? 15. DOK-1 Challenge them to write an equation for the tape diagram they created to find the number of windows. 9\times6 How do you know the multiplication sentence is true using the tape diagram? Part II 1. Distribute a copy of the Student Journal to each student and a set of Scenario Cards to each pair. 2. Tell students that they will have 8 scenarios to collaborate with a partner. 3. Encourage students to use linking cubes and dry-erase markers to help build and discuss a tape diagram that represents the problem. 4. Explain that they will record their models and solutions in their copy of the Student Journal. 5. Monitor students as they collaborate on their work, asking the following questions to assess understanding: a. DOK-2 How does knowing the “groups of” help you draw your tape diagram? b. DOK-2 Why should parts of the tape diagram be the same size? c. DOK-1 How would you write the multiplication sentence? d. DOK-1 What are the factors in the tape diagram? e. DOK-1 How does the tape diagram help you find the product? 6. If students have completed the Scenario Cards before classmates are done, challenge them to create their own word problems with their partner and have each other draw a tape diagram and multiplication sentence to match. 7. After the Explore, invite the class to a Math Chat to share their observation and learning. When students are done, have them complete the Exit Ticket to formatively assess their understanding of the concept.” 

• Scope 12: Apply the Area Formula, Explore, Explore 1–Relating Tiling to Multiplication, Standards of Mathematical Practice, “MP.1 Make sense of problems and persevere in solving them: Students will analyze the context of a real-world problem involving area, using concrete objects to support conceptualizing the problem.” Area of Rectangles Exit Ticket, “The farmer needs help! The Sun is setting and the pumpkin seeds need to be planted. You need one scoop of seeds per square yard. The farmer gave you the plans below. You need to know how many square yards the section is so you’ll get enough pumpkin seeds!” An image of a rectangle with the 5 squares in the top row and 6 squares in the first column but no other squares in the figure are shown. “How many square yards is the pumpkin section? ____ Write an equation that represents how you found the area of the pumpkin section.”

• Scope 19: Time, Explore, Explore 1–Telling Time to the Nearest Minute, Standards of Mathematical Practice, “MP.1 Make sense of problems and persevere in solving them: Students will determine what the problem is asking for, such as the exact time needed for a task or showing a specific time on a clock. Students will also decide whether concrete or representation models, mental mathematics, or equations are the best tools for solving the problem.” Scenario Cards Card, “Science lab is one of our favorite times of the day! First we grab our safety equipment and set up our lab tools to make sure we are ready to explore and experiment. By the time we are all finished setting up, it is eight-twelve in the morning.” Card 3: “After returning from the science lab, we put our science notebooks and materials away and start at our math stations. After the teacher explains what we will focus on, the clock usually reads nine twenty-seven in the morning.”

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 2: Addition and Subtraction Fluency, Explore, Explore 2–Adding Using Number Line Strategies, Standards of Mathematical Practice: “MP.2 Reason abstractly and quantitatively: Through the process of bundling numbers into units of tens and hundreds, students use the place values of base ten numbers to compose and decompose in determining sums and differences.” Procedure and Facilitation Points: “Distribute a Student Journal to each student, and a Number Line and a dry-erase marker to each group. Play spy music in the background as you read the following scenario: Around the room, you will find five missions you must complete. You will have 5 minutes to solve each mission. On each mission, there is a “Mission Challenge.” This number challenges your skills to solve the problem in the indicated number of jumps. Remember, agents, the challenge is not an obligation as long as you complete the challenge. Collaborate with your team of agents, but try to complete the final one on your own. Good luck, agents.Invite each group to find a card to start with. Encourage students to use the number lines as needed to work out problems.Inform students that they will complete the missions in order from here. Example: A group starting on mission 3 will continue on to 4.Point out to students that each group of agents will start recording at a different place in their copy of the Student Journal. Allow students about 5 minutes at each mission. While students are working, monitor groups to listen to the discussions. Monitor as students decide on larger jumps versus smaller ones. If students are not adding in the most effective way, guide students by asking the following: DOK-1 How could you decompose the addend? DOK-1 How could you add now that you see the values of the digits?...”

• Scope 7: Multiply by Multiples of Ten, Explore, Explore 2–Multiplying by Multiples of 10 with Arrays, Standards of Mathematical Practice, “MP.2 Reason abstractly and quantitatively: Students reason abstractly while using strategies of the associative property to make numbers easier to use. Quantitative reasoning is when students apply base-ten number strategies in multiplication to solve one-digit whole numbers by multiples of ten.” Procedure and Facilitation Points: “Share the following scenario with the students:You and a friend are opening up a bed-and-breakfast! This is a place that is similar to a hotel but typically much smaller with only a few rooms. You are planning a breakfast feast for your guests and want to make sure that they have plenty to eat. In order to ensure that you are all stocked up, you have to take inventory to see how much food you have. Tell students that there are grocery items around the room. Their job is to “take inventory” of each item. Explain that you need a visual model to help you and your friend keep track of all of the items you have, and you will show the total amount of each item using an array. Encourage students to collaborate and use the manipulatives to arrange the best array for each item, and then record the model in their Student Journals. Monitor students as they work, asking the following guiding questions: DOK-2 How did you and your partner set up the array in order to take inventory of the items? DOK-1 Where do you observe equal groups in the models we just built? DOK-2 How could you find the total number of items? ...”

• Scope 16: Compose and Decompose Fractions into Units, Explore, Explore 1–Unit Fractions in a Whole, Standards of Mathematical Practice, “MP.2 Reason abstractly and quantitatively: Students make sense of unit fractions and their relationship to the whole. They will connect the unit fraction to how it is written in fractional notation.” Procedure and Facilitation Points, “1. Tell students the following scenario: a. A resale shop has received a bag full of puzzle pieces from someone who told them the pieces belong to five different puzzles. The resale shop has asked you to sort out the pieces into whole puzzles and identify what fraction of the whole puzzle each piece represents. 2. give each group a bag of mystery units. Instruct students to take the pieces out of the bag and place them in a pile on the desk. 3. Tell students they should find matching pieces of the mystery units from the pile, put the pieces together to build a whole puzzle, and identify what the fraction of the whole each mystery piece is. 4. As students are finding matching pieces, monitor student conversations. 5. Encourage student thinking with the following guiding questions: a. DOK-2 How do you know those mystery pieces belong together? b. DOK-1 What is one piece? c. DOK-1 How many pieces do you have? What fractions does each mystery piece equal? d. DOK-2 How many more pieces do you think you need to find to make a whole? How do you know? 6. After students find all the pieces necessary to build each whole puzzle, have them use the whole circles provided on their copy of the Student Journal to generate their report to the shop owner. 7. Students should name each puzzle and partition each circle into the same number of pieces as the original puzzle. 8. Students should also label each piece of their drawing with the fraction of the whole puzzle it represents and identify the unit fractions. 9. After students have built all of the whole puzzles and identified the unit fraction for each puzzle piece, challenge them to work together to develop a definition of a unit fraction. 10. Guide students to identify a unit fraction as one part of the whole, and explain that a whole is divided into two or more equal unit fractions. 11. After the Explores, invite the class to a Math Chat to share their observations and learning. 12. When students are done, have them complete the Exit Ticket to formatively assess their understanding of the concept.”

The materials reviewed for STEMscopes Math Grade 3 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 5: Division Models, Standards for Mathematical Practice and Explore, Explore 1–Equal Groups and Shares, Math Chat, Standards for Mathematical Practice, “MP.3 Construct viable arguments and critique the reasoning of others: Students will have the opportunity to make conjectures and justify their conclusions when determining why division should be the chosen operation to solve. Counterexamples may be given when analyzing the reasoning of others.” Math Chat, “DOK-2 What did you notice about what was happening in the scenarios? DOK-2 What process did you use to divide the totals into their groups? DOK-3 How did you know if the scenario was asking for the number of objects in each group rather than the number of groups? DOK-2 What did you do if the scenario was asking for the number of groups instead of objects in each group? Explain how you did it. DOK-2 Do you think that what you’re doing is related to addition or subtraction? How do you know? DOK-1 Now that you have had some practice, what is division, in your own words?”

• Scope 9: Multiplication and Division Problem Solving, Standards for Mathematical Practice and Evaluate: Decide and Defend, Student Handout, Standards for Mathematical Practice: “MP.3 Construct viable arguments and critique the reasoning of others: Students may use concrete objects or drawings to explain their thinking to others as they problem solve. Students will justify their thinking and critique the conjectures of their peers.” Decide and Defend: Game Snacks: “Tyler’s parents bought snacks and drinks for the basketball teams to enjoy after the game. The box of snacks they bought had 36 snack bags in each box. They were not told the number of players on each team, but were told that the 36 snacks were enough for each player to have at least two snacks and that each player would get the same amount. Below you will find the expression they used to find the number of snacks for each player. Draw and describe all the different ways the snacks could have been packed. Explain why the snacks could be grouped in different ways.” Equations are listed: "36\div x=3; 36\div x=2; 36\div x=4; 36\div x=6”.

• Scope 16: Compose and Decompose Fractions into Units, Explore, Explore 2–Combining Fractional Units, Standards for Mathematical Practice, Procedure and Facilitation Points, students “Construct viable arguments and critique the reasoning of others: Students will make conjectures and explore their solutions, looking for evidence of proof as they describe the fractional part of an area. Students listen to others asking clarifying questions and expecting feedback. They may provide counterexamples to justify conclusions.” Procedure and Facilitation Points, “1. Place students in groups of 4 or 5. 2. Discuss the following questions: a. DOK-1 Have you had cake on your birthday? How do you serve that cake? b. DOK-1 Does each person eat a whole cake? c. DOK-1 Ask students to remind their shoulder partner what a unit fraction is based on the definition that was agreed upon as a class during Explore 1. 3. Tell students that they are surrounded by unit fractions every day, and that today they will be seeing them in different ways. 4. Explain to students that they will be doing fractional activities at 5 different stations. In each station, they must look for the different unit fractions within the objects they are exploring. 5. Ask students to read the Station Cards and use the objects along with their dry-erase board to model the parts that make up the whole. 6. Encourage students to work together in their groups to decompose the wholes into unit fractions and make a numerical equation that represents the whole. 7. Encourage thinking by asking the following questions, using the objects to help understanding: a. DOK-1 How many equal pieces is this whole partitioned into? b. DOK-1 How would you decompose this whole into its fractional units? c. DOK-1 If I am combining several units together, what operation am I doing? d. DOK-1 When we compose the whole, how would you describe it in a numerical equation? 8. Students should record their models and equations on their copy of the Student Journal. 9. As students rotate through the different stations, monitor for students who may need extra guidance or have misconceptions. 10. Students should complete the challenge at each station, if there is one. 11. After the Explore, invite the class to a Math Chat to share their observations and learning. Math Chat: DOK-2 What are some observations you made through the activities? DOK-3 After having interacted with these fractions in their individual units, how can we define a unit fraction? DOK-1 How can you decompose, or break apart, a fraction? DOK-2 What can you tell me about the fractional pieces in relation to the whole? DOK-2 What do you notice about the fractions that represent each whole? 12. When students are done, have them complete the Exit Ticket to formatively assess their understanding of the concept.” 

• Scope 19: Time, Evaluate, Decide and Defend, students critique the reasoning of others by creating a model and comparing the effectiveness of two plausible arguments as they work with elapsed time. Given 6 films with times from which to choose, “Abby and Carla want to watch a film at Stem Cinema Theater before going to soccer practice. Abby suggests watching the film Missing Factor at 2:08, because it will conclude before soccer practice. Carla argues that the film Missing Factor will conclude when soccer practice begins at 4:15, because there is a seventeen-minute intermission for the audience to take a break to refresh beverages and snacks. The duration of the films at Stem Cinema Theater is 1 hour and 50 minutes. Who is correct? What time and film are they able to watch before soccer practice begins? Explain your reasoning. Use the number line diagram to represent the problem.”

The materials reviewed for STEMscopes Math Grade 3 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 9: Multiplication and Division Problem Solving: Explore, Explore 1–The Commutative Property, Print Files, Exit Ticket, students build experience with MP4 as they create a model to show if the order of the multiplication problem impacts the solution. “Does Order Matter? Create a model of each equation, and fill in the product. 8\times5= ___ 5\times8= ___.” Below each equation is a space for a model and under 5\times8= ___ , is a line. “Circle the word or phrase that best completes the statement. The numbers in each equation are different / the same. The order of the numbers in each equation is different / the same.  The products in the equations are different / the same.  The order of the numbers being multiplied does/does not matter.”

• Scope 11: Area in Square Units, Explore, Explore 1–Recognizing Unit Lengths and Tiling Area of Plane Figures, Print Files, Older Book Station Cards, students build experience with MP4 as they make the connections between the area covered and the square units used to measure. There are ten cards with images of book covers that students must measure with tiles. “Using the square tiles, determine the length and width of this mystery novel. Then, tile the whole cover and count to find the area. Write down your findings on your Book Cover Log.”

• Scope 19: Time, Explore, Explore 1–Telling Time to the Nearest Minute, Standards for Mathematical Practices, Procedure and Facilitation Points, Standards for Mathematical Practice, “MP4 Model with mathematics: Students use multiple methods to represent their thinking. They can use concrete models (such as a small clock), representations of time intervals (including number lines, drawings, etc.), or equations to help them find the solution to the problem. In Procedure and Facilitation Points, “1. Hand students the geared clocks. 2. Invite the students to turn and talk to their shoulder partner and talk about what they notice about the geared clocks. … 4. Explain the scenario: Last night there was a storm and ALL of our digital clocks went out, and they are all blinking a big, red 12:00! In order to stay on schedule, we must determine what the analog clock will look like for each part of our day. 5. Place students into groups of three. 6. Explain that they will rotate through the stations with their clocks. 7. Let students know that at each station is a description of the scheduled activity and the time the class usually does it. 8. Explain that they will use the analog clocks provided to determine what the clock should look like as well as write down the corresponding digital time on their copy of the Student Journal. 9. Walk around and observe students working. Be on the lookout for misconceptions like which hand represents hours and which one represents minutes. Ask the following guiding questions: a. Where do you think the hour hand is going to be? b. How will you count the number of minutes described? c. Which direction should we move the hands?”

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 3: Rounding, Evaluate, Skills Quiz, Question 5, students build experience with MP5 as they use a thermometer to round the temperature in Fahrenheit. Students see a thermometer with both Celsius and Fahrenheit measurements. They need to realize which side of the thermometer is Fahrenheit and then complete the rounding of the number. “Round the temperature to the nearest 10 degrees Fahrenheit. ____” 

• Scope 13: Perimeter, Explore, Explore 2–Finding the Missing Length, Standards for Mathematical Practice, Procedure and Facilitation Points, Standards for Mathematical Practice, “MP5 Use appropriate tools strategically: Students use non-standard measuring tools, tiles, graph paper, pegboards, rulers, and other resources as appropriate to aid in their understanding of the concept and solving the problem. Procedure and Facilitation Points, “1. Explain that each group will be going to six different stations. At each station, students will read the station card and use the dimensions on the card to build the figure described, with the objects provided. 2. Tell students that each object represents one unit of measurement as described on the station card. a. For example, each craft stick in Station 2 represents 1 foot, each toothpick in Station 4 represents 1 mile, and so on.  3. Have students use sticky notes to label the length of each side. (Note: After groups are finished at their station, have them save the unused sticky notes for use by the remaining groups.) 4. Students will then collaborate to answer the corresponding questions on the Student Journal. 5. Tell students they will have a set amount of time at each station. When the time is up, they will clean up the stations and stack the sticky notes neatly. 6. Assign each group to a station. Monitor and check for understanding. 7. As you walk around, make sure students are counting and labeling the outside of their figures. a. Guide students toward being more efficient by asking the following: What operation could help in finding the remaining length without counting each of the objects? 8. As students get more comfortable, challenge them to make drawings of the figures and use computation instead of building them with the materials…” 

• Scope 20: Volume and Mass, Explore, Explore 1–Mass (Grams and Kilograms), Student Journal, Part I, students build experience with MP5, recognize the insight to be gained and limitations of using a scale to find the mass of a variety of objects found around the classroom, looking for objects that weigh about a gram and about a kilogram. “Grams vs. Kilograms Find objects around the classroom that are close to the following measurements. Use the scale to test the objects you find. Measurement Object 1 Object 2 Object 3 1 kilogram 1 gram What do you notice about a kilogram? ___ What do you notice about a gram? ___ What tool did you use to measure the weight of each object? ___ Name an object that weighs about 1 kilogram. About how much would five of these objects weigh? ___ Which weighs more: a gram or a kilogram? Explain how you know. ___ Volume and Mass Explore 1 Mass 1 Part II: Pack the Classroom! With your group, help to pack your belongings in boxes. Each box has a maximum limit of 10 kilograms. Estimate which objects you think will have a mass of 10 kilograms first before weighing them. Once you have reached an estimate of 10 kilograms, measure the actual mass to check if you were right! When you reach the limit, draw a line and write “Box #” on the side. Object Estimated Mass (kg) Actual Mass (kg) Quantity Total Mass (kg) Number of Packing Boxes Needed: Volume and Mass Explore 1 2 How did you decide to box up all the materials? ___ Why do you think we should measure the mass in kilograms and not grams? ___ What kinds of objects would make sense to weigh using kilograms? ___”

The materials reviewed for STEMscopes Math Grade 3 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 6: Multiplication and Division Strategies, Explore, Explore 3–Distributive Property, Print Files, Exit Ticket, engages students in attending to precision and the specialized language of mathematics. “Distributive Property of Multiplication Exit Ticket: The newly released superhero film is playing at Illumination Theater. Due to its popularity, they are showing the film in six theaters at one time. If each theater can hold 9 customers, how many people will be able to watch the movie at once?  Expression: ___ \times ___  Draw an area model and part of the area model on the grid provided to solve. Fill in the blanks below, using the original equation and information from your area model. ___ \times ___ = ___ (___ + ___) = ___ + ___ = ___ ___ \times ___ = (___ \times ___) + (___ \times ___) = ___ + ___ = ___”

• Scope 11: Area in Square Units, Explore, Explore 1–Recognizing Unit Lengths and Tiling Area of Plane Figures, Exit Ticket, students build experience with MP6 as they attend to precision when measuring and drawing a shape,labeling the width, length and area accurately. “You have some leftover fabric from creating all those book covers. You want to create a patch to remember this good deed. Use square tiles to determine the area of the patch in square units. Draw your patch below, and label the width, length, and area. Design it how you want!”

• Scope 21: Represent and Interpret Data, Evaluate, Skills Quiz, Question 7, students build experience with MP6 as they attend to precision when creating an accurate bar graph. Exit Ticket, students are given a table of colors and the number of times (frequency) those colors are in a bag of candy. They then create a bar graph to represent that data. “Create a bar graph by using the data in the frequency table. Frequency of Colors in a Bag of Candy, Color Choices, Frequency, Purple 4, Yellow 8, Red 7, Green 9, Blue 5, Orange 4, Title: ___”

The materials reviewed for STEMscopes Math Grade 3 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 2: Addition and Subtraction Fluency, Explore, Explore 2–Adding Using Number Line Strategies, Procedure and Facilitation Points, students build experience with MP7 as they recognize patterns in the structure of base ten numbers. “... 2. Play spy music in the background as you read the following scenario: Around the room, you will find five missions you must complete. You will have 5 minutes to solve each mission. On each mission, there is a “Mission Challenge''. This number challenges your skills to solve the problem in the indicated numbers of jumps. … 3. Invite each group to find a card to start with. 4. Encourage students to use the number lines as needed to work out problems. … 8. While students are working, monitor groups to listen to the discussions. a. Monitor as students decide on larger jumps versus smaller ones. If students are not adding in the most effective way, guide students by asking the following: DOK-1 How could you decompose the addend? DOK-1 How could you add now that you see the values of the digits?” 

• Scope 8: Arithmetic Patterns, Explore, Explore 2–Evaluating Multiplication Tables, Procedure and Facilitation Points, students build experience with MP7 as they identify patterns involving operational relationships. “Part I: Reading a Multiplication Table…3. Display a multiplication table. Highlight the first row and first column of the multiplication table. 4. Explain that the highlighted row and column are the factors being multiplied. The numbers to the right of the highlighted column and below the highlighted row are the products of those numbers being multiplied. Part II: Packing Boxes 1. Read the following scenario to the class: Fantastic Food Bank received donations from their local community of items that will help those in need. The donation boxes had the same number of objects in each box. The food bank staff recorded the number of items in a table in which, if you multiplied the number of items in each box by the number of boxes, then you could find the total amount of items in all the boxes. Look at the table the staff made and see what patterns you notice. … 3. While students are working, monitor and ask them the following questions to check for understanding. a. DOK-1 What did you notice about the multiplication table? b. DOK-2 What is the pattern of this row or column (point to a row or column)? Why does this pattern make sense? 4. Encourage students to look for similarities and differences between their strategy and the strategies of others. 5. Students can use the counters to model the relationship, if needed. Modeling the relationship can help students see if there are a certain number of equal groups.” 

• Scope 18: Compare Fractions, Explore, Explore 2–Compare Fractions with Like Numerators, Procedure and Facilitation Points, students build experience with MP7 as they understand the structure of fractions and that the larger the denominator, the smaller the fractional unit. “1. Let students know that today they will serve as judges in court cases regarding fractions…. 4. Have the class stand and repeat the Judge’s Fractional Oath: 1, ___, do solemnly swear that I will administer comparative justice to all fractions, in respect to denominators, numerators, and fraction bars, whether they be greater than, less than, or equal to each other under Mathtitutional Law. 5. Once students have taken their Judge’s Fractional Oath, explain that in order to make a decision in each case, they must use the manipulatives as tools to gather evidence. 6. In each case, the evidence must be presented as words, using symbols in two ways (> and <), using pictorial models (number lines, tape diagrams), as well as sketching how they used the manipulatives. 7. Encourage them to talk about observations they make about the numerators and denominators as they are modeling the fractions. 8. Give students about 30 minutes to make a decision about all four cases. 9. Walk around, encouraging conversation focusing on the inverse relationship between the number of equal pieces (denominator) and the size of the pieces of the whole. 10. For students struggling to see the connection, help them place the manipulatives for each fraction right under each other. a. DOK-1 What do you notice about these two fractions? b. DOK-1 What is different about these two fractions? c. DOK-1 What do you notice about the size of the pieces in fractions with a larger denominator? d. DOK-2 Why would the greater-number denominator give you smaller pieces?”

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 5: Division Models, Explore, Explore 1–Equal Groups and Shares, Procedure and Facilitation Points, students build experience with MP8 as they work to understand the relationship between multiplication and division. “... 3. As a whole group, work through Scenario 1. Read the scenario out loud to the students: a. Mrs. Lopez is making 40 mini cupcakes for her after-school club. She has 8 students in her after-school club. How many mini cupcakes can each student have? 4. DOK-1 Ask students to discuss with their groups, and then share: What information do we have? DOK-1 What do we need to find out? … Ask the following questions: a. DOK-1 What did your plates represent? b. DOK-1 What did your counting objects (cubes, pom-poms, beans, or beads) represent? c. DOK-1 What did you do with the total number of cupcakes? d. DOK-1 What is another word we could use to describe how you divided up the cupcakes? e. DOK-1 How many cupcakes will each student get? How do you know? f. DOK-2 Look at your model again. Does this model make you think of another math operation? Explain your reasoning. g. DOK-1 How could we check our division work by using multiplication?... 9. Discuss the following with students: a. DOK-1 How many cupcakes did we start with?... d. DOK-1 How many groups did we have, and what did each group represent from the scenario? e. DOK-1 How many cupcakes did each student get? f. DOK-3 Is there a way we could change the question in this scenario to find the number of groups instead of the number of objects in each group?”

• Scope 10: Problem Solve Using the Four Operations, Explore, Explore 2–Problem Solve Using the Four Operations Part 2, Procedure and Facilitation Points, students build experience with MP8 as they look for generalizations as they solve problems and evaluate the reasonableness of their work. “1. Present the following scenario to the class: Congratulations! You are now the proud owner of a doughnut shop called the Dapper Doughnut. Before you can officially open, you will need to learn some of the basics of the business. Read each problem together with your group and then solve. When you are done, you will attempt to learn more about the business by creating and solving your own word problem. 2. Tell students that each of the posters will designate a station. 3. Explain that they will need to represent each problem with a model, build an equation using a letter for an unknown quantity (maybe even two letters for two unknown quantities), estimate the solution, and then solve. 4. Encourage students to use manipulatives to help create the models that represent the problems. 5. Emphasize collaboration and discussion, since there may be different ways of solving the same problem. 6. Allow sufficient time for students to solve a problem before rotating to the next station. 7. Present the final challenge! Groups will create their own two-step problem for a situation that can arise with their new business. 8. Instruct them to write out the problem and come up with a model to represent it. Ask them to use estimation to find a reasonable answer and, finally, solve the problem. 9. If time permits, allow groups to challenge the class with their own two-step problems. 10. Monitor student collaboration and discussions. Assess for understanding and misconceptions using the following guiding questions: a. What is the question asking you for? b. What information does the problem give you? c. What information is missing? d. How could you model what is happening in the problem? e. What manipulatives could you use to help you visualize the math in the problem?” 

• Scope 19: Time, Explore, Explore 2–Problem Solving with Time on a Number Line,  Procedure and Facilitation Points, students build experience with MP8 as they use patterns discovered in telling time to solve problems. “...3. Give groups the four bags with the Time Interval Cards and the sets of Scenario Cards. 4. Explain to students how to complete the following activity: a. Students will place the Scenario 1 Time Interval cards in the correct positions on the floor number line. b. Student 1 will start as the number line time walker. Student 2 will read the first sentence of the Scenario 1 card. The number line time walker will stand at the starting time on the floor number line. c. Student 3 will read the next sentence, and the group will decide whether the time interval should be added to or subtracted from the starting time. The number line time walker will walk backward or forward to move to the new location. e. As the walker walks on the number line, teammates mirror his or her moves on the analog clock. They can also use the clock to determine which direction to move. f. The number line time walker will state the answer to the question on the scenario card. g. Students will check with you to see if their answer is correct. If the answer is incorrect, groups should repeat the scenario. If the answer is correct, students will move on to the next scenario. h. After Scenario 1 is complete, the students will switch jobs so that when all 4 scenarios are complete, each student will have done each job. i. Scenario answers: i. ___ ii. ___ iii ___ iv ___ 5. Once students have acted out the first four scenarios, have them work together to complete scenarios 5 and 6 without building the number line.”