4th Grade - Gateway 1

The materials reviewed for STEMscopes Math Grade 4 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

The curriculum is divided into 22 Scopes, and each Scope contains a Standards-Based Assessment used to assess what students have learned throughout the Scope. Examples from Standards-Based Assessments include:

• Scope 4: Addition and Subtraction Algorithms, Evaluate, Standards-Based Assessment, Question 8, “A train is carrying 7,892 pounds of lumber in a boxcar. It makes a stop along its route and picks up another 5,329 pounds of lumber that go in a second boxcar. How many pounds of lumber is the train transporting? Write your answer and show your work.” (4.NBT.4)

• Scope 8: Equivalent Fractions, Evaluate, Standards-Based Assessment, Question 1, “Selena and Juan each have a bag of stickers. Selena’s bag of stickers has: A total of 5 stickers; Exactly 2 dog stickers. Juan’s bag of stickers has: A total of 10 stickers; Exactly ____ dog stickers. Part A: Juan has the same fraction of dog stickers in his bag as Selena has in her bag. How many dog stickers does Juan have? Part B: Explain how the fraction of dog stickers in Selena’s bag has the same value as the fraction of dog stickers in Juan’s bag, even though they each have a different number of stickers.” (4.NF.1)

• Scope 11: Problem Solve with Measurement, Evaluate, Standards-Based Assessment, Question 10, “A puppy at the pet store weighed 128 ounces. There are 16 ounces in each pound. How many pounds did the puppy weigh? 4 pounds; 5 pounds; 6 pounds.” (4.MD.2)

• Scope 15: Prime and Composite Numbers, Evaluate, Standards-Based Assessment, Question 6. Students see a box labeled 12 Crayons: “A box contains 12 crayons. List the first 3 multiples of 12 to determine how many crayons are in 3 boxes.” (4.OA.4)

• Scope 21: Properties of Two-Dimensional Figures, Evaluate, Standards-Based Assessment, Question 1. Students see four figures:  A is a heart;  B is a two-way arrow; C is a trapezoid; and D is a rectangle. “Which two figures appear to have more than one line of symmetry? Figure A, Figure B, Figure C, Figure D.” (4.G.3)

The materials reviewed for STEMscopes Math Grade 4 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials provide extensive work in Grade 4 as students engage with all CCSSM standards within a consistent daily lesson structure, including Engage, Explore, Explain, Elaborate, and Evaluate. Intervention and Acceleration sections are also included in every lesson. Examples of extensive work to meet the full intent of standards include:

• Scope 4: Addition and Subtraction Algorithms, Explore 1 and 2, engages students in extensive work to meet the full intent of 4.NBT.4 (Fluently add and subtract multi-digit whole numbers using the standard algorithm.) Explore 1-Multi-digit Addition, Student Journal, students work with different multi-digit numbers measuring travel distances between cities to determine the trip distance as well as total distance using addition strategies and then the addition algorithm. Students are given Boarding Passes for each flight to use with their journal pages. “Complete the following steps to find the total distance traveled. Find the two boarding passes that match with the trip. Use a strategy of your choosing, as well as the standard algorithm, to solve for the sum of each trip. Strategy options: open number line, partial sums. For the last question, find the total distance traveled for all 3 trips. Trip 1, Atlanta, Philippines, Australia, Your Strategy, Standard Algorithm, Trip 2, Los Angeles, Paris, Mexico, Your Strategy, Standard Algorithm, Trip 3, Canada, Dubai, New Zealand, Your Strategy, Standard Algorithm, Total Travel, Reflect, Explain the reason you chose a certain strategy on a trip and why. How are the open number line, partial sums, and standard algorithm similar? Is the standard algorithm always the most efficient way to solve addition problems?” Explore 2–Multi-digit Subtraction, Exit Ticket, students use the standard algorithm for subtraction to solve a multi-digit problem. “Read the scenario below and solve the problem by showing your work. Record your solution as a statement. Carnival workers were standing outside the venue giving away prizes to the raffle ticket winners. They started with 33,500 prizes and gave away 28,833 of those prizes. How many prizes did carnival workers have left? Solve. Write the solution as a statement. ___”

• Scope 6: Compose and Decompose Fractions and Mixed Numbers, Explore 1 and 2, Explain, and Evaluate engages students in extensive work to meet the full intent of 4.NF.3b (Understand a fraction a/b with a>1 as a sum of fractions \frac{1}{b}. b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model…) Explore 1, Station one: “At each station, assemble the pie pieces into as many whole pies as possible and complete the table below. Serving Station 1: Cherry Pie, Each cherry pie is sliced into 6 equal pieces. The bakery handed out 5 slices. Assemble the slices of pie that were given away and draw the slices below. What fractional part of the whole is each slice of pie? Write an equation to represent how much pie was given away. How much cherry pie was given away? How many more slices do they need to hand out to make a whole pie?” Station 2: Pumpkin Pie, Each pumpkin pie is sliced into 8 equal pieces. The bakery handed out 12 slices. Assemble the slices of pie that were given away and draw the slices below. What fractional part of the whole is each slice of pie? Write an equation to represent how much pie was given away. How many whole pumpkin pies were given away? Write the total amount of pie given away as a mixed number.” Reflect Questions at the end of the station activities: “What can you determine from a fraction that has a numerator greater than the denominator? What is it called? Explain why the equation you wrote represents the amount of pie that was given away. How could you develop a mixed number from an improper fraction with no model?” Explain, Show What You Know, Part 1: “Part 1: Compose and Decompose into Unit Fractions Compose and Decompose Fractions and Mixed Numbers, A restaurant prepares rectangular-shaped pans of lasagna. Each pan is cut into 5 equal pieces. On Monday, the restaurant served 11 pieces. Draw a model to show the pans of lasagna and total amount of pieces served. What fractional part of each pan represents one piece? Write an equation to represent how much lasagna was served. How many whole pans were served? Write the total amount of pieces served as a mixed number. On Tuesday, the restaurant served 18 pieces. Which of the following statements are true? Select three statements. A. The restaurant served more than 4 pans of lasagna. B. The restaurant served more than 3 pans of lasagna. C. The restaurant served pans of lasagna. D. The restaurant served 3 pans of lasagna.” Explore 2, “Bag 1: Cookie Cakes Assemble each cookie cake. Draw a model of the cakes in the circles below. Label the names of the cakes on each line. Be sure to draw lines to show how many pieces each cake was cut into.” Images of three circles included for students to partition. “Write a fraction that represents 1 slice of cookie cake. Seventeen slices of cookie cake were handed out at the grand opening. What fraction of cookie cake was handed out? Count out 17 slices of cookie cake using any combination of the 3 flavors. Write a number sentence that represents the fractional amount of cookie cake for each flavor combined. Label each fraction by the flavor it represents. Choose a new combination of 17 slices and write another number sentence to represent the combination. Describe how each combination is the same and how they are different.” Evaluate, Skills Quiz: “Decompose the given fraction into the sum of its unit fractions. Compose and Decompose Fractions and Mixed Numbers 1. \frac{3}{5}  2. \frac{7}{4} 3. \frac{8}{8} 4. \frac{4}{12} 5. 1\frac{2}{6}.”

• Scope 15: Multiplicative Comparisons in Multiplication and Division, Explore 1, Evaluate & Elaborate engages students in extensive work to meet the full intent of 4.OA.1, (Interpret a multiplication equation as a comparison… Represent verbal statements of multiplicative comparisons as multiplication equations.) Explore 1, Scenario card 2, “Farmer Susan bought a bag of chicken feed. One serving feeds 7 chickens. Susan needs 3 times that amount to feed all of her chickens. How many chickens does Susan have?” The card has an image of feed and 7 chickens. Scenario card 3, “Farmer Joe has 24 Arabian horses. That is 4 times more than a barn can hold. Help Joe figure out how many horses each barn can hold.” The card has an image of 24 horses and a barn. Students are asked to write an equation and give a description. Explore 1, Exit Ticket, “Farmer Joe has 35 acres of farmland. This is 5 times more than the acres that Farmer Susan owns. How many acres does Farmer Susan own?” Students complete a chart with a model, equation and explanation. Evaluate, Decide and Defend, “A florist is making flower arrangements for a bridal shower. Each of the dining tables at the shower will display a small vase of flowers. The four food stations will each have a large vase of flowers. The small vases will each hold 6 flowers, and the large vases will each hold 3 times as many flowers as a small vase. The total number of flowers is 10 times the number in a large vase. Explain how you would find the total number of flowers at the shower.” Elaborate, Math Stories, Question 3, “If Jane got 6 times more peace than the 5 minutes she wished for when she put on an animal detective show, how many minutes of peace did she earn? A. 11 minutes B. 30 minutes C. 35 minutes D. 1 minute.” Question 7, “Keith found 10 times as many buttons as Kylie did in the Find the Buttons game. If Kylie found 6 buttons, which equation represents how many buttons Keith found? A. 10-6=4 B. 10\times6=60 C. 100-(10\times6)=40 D. 100-66=34.” Standards-Based Assessment Question 1, “Atticus and Nina kept track of how many text messages they each received in one day. Atticus received 20 text messages, while Nina received 5. Which two statements are correct? A. Atticus received 4 times as many messages as Nina. B. Atticus received 15 times as many messages as Nina. C. Atticus received 15 more messages than Nina. D. Nina received one-fifth of the number of messages as Atticus.”

• Scope 19: Angles, Explore 2 and 3, engages students in extensive work to meet the full intent of 4.MD.6 (Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.) In Explore 2-Measuring Angles, students use a protractor to measure a given angle. “1. Ask the following questions. a. DOK–1 When we want to find the exact measurement of something, what do we do? b. DOK–1 Angles can be many different sizes. How do you think we can figure out the exact measurement of an angle? 2. Show students a protractor, and explain that it is a measurement tool used to measure angles in degrees. 3. Give each student a protractor. Have student pairs put two protractors together to form a circle. Ask the following questions. a. DOK–1 What do you notice about the protractors when they are together? b. DOK–1 In Explore 1, we found out a circle is how many degrees? c. DOK–1 How are the numbers arranged on one protractor? d. DOK–1 What is 180 plus 180? 4. Allow students to discuss why they think there are two sets of numbers on the protractor and then share their ideas with the class. 5. Explain that a protractor has two sets of numbers because sometimes the angle is open to the right and sometimes the angle is open to the left. These two sets of numbers, called number scales... 6. Have students look at the protractor numbers again. Ask the following questions. a. DOK–1 How many lines are there between the numbers? b. DOK–1 What do you think those lines represent? c. DOK–1 If an angle measured 5 lines past 40, what would the measurement of the angle be? 7. Tell students that the protractor uses the vertex and the sides, or rays, of an angle to measure the size of the angle. 8. Show students where the vertex of an angle should be placed on the protractor. Have students look at the angle made with the first turn of robot 1 (\angle ABC). Students should take turns following these steps: a. Place the midpoint of the protractor on the vertex of the angle… b.The flat edge of the protractor is called the zero line. Line up one side of the angle with the zero line of the protractor... c. Explain that if a line is too short and does not cross the angle measurements on the protractor, they should line up the edge of the protractor to the ray and draw the extension so that they are able to measure the angle more easily. d. Count the degrees, starting from 0, until you get to where the other side of the angle crosses the number scale. 9. Students should determine this angle’s measurement and record it … Students may need assistance with naming the angles. a. If needed, draw an angle on the board. Demonstrate how to write A on one side of the angle, B at the vertex of the angle, and C on the other side of the angle, just like the first turn of each robot. b. Explain to students that they read this angle as, “angle ABC” or “angle CBA.” Show students this angle would be written as \angle ABC or \angle CBA. 10. Have each student in the group take a card and measure the angles for the pathway. Students will exchange cards until they have measured the angles for each pathway. 11. As students are working, monitor and check for understanding. Ask the following questions. a. DOK–1 How did you find that angle’s measurement? b. DOK–1 How did you name the angles? 12. Students should compare their measurements. If there is a discrepancy, have them remeasure the angle and come to an agreement.” Explore 3–Sketching Angles, Exit Ticket, students use a protractor to measure and draw angles for a boat cover they are buying. “Congratulations! You won the fishing contest at the Angler Fishing Tournament! You can hardly wait until next year’s tournament! You want to keep your new fishing boat in tip-top shape throughout the year. You decide to get a custom cover made to protect your boat from bad weather, the Custom Cover Company needs a drawing and the angle measurements and types of angles of your boat before they can make the cover. Complete the order form for Custom Cover Company, and your new boat cover will be on its way! Custom Cover Company Order Form, \angle BAE:135\degree, \angle ABC:90\degree, \angle BCD:135\degree, \angle CDE:___, \angle DEA:___, Boat drawing (Be sure to label your angles!)”

• Scope 20: Points, Lines, and Angles, Explore 1-3, engages students in extensive work to meet the full intent of 4.G.1 (Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.) In Explore 1-Draw and Identify Points, Lines, Rays, and Angles, Procedures and Facilitation Points, students work with constellations to identify points, lines, rays, and angles in each constellation. “1. Show students the Constellation Cards. Read the following scenario to students: a. You are planning to join a group of astronomers who identify new constellations. Constellations can be described using various geometric attributes. When a new constellation is discovered, the local science museum likes to display a model of it. To create a model of the constellation, you must learn what the geometric attributes are and how to identify them. 2. Give each group a can of modeling dough. Give each student three plain craft sticks and two craft sticks with small triangles glued to one end. Give each student four small circle stickers. Tell them they can carefully put the stickers on the ends of their table to grab when needed. 3. Tell students to divide the modeling dough equally among group members. 4. Begin by telling students to take four small pieces of their modeling dough and roll each piece into a ball. Then have them put their four stickers on top of their pieces of modeling dough and label them A, B, C, and D… 5. Have students draw this on their Student Journal and write a short description for their model in their own words. As a class, discuss descriptions. Ensure students understand that a point is one specific location, and each point has been named A, B, C, or D. 6. Have students take one of the craft sticks with the small triangle glued to it and put one of their points at the opposite end of the triangle. Have them put another point somewhere else on the stick. Discuss the following: a. DOK–1 Describe this model. b. DOK–1 What is a line? 7. Explain that this is called a ray. Have students draw this on their Student Journal and write a short description for their model. As a class, discuss descriptions. Ensure students understand that a ray starts at one point and goes on forever in one direction. Explain that there can be other points on the ray. 8. Show students how to name their ray. Tell them it should be the two letters of the points with an arrow extending in one direction above the letters. Tell students the first letter listed should be the endpoint, and the second letter should be a point on the ray. See the Student Journal answer key for examples. 9. Have students put the two craft sticks with arrows on the ends side by side with arrows facing away from each other. Have students put two points anywhere on the sticks. Ask the following question: a. DOK–1 What do you notice about this model? 10. Explain that this is called a line. Have students draw this on their Student Journal and write a short description for their model. As a class, discuss descriptions. Ensure students understand that a line has no endpoints; it extends forever in both directions. 11. Show students how to name their line. Tell them it should be the two letters of the points on the line with an arrow extending in both directions above the letters. See the Student Journal answer key for examples. 12. Have students make two endpoints using the modeling dough on the end of one plain craft stick. Ask the following questions: a. DOK–1 What do you notice about this model? b. DOK–1 What do you think the craft stick represents? c. DOK–1 Does our line extend forever in either direction? 13. Explain that this is called a line segment. Have students draw this on their Student Journal and write a short description for their model. As a class, discuss descriptions. Ensure students understand that a line segment is a line with two endpoints. Tell them the line does not extend in either direction forever; a line segment is a piece of a line. 14. Show students how to name their line segment. Tell students it should be the two letters of the points with a short line above the letters. See the Student Journal answer key for examples. 15. Have the students create two rays. Arrange the rays to have the same endpoint. The students will need to remove the endpoint from one ray to do this. 16. Ask the following question: a. DOK–1 What do you notice about this model? 17. Explain that this is called an angle (if students did not already recognize it). Have students draw this on their Student Journal and write a short description for their model. As a class, discuss descriptions. Ensure students understand that angles are formed by two rays that share an endpoint. 18. Refresh students’ memories on how to name angles. Tell them it should be the three letters of the points, with the middle letter being the point where the lines meet. Explain that this particular point is called the vertex of the angle. Instruct students to use the < symbol in their naming. See the Student Journal answer key for examples. 19. Now that students have had practice creating models of geometric attributes, have them practice identifying these attributes around the classroom. Take some time to practice by calling out an attribute, having them show the attribute using their materials, and then finding something in the room with that attribute…” In Explore 2–Draw and Identify Types of Angles, Exit Ticket, students measure and identify an angle. Students see an acute angle made with a fishing pole and line. “All your practice paid off! You caught a gigantic fish! Your friend took a picture of the angle your pole and line made so that you could try to cast the line at the same angle during the tournament. Measure and record the size of the angle. Name the angle with proper notation, and describe the type of angle that was made. The measure of ___ (name of the angle) is ___ (measurement in degrees). This angle is a(n) ___ angle.”  In Explore 3–Draw and Identify Line Types, Student Journal, students draw figures and identify each type of line used. “Part 1.a: Creating Perpendicular Lines, Use the tape to create a four-square court. Draw your model in the space below, Name the two interior lines. Use symbols to show their relationship. What types of lines make a four-square court? What kind of angles are made when these lines intersect? What would happen to the spaces if the lines were not like this? Part 1.b: Creating Parallel Lines Draw a model of your parallel tape lines in the first box. In the next box, change one line to show that the model is no longer parallel. Name the lines. Use symbols to show the relationship between the parallel lines in the first box. What types of lines make the racetrack? Does the distance between these types of lines matter? Explain. How are these lines different from the lines needed to create a four-square court?”

The materials reviewed for STEMscopes Math Grade 4 meet expectations that, when implemented as designed, the majority of the materials address the major cluster of each grade.

The instructional materials devote at least 65% of instructional time to the major clusters of the grade:

• The approximate number of scopes devoted to major work of the grade (including assessments and supporting work connected to the major work) is 14 out of 22, approximately 64%.

• The number of lesson days and review days devoted to major work of the grade (including supporting work connected to the major work) is 116 out of 150, approximately 77%.

• The number of instructional days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 132 out of 180, approximately 73%.

An instructional day analysis is most representative of the instructional materials because this comprises the total number of lesson days, all assessment days, and review days. As a result, approximately 73% of the instructional materials focus on the major work of the grade.

The materials reviewed for STEMscopes Math Grade 4 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Materials are designed so supporting standards/clusters are connected to the major standards/ clusters of the grade. Examples of connections include:

• Scope 11: Problem Solve with Measurement, Explain, Show What You Know–Part 2: Converting Units of Weight and Mass, connects the supporting work of 4.MD.2 (Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals…) to the major work of 4.OA.3 (Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity…) Students use weight and mass conversions to solve multi-step problems. Students are shown a table with the weight of the dog and the number of tablets of medicine for the first problem. “1. Maggie Mae, a medium-sized dog, went to the vet and was diagnosed with allergies. To determine her medicine dosage, the vet measured her weight. Maggie Mae weighs 640 ounces. Based on the chart, how much medicine will Maggie Mae need to take? Record your answer in the box below. Weight, Medicine Dosage, 10-20 lb., 1 tablet, 20-30 lb., 2 tablets, 30-40 lb., 3 tablets,  ___ounces = 1 pound, How much does Maggie Mae weigh in pounds?___, How many tablets of medicine does Maggie Mae need to take?___, 2. The next pet to visit the vet was a rabbit. The rabbit weighs 6,000 grams. How many kilograms does the rabbit weigh? ___ grams = ___ kilogram, The rabbit weighs ___ kilograms. 3.  The third animal being seen by the vet was a bull. The bull weighs 1.5 tons. How many pounds does the bull weigh? ___ ton = ___ pounds, The bull weighs ___ pounds.”

• Scope 18: Area and Perimeter Problem Solving, Explore, Explore 3–Real World Problems, Task Cards 3 and 7, connects the supporting work of 4.MD.3 (Apply the area and perimeter formulas for rectangles in real world and mathematical problems...) to the major work of 4.OA.2 (Multiply or divide to solve word problems involving multiplicative comparison....) On Task Card 3, students use the formula for area and multiplication to find the space needed to create a cage. On the Task Cards, students see a drawing of the rectangle they are creating. “Great Horned Creature’s Cage, You are designing a cage to hold the Great Horned Beast. How much space on the floor will children need to play with the beast’s cage?” On Task Card 7, “Red Headed Spotter’s Treasure You are designing a treasure box accessory for the Red Headed Spotter. How many square millimeters of plastic material will be needed for the bottom of the treasure box?”

• Scope 22: Generate Patterns, Explain, Show What You Know–Part 2: Number Patterns, connects the supporting work of 4.OA.5 (Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself...) to the major work of 4.NBT.5 (Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations…) Problem 2, students are given a pattern with the change being a multiple of 11. The last number in the pattern was 176, which would be 11 times 16.  “Look at the patterns below and answer the questions that follow. 1. 44, 56, 68, 80, 92, ___ What is the next number in the pattern? ___ What is the rule?___”

The materials for STEMscopes Math Grade 4 meet expectations that materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade. 

Materials are coherent and consistent with the Standards. These connections are sometimes listed for teachers in one or more of the three sections of the materials: Engage, Explore and Explain. Examples of connections include:

• Scope 8: Equivalent Fractions, Explore, Explore 4–Equivalent Fractions with Denominators of 10 and 100, Procedure and Facilitation Points, connects the major work of 4.NF.A (Extend understanding of fraction equivalence and ordering.) to the major work of 4.NF.C (Understand decimal notation for fractions, and compare decimal fractions.) Students work in groups to generate and compare fractions. “1. Give each student a copy of the Student Journal. Distribute one set of Package Cards to each group. 2. Read the following scenario to students. A local Boy Scouts troop needs your help sorting some mail to determine how much postage will cost for the shipments. They have been busy putting together care packages for the less-fortunate citizens in our city. Now they need to know how much postage they will use so they can gather the money to pay for the packages to be sent out. The price of postage depends on how much each package weighs. 3. Tell students that in each package, there are different items weighing different amounts. Their goal is to find the total weight of the package and determine the cost of the postage.”

• Scope 10: Multiply Fractions by Whole Numbers, Evaluate, Decide and Defend, connects the Number & Operations - Fractions domain to the Operations & Algebraic Thinking domain. “Jamie’s mom gave her a \frac{1}{3} pizza for lunch. Jamie was still hungry after, so she left her mom the following note: Mom, I was so hungry I could have eaten 5 times as much pizza! Next time please give me the amount shown in the picture!” An image of five thirds of a pizza is shown. “Five times as much pizza would be the same as 5 multiplied by \frac{1}{3} of the pizza she originally ate. Does the picture in Jamie’s note match this expression and amount of pizza? Explain your reasoning. Write the expression represented by Jamie’s picture.” 

• Scope 12: Represent Measurement with Line Plots, Explore, Explore 2–Problem Solving Using Line Plots, Student Journal, Station Card One connects the supporting work of 4.MD.B (Represent and interpret data.) to the supporting work of 4.MD.A (Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.) On Station Card One, a line plot titled “Lengths of Insects (cm)” is  iterated into eighths from four to seven and five eighths is shown Xs marking the lengths of the insects is shown. Student Journal for Station Card One: “How long was the longest insect? How long was the shortest insect? What is the difference between the longest and shortest insect? How many insects were measured in this study?”

• Scope 21: Properties of Two-Dimensional Figures, Explore, Explore 1–Classifying Shapes by Lines and Angles, connects the Geometry domain to the Measurement & Data domain. “Read the properties of two-dimensional figures listed on the left. Write the corresponding numbers for the properties it displays. Some pictures might have more than one property that describes them.” Students are then shown a chart with the following shapes and descriptors that must be matched: first column of table: “Properties: 1. One or more sets of perpendicular lines 2. At least two acute angles 3. At least one right angle 4. One or more sets of parallel lines 5. At least one obtuse angle 6. One set of parallel lines and no right angles” Second column: Two-Dimensional Figure with images of pentagon, trapezoid, right triangle, rhombus. Third column:  Property Matches.”

The materials reviewed for STEMscopes Math Grade 4 meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

Prior and future connections are identified within materials in the Home, Content Support, Background Knowledge, as well as Coming Attractions sections. Information can also be found in the Home, Scope Overview, Teacher Guide, Background Knowledge and Future Expectations sections. 

Examples of connections to future grades include:

• Scope 2: Place Value of Whole Numbers, Content Support, Coming attractions connects the work of 4.NBT.2 (Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols…) to the work of 5.NBT.6 (Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division…) and to the work of 5.NBT.7 (Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.) “In grade five, students will understand how division works based on the meaning of base-ten numerals and properties of operations. As their understanding and fluency in these concepts solidify, students will begin to utilize algorithms for multi-digit operations. Students will use and apply their knowledge of place value to understand the relationship of fractions and decimals to whole numbers. They will compute products and quotients of decimals to hundredths.”

• Scope 11: Problem Solve with Measurement, Acceleration, Student Handout connects the work of 4.MD.1 (Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table …) to the work of 5.MD.1 (Convert among different-sized standard measurement units within a given measurement system…) “Landslides are fast and powerful. 1. The destroyed home had a fence around a raised garden bed in the backyard in the shape of a rectangle that measured 22 feet by 10 feet, 6 inches. How many feet of replacement fencing were needed to border this plot of land? 2. After the landslide took place, a nearby relative took his grandmother to safety in Illinois. It takes 1 hour and 40 minutes by car to travel from Whidbey Island to the Seattle airport. They spent 2 hours at the airport and then took a flight from Seattle to Chicago, Illinois. The flight took 3 hours and 35 minutes. What was their total travel time? 3. A local home was flooded and needed to have water damage repaired in their kitchen. The kitchen is a rectangle measuring 8 feet by 12 feet. The repair cost $4.00 per square foot. How much did it cost to repair this room?”

• Scope 17: Problem Solve Using the Four Operations, Home, Content Support, Coming Attractions connects 4.OA.3 (Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted…) to future learning. “In fifth grade, students use parentheses, brackets, or braces to write and evaluate multi-step numerical expressions. Fifth-grade students generate two numerical patterns using two given rules, graph the pairs of corresponding terms on a coordinate plane, and identify relationships between them. Starting in grade six, properties and relationships between operations extend to arithmetic that involves negative numbers. Knowledge gained about solving problems with base-ten numbers between kindergarten and grade five builds an essential foundation that is used to support algebraic thinking in later grades. Sixth-grade students make tables to compare equivalent ratios and plot corresponding values on the coordinate plane. In seventh grade, students recognize and represent proportional relationships between quantities. Seventh-grade students solve real-life and mathematical problems using numerical and algebraic expressions and equations. In eighth grade, students compute unit rates associated with ratios of fractions and recognize and represent proportional relationships between quantities. Eighth-grade students use proportional relationships to solve multi-step ratio and percent problems. 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.”

Examples of connections to prior grades include:

• Scope 3 Rounding, Home, Content Support, Background Knowledge, connects 4.NBT.3 (Use place value understanding to round multi-digit whole numbers to any place.) to previous work. “Kindergarten students gain a foundation for the base-ten system as they work with teen numbers. In first grade, students view 10 ones as a new unit called a ten, and they begin to engage in mental calculation to determine 10 more or 10 less than a given two-digit number. In second grade, students extend their understanding of base-ten numbers through the hundreds place. Second-grade students become proficient using the structure of the base-ten system by repeated bundling in groups of 10, with each unit being ten times as much as the unit to the right. Grade three students use place value to round numbers to the nearest 10 or 100. Third graders begin to see that rounding is valuable when estimating and for predicting and justifying the reasonableness of solutions while problem solving.”

• Scope 6: Compose and Decompose Fractions and Mixed Numbers, Home, Content Unwrapped, Implications for Instruction connects the work of 3.NF.1 (Understand a fraction \frac{1}{b} as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction \frac{a}{b} as the quantity formed by a parts of size \frac{1}{b}.) to 4.NF.3a (Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.) “In previous grade levels, students have had experiences representing fractions with denominators of two, three, four, six, and eight as well as counting unit fractions. The skill of iteration, or counting or repeating fraction parts, allows students to visualize how multiple parts compose a whole, which helps them see the relationship between the numerator and the denominator.”

• Scope 14: Division Models and Strategies, Engage, Accessing Prior Knowledge,Procedure and Facilitation Points connects the work of 3.OA.2 (Interpret whole-number quotients of whole numbers, e.g., interpret 56\div8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each…) to the work of 4.NBT.6 (Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.) “Procedure and Facilitation Points 1. Project the slideshow to the class, one slide at a time. 2. Invite students to read together. 3. Have pairs of students use manipulatives to model the scenario on their desk. 4. Challenge students to create a multiplication (first slide) or division (second slide) sentence to represent their model. 5. Facilitate a class discussion about how they modeled the division problems and what each part means. In the first problem, we got 36 blocks to represent the P.E. students. Then we counted out 6 and put them in a group. We kept counting out 6 for each group until there were no more blocks left. It turned out that we also had 6 groups. The 6 different groups are the teams, so there will be 6 teams, with 6 students (blocks) on each team. In the second problem, we got 28 blocks to represent Mrs. Ihedowa’s students. Since she wants 7 groups, we took 7 blocks and spread them out across our desks to represent the different groups. Then we just split the remaining blocks into those 7 groups. In the end, 4 blocks were in each group. That means 4 students would be in each of the 7 groups. 6. If students are struggling to complete this task, move on to do the Foundation Builder in order to fill this gap in prior knowledge before moving on to other parts of the scope.”