CCSS Activity 1 with Student Master

GRADE 3 CCSS Activity 1 with Student Master In Unit 1, Lesson 1: First Names, students collect data about how many letters are in their first names and use the data to make a bar graph. After the class has graphed the data, explain that another way to show data is in a picture graph, and that a picture graph uses pictures to show information. Together with the class, make a picture graph of the first names data. Begin by asking students what picture they should use for their graph: On our bar graph, we show how many students have different numbers of letters in their first names. What picture could we use to show or represent one student? (Sample answer: a smiley face) Draw a smiley face on the board. Next, we must decide on a key for the graph. A key shows how many students one picture represents. For our graph, let s say 1 smiley face represents 1 student. Write Key: A = 1 student on the board. Distribute CCSS Activity 1 Student Master, Showing Data on a Picture Graph. Draw the frame for the picture graph on the board. (See Figure 1 below.) Using the table on Discovery Assignment Book, page 5, complete a few rows of the graph together as a class. Then have students complete the rest of the graph independently or in pairs. Number of Letters in First Name 1 2 3 4 5 6 7 8 9 10 11 Number of Students Figure 1: Graphing the data on a picture graph Common Core State Standard 3.MD.3: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step how many more and how many less problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. MTB Grade 3 CCSS Teacher Notes 1

CCSS Activity 1 Student Master Name Date Showing Data on a Picture Graph Make a picture graph to show the First Names data. Number of Letters in First Name 1 First Names Data Number of Students 2 3 4 5 6 7 8 9 10 11 Key: A = 1 student 2 MTB Grade 3 CCSS Teacher Notes

CCSS Activity 2 with Student Master In Unit 1, Lesson 3: Kind of Bean, students make and interpret bar graphs about animals in the rainforest and different kinds of beans. Extend the lesson to provide practice in making picture graphs. After students have completed the lesson, distribute CCSS Activity 2 Student Master, Making a Picture Graph, which shows a data table from Unit Resource Guide, page 57 (shown below). Kind of Bean Number of Beans Pulled Pinto 14 Black 5 Navy 8 Lima 1 Have students make a picture graph for the data. Remind students that they first need to decide what picture to use to show the data. Then they will need to decide on the key: How many beans will each picture represent? Explain that if students decide that each picture will represent 2 beans, they will need to draw half a picture to represent 1 bean. For example, if represents 2 beans, the picture for Lima beans would show. Common Core State Standard 3.MD.3: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step how many more and how many less problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. MTB Grade 3 CCSS Teacher Notes 3

CCSS Activity 2 Student Master Name Date Making a Picture Graph Make a picture graph to show the data in the table. Kind of Bean Number of Beans Pulled Pinto 14 Black 5 Navy 8 Lima 1 Kinds of Beans Kind of Bean Number of Beans Pulled Pinto Black Navy Lima Key: = beans 4 MTB Grade 3 CCSS Teacher Notes

CCSS Activity 3 In Unit 3, Lesson 1: T-Shirt Factory Problems, students interpret a bar graph showing the number of letters in students first names. This activity builds on the data collecting students did in Unit 1, Lesson 1. After students have completed the activity, explain that making measurements is another way to generate data. Have students divide into pairs. Ask them to measure their partner s feet to the nearest ½ inch, from heel to toe, and write down the measurement. While students are measuring, draw the following base of a line plot on the board: 3 3 ½ 4 4 ½ 5 5 ½ 6 6 ½ 7 7 ½ 8 8 ½ 9 After students have finished measuring, explain that their measurement data can be shown on a line plot. Show students how to mark a measurement on the line plot: ask a volunteer to read his or her measurement, and put an X above the corresponding number. For example, for a measurement of 6 ½ inches, put the X directly above 6 ½. Invite pairs of students to plot their data on the board. Explain that if a measurement has more than one X, the Xs go directly above each other. See Figure 2 for a completed line plot of sample data. X X X X X X X X X X X X X X X X X 3 3 ½ 4 4 ½ 5 5 ½ 6 6 ½ 7 7 ½ 8 8 ½ 9 Figure 2: Sample line plot of foot measurements Finally, ask questions to help students interpret the line plot: How many children's feet are 6 inches? (Sample answer: 5) How many children's feet measured 8 inches? (Sample answer: 1) How many children's feet measured 4 ½ inches? (Sample answer: 0) Common Core State Standard 3.MD.4: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units whole numbers, halves, or quarters. MTB Grade 3 CCSS Teacher Notes 5

CCSS Activity 4 with Student Master In Unit 3, Lesson 2: In Twos, Threes, and More, students create lists of things that come in groups and use the lists to write their own multiplication problems. They also write number sentences to model the problems. After students have completed a few problems, show them how to write number sentences with an unknown number to help solve a problem. Using the List of Things That Come in Groups on page 34, write the following problem on the board: How many hours are there in 5 school days? Then write the number sentence 5 7 =? on the board. Tell students that the question mark stands for the missing information, or what they need to find out. Through a class discussion, help students connect the number sentence to the given and missing information in the problem. In this problem, for instance, students know that there are 5 school days, and that there are 7 hours in 1 school day. They want to find out how many hours there are in 5 school days. Work through more examples as a class, including problems in which one of the factors is missing. For example: We see 24 spider legs! How many spiders are there? For this problem, the number sentence is? 8 = 24. Ask students to solve the equation, and have them share their solution strategies. To provide more practice in determining the unknown number in a multiplication equation, have students complete CCSS Activity 4 Student Master, Finding the Missing Number. Questions 1 and 2 involve a multiplication problem. The equation with the unknown number is given. Question 3 asks students to write an equation with an unknown number to model the problem. Remind students to use a question mark for the missing information. Questions 4 and 5 give students more practice solving equations with unknown numbers. Common Core State Standard 3.OA.4: Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8? = 48, 5 =? 3, 6 6 =?. 6 MTB Grade 3 CCSS Teacher Notes

CCSS Activity 4 Student Master Name Date Finding the Missing Number Solve. 1. How many mittens are there on 9 children? Equation: 2 9 =? mittens 2. Each student in Ms. Gilleylen s third grade class donated a pair of old shoes for the clothing drive. All together, the students donated 30 shoes. How many students are in Ms. Gilleylen s class? Equation: 2? = 30 students 3. How many corners are there on 5 triangles? Equation: corners 4. A. 3? = 27 B.? 3 = 12 C. 6? = 24 5. A.? 10 = 30 B. 2? = 18 C. 7 3 =? MTB Grade 3 CCSS Teacher Notes 7

CCSS Activity 5 In Unit 3, Lesson 6: More T-Shirt Problems, students solve multistep word problems involving multiplication and division. As students solve the problems, continue to model the connection between the problems and multiplication and division number sentences. Encourage students to first write an equation with a question mark or other symbol to represent the missing information. Then have students solve the problem. For example, for Question 5, students could write the equation 4 5 =? to help them solve the problem. Common Core State Standard 3.OA.4: Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8? = 48, 5 =? 3, 6 6 =?. 8 MTB Grade 3 CCSS Teacher Notes

13 22 31 6 14 23 15 24 SG Grade 3 Unit 5 Lesson 1 31 1 2 3 4 5 32 7 8 9 10 11 12 16 25 17 26 18 27 19 28 20 29 32 21 30 Measuring Area CCSS Activity 6 In Unit 5, Lesson 1: Measuring Area, students measure area by counting square centimeters and solve problems involving area. Extend the lesson so that students understand that area is additive. In other words, help students see that the area of a figure made up of two adjacent shapes can be found by adding the area of each shape. For example, Student Guide, page 58 shows an octagonal shaped living room attached to a rectangular hall. After students have answered Question 3, ask the following questions: How could we find the area of the living room and the hall? (Find the area of the living room, and add it to the area of the hall) What is the area of the living room? (64 square tiles) What is the area of the hall? (20 square tiles) What is the area of the living room and hall combined? (84 square tiles) Measuring Area What is area? Area is a measurement of size. We measure the area of a floor to find the amount of carpet needed to cover the floor. We can also use area to measure the amount of paper needed to wrap a present. Area is the amount of surface that is needed to cover something. To measure the area of a shape, we tell the number of squares needed to cover the shape. Professor Peabody has started to cover his living room and hall with square tiles. The living room is in the shape of an octagon. The hall is a rectangle. 58 1. How many square tiles did Professor Peabody use to cover the hall? 2. Professor Peabody has covered half of his living room with tiles. These tiles have been counted for you. Why are the numbers 31 and 32 used twice? 3. How many square tiles will it take to cover the whole living room? Student Guide - page 58 (Answers on p. 29) 1 31 2 3 4 5 32 31 6 7 8 9 10 11 12 32 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Teaching the Activity Begin this activity by having students describe their understanding of area and how it can be measured. One way to reinforce students concept of area is to draw a nonrectangular shape made of a whole number of square centimeters on a transparency of Centimeter Grid Paper and then ask students to find the area by counting square centimeters. Another way to review area is to ask students how they could measure the area of the floor in the classroom. If you have a tile floor, they can measure its area by counting the number of tiles. In this case, the unit of measure would be the tiles, which are probably square. As your students work on this problem, they may discover that some tiles are not complete, but are tile pieces. Discuss how to count the tiles that are not whole. One convenient method is to find mates that add up to a whole when put together. It is possible, but not practical, to cover the floor with square-inch tiles so it can be measured in square inches. Discuss how the number of tiles you need changes if the size of the tile changes. Stress that even if the unit of measure changes, the area the amount of surface to be covered stays the same. Have students read the introduction to area on the Measuring Area Activity Pages. Direct their attention to the picture that shows Professor Peabody working on his floor and the diagram of his living room and hall. To answer Question 1, students can count the square tiles to find the area of the hallway. For Question 2, students should see that Professor Peabody counted halves of tiles by piecing them together to make whole squares; thus, two squares can each be numbered with the same number to show that two halves together are one whole. Figure 1 shows how to count area this way. living room Name Date Figure 1: Counting the area of a polygon hall Area of Five Shapes 24 URG Grade 3 Unit 5 Lesson 1 Unit Resource Guide - page 24 Find the area of each of the shapes on the grid below. A B As students are assigned Discovery Assignment Book, page 87, encourage them to check their answers by dividing Shapes A D into smaller rectangles (or triangles), find the areas of those rectangles or triangles, and then add the areas to check that the area of the whole shape matches their answer. C D Copyright Kendall/Hunt Publishing Company E Measuring Area DAB Grade 3 Unit 5 Lesson 1 87 Discovery Assignment Book - page 87 Common Core State Standard 3.MD.7d: Recognize area as additive. Find areas of rectilinear figures by decomposing them into nonoverlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. MTB Grade 3 CCSS Teacher Notes 9

CCSS Activity 7 In Unit 6, Lesson 8, students play the Digits Game to practice addition and place-value skills. Extend the lesson to provide practice in rounding whole numbers. Before students begin to play, briefly review the concept of rounding introduced in Lesson 5. Write a few numbers on the board and ask students to round the numbers to the nearest hundred. For example: 345 (300) 453 (500) 289 (300) 124 (100) Then ask students to round the same numbers to the nearest 10. 345 (350) 453 (450) 289 (290) 124 (120) For additional practice in rounding, have students round the sums of their numbers to the nearest 10 as they play the Digits Game. Common Core State Standard 3.NBT.1: Use place value understanding to round whole numbers to the nearest 10 or 100. 10 MTB Grade 3 CCSS Teacher Notes

CCSS Activity 8 with Student Master In Unit 8, Lesson 2: Sara s Desk, students make and use a scale map and measure lengths in centimeters. Extend the lesson to provide practice in measuring in inches and ½ inches. After students have completed the scale map of Sara s desk, explain that they will now measure objects in their own desks. Distribute CCSS Activity 8 Student Master, Plotting Measurement Data, and have students complete Part A. Part B asks students to make a line plot of their pencil lengths. On the board, draw a line plot to match the one shown in Part B. Invite students to come to the board, one at a time, to plot the pencil length data they found in Part A. Students should plot this same data on the student page. Common Core State Standard 3.MD.4: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units whole numbers, halves, or quarters. MTB Grade 3 CCSS Teacher Notes 11

CCSS Activity 8 Student Master Name Date Plotting Measurement Data Part A Find each object in your desk. Measure the length of each object to the nearest ½ inch. crayon 3 ½ in. scissors in. pencil in. eraser in. glue stick in. marker in. eraser in. colored pencil in. Part B With your class, make a line plot to show the measurement of each child's pencil. Use your line plot to answer the questions. 1 ½ in. 2 in. 2 ½ in. 3 in. 3 ½ in. 4 in. 4 ½ in. 5 in. 5 ½ in. 6 in. 6 ½ in. 7 in. 7 ½ in. 1. How many pencils measured 3 ½ inches? 2. How many pencils measured 5 inches? 3. How many pencils measured 2 inches? 12 MTB Grade 3 CCSS Teacher Notes

CCSS Activity 9 In Unit 9, Lesson 3: More Mass Problems, students study a data table in which spilled paint covers some of the numbers. They look for patterns in the table and estimate the missing numbers. Explain that solving these problems is a lot like solving equations with missing numbers. Extend the lesson to provide practice in solving equations with unknown numbers. Draw a simple table on the board that shows missing information. Figure 3 provides an example. Object Mass of Number of Object Objects Total Mass Pencil 2 grams 10 grams Ham sandwich 200 grams 2 Penny 4 8 grams Piece of chalk 5 grams 3 Marble 5 30 grams Figure 3: An example of a table showing missing numbers used to write and solve equations with unknown numbers Ask students to write equations for the following questions: How many pencils have a mass of 10 grams? (2? = 10) What is the mass of two ham sandwiches? (200 2 =?) What is the mass of one penny? (? 4 = 8 or 8 4 =?) What is the mass of two pieces of chalk? (5 3 =?) What is the mass of one marble? (? 5 = 30 or 30 5 =?) Then have students find the missing number in each equation. Ask students to explain how they found their answers. Common Core State Standard 3.OA.4: Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8? = 48, 5 =? 3, 6 6 =?. MTB Grade 3 CCSS Teacher Notes 13

CCSS Activity 10 with Student Master In Unit 10, Lesson 1, Stencilrama, students cut a stencil into an index card to make a pattern. To find out how many stencils it would take to make a border around a doorway, a bulletin board, or a window, they measure the lengths of these perimeters to the nearest ¼ inch. They also collect, organize, and graph data about the length of borders using a stencil and a small number of times. To provide more practice in measuring to the nearest ¼ inch, have students complete CCSS Activity 10 Student Master, Measuring to the Nearest ¼ Inch. Common Core State Standard 3.MD.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units whole numbers, halves, or quarters. 14 MTB Grade 3 CCSS Teacher Notes

CCSS Activity 10 Student Master Name Date Measuring to the Nearest 1 4 Inch Measure each insect to the nearest ¼ inch. 1. 2. inches 3. inches inches Measure the length of each object to the nearest ¼ inch. 4. Student desk: width inches length inches 5. Math book: width inches length inches 6. Pencil case: width inches length inches MTB Grade 3 CCSS Teacher Notes 15

CCSS Activity 11 with Student Master In Unit 10, Lesson 4, Word Problems for Review (Student Guide, p. 136), students use addition and subtraction to solve multistep word problems. To provide practice in rounding numbers, have students use rounding to estimate answers for the problems. For example, for Question 2, have students round each number to the nearest hundred and subtract the rounded numbers to make an estimate. (1,300 900 = 400) Then, after students solve each problem, have them check the answer against their estimate to make sure it makes sense. To provide more practice in rounding numbers to the nearest 10 or 100, have students complete CCSS Activity 11 Student Master, Rounding Whole Numbers. Common Core State Standard 3.NBT.1: Use place value understanding to round whole numbers to the nearest 10 or 100. 16 MTB Grade 3 CCSS Teacher Notes

CCSS Activity 11 Student Master Name Date Rounding Whole Numbers Round each number to the nearest 10 and 100. Number 1. 824 2. 638 3. 246 4. 777 5. 521 6. 892 7. 555 8. 219 9. 292 10. 343 11. 567 12. 345 Rounded to the Nearest 10 Rounded to the Nearest 100 MTB Grade 3 CCSS Teacher Notes 17

CCSS Activity 12 with Student Master Part A In Unit 11, Lesson 3, Multiplication in Rectangles, students represent multiplication using rectangular arrays. Extend the lesson to apply the concept of area. Remind students that area is the amount of surface inside a shape. Have students look at the rectangles they made for Question 1 on Student Guide, p. 146, and ask: How many tiles fit in these rectangles? (6) What is the area of all of the rectangles you made? (6 square units) Draw a 4 3 rectangle on the transparency of Centimeter Grid Paper. Model how to use multiplication to find the area of a rectangle. Point to each side of the rectangle as you ask the corresponding questions: How many tiles long is this side of the rectangle? (3) How many tiles long is this side of the rectangle? (4) What multiplication sentence could you write to model this rectangle? (3 4 = 12 or 4 3 = 12) What is the area of this rectangle? (12 square units) Count the squares inside the rectangle. How many are there? (12) 3 4 Figure 4: Multiplying the sides of a rectangle to find the area Students should see that the area of a rectangle can be found by multiplying the side lengths of the rectangle. Using the transparency, draw a few larger rectangles and label the side lengths. Suggestions: 6-by-8; 7-by-9; and so on. Have half of the students find the area by multiplying the side lengths. Have the other half find the area by counting the squares. Students will see that multiplying the side lengths results in the same area, and it is faster! For more practice, have students complete Part A of CCSS Activity 12 Student Master, Multiplication and Area. Common Core State Standard 3.MD.7: Relate area to the operations of multiplication and addition. Common Core State Standard 3.MD.7a: Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. Common Core State Standard 3.MD.7b: Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. 18 MTB Grade 3 CCSS Teacher Notes

CCSS Activity 12 Part B In Part B of Activity 12 Student Master, Questions 7 and 8 ask students to add the areas of two adjacent rectangles to find the total area of the shape. Adding the areas of two adjacent rectangles can also help students gain a better understanding of the distributive property. For example, the figure below shows a concrete model of breaking apart numbers when multiplying 7 9. In other words, 7 9 is the same as 7 5 + 7 4. Before students begin Part B, draw a 7 9 rectangle on a transparency of Centimeter Grid Paper. Discuss the connection between area and the distributive property. 7 5 7 4 7 cm 9 cm What multiplication sentence describes the area for the whole rectangle? (7 9 = 63 ) What multiplication sentence describes the area for the shaded part? (7 5 = 35 sq cm ) What multiplication sentence describes the area for the unshaded part? (7 4 = 28 sq cm ) What is 7 5 + 7 4? (63) Have students complete Part B. Questions 9 and 10 provide practice in using centimeter grid rectangles to model the distributive property. Common Core State Standard 3.MD.7c: Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a b and a c. Use area models to represent the distributive property in mathematical reasoning. Common Core State Standard 3.MD.7d: Recognize area as additive. Find areas of rectilinear figures by decomposing them into nonoverlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. MTB Grade 3 CCSS Teacher Notes 19

CCSS Activity 12 Student Master Name Date Multiplication and Area Part A Count the squares to find the area of each rectangle. Then write a multiplication sentence to model the area of the rectangle. 1. Area square cm Multiplication sentence 2. Area square cm Multiplication sentence 3. Area square cm Multiplication sentence 20 MTB Grade 3 CCSS Teacher Notes

CCSS Activity 12 Student Master (continued) Name Date Use multiplication to find the area of each rectangle. 4. 2 cm 8 cm Area square cm Multiplication sentence 5. 4 cm Area square cm Multiplication sentence 6. 1 cm 6 cm 7 cm Area square cm Multiplication sentence Part B Divide each shape into two rectangles. Find the area of each rectangle. Then add to find the area of the whole shape. 7. Area square cm + square cm = square cm MTB Grade 3 CCSS Teacher Notes 21

CCSS Activity 12 Student Master (continued) Name Date 8. Area square cm + square cm = square cm Use the grid to break apart one of the numbers in each multiplication problem. 9. Number sentence for the whole figure: 6 8 =? Add the sums of the shaded and unshaded parts: + = square cm Number sentence for the shaded part: = square cm Number sentence for the unshaded part: = square cm 10. Number sentence for the whole figure: 7 6 =? Number sentence for the shaded part: = square cm Number sentence for the unshaded part: = square cm Add the sums of the shaded and unshaded parts: + = square cm 22 MTB Grade 3 CCSS Teacher Notes

CCSS Activity 13 In Unit 11, Lesson 4: Completing the Table, students practice multiplication facts. After students have completed Part 2 of the lesson (URG p. 63), lead them in a discussion about the associative property of multiplication. Write the following number sentence on the board: 2 3 5 =? Ask students to solve the problem and share their strategies. Encourage students to see that the order in which the numbers are multiplied does not matter. For example, one student might multiply from left to right: I started with 2 3 and got 6. Then I multiplied 6 by 5 to get 30. Another student might start with an easy fact: I know that 2 5 is 10, so I did that first. Then I multiplied 10 by 3 to get 30. Explain that just as the order does not matter when three numbers are added, the order in which three numbers are multiplied does not affect the answer. This is called the associative property of multiplication. If time permits, write a few more number sentences on the board and divide students into three groups. Have one group solve the number sentences from left to right; one from right to left; and one start with an easy fact. Here are a few examples: 3 10 2 =? 4 2 5 =? 8 3 3 =? 1 6 0 =? Common Core State Standard 3.OA.5: Apply properties of operations as strategies to multiply and divide. Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication.) 3 5 2 can be found by 3 5 = 15, then 15 2 = 30, or by 5 2 = 10, then 3 10 = 30. (Associative property of multiplication.) Knowing that 8 5 = 40 and 8 2 = 16, one can find 8 7 as 8 (5 + 2) = (8 5) + (8 2) = 40 + 16 = 56. (Distributive property.) MTB Grade 3 CCSS Teacher Notes 23

CCSS Activity 14 with Student Master Part A In Unit 11, Lesson 5, Floor Tiler, students play a game in which they spin two numbers and use their product to color in grid squares in the shape of a rectangle. As students play the game, explain that their products tell them the area of each rectangle. For example, if a student spins a 2 and a 6, multiplies those numbers to get 12, and colors in two rows of 6 squares, that student is creating a rectangle with an area of 12 square units. Encourage students to see that multiplying the side lengths of a rectangle is another way to find the area of the rectangle. Next, remind students that the game is called Floor Tiler because figuring out how much tile is needed to cover a floor is a real-world example of finding the area. Ask students to give a few other examples of when they would need to find the area. (Sample answers: Ordering carpet; planning a playground space; buying paint for a wall) Then explain to students that in many real-world situations, they might need to also find the perimeter of a space. For example: putting a border around a window or a fence around a garden. To review how to find the perimeter, draw a rectangle on the board with given side lengths, such as 2 cm and 7 cm. Ask students how they would find the perimeter of the rectangle. Students should understand that the perimeter can be found by adding the lengths of all four sides of the rectangle. To provide practice finding the perimeter and using multiplication to find the area of rectangles, have students complete CCSS Activity 14 Student Master, Finding the Area and Perimeter. In Part A, students find the area and perimeter of rectangles. For Questions 1 3, students match rectangles on a centimeter grid with the corresponding multiplication sentence. Questions 4 and 5 show shapes that are divided into two rectangles. Students need to add the areas of the rectangles to find the area for the shape. In Part B, Questions 6 and 7 ask students to solve a real-world problem involving area and perimeter. After students finish Problems 6 and 7, discuss how even though Maya s garden has 8 square feet, students might have gotten different perimeters for the garden depending on the rectangles they drew. Common Core State Standard 3.MD.7: Relate area to the operations of multiplication and addition. Common Core State Standard 3.MD.7a: Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. Common Core State Standard 3.MD.7b: Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. Common Core State Standard 3.MD.7d: Recognize area as additive. Find areas of rectilinear figures by decomposing them into nonoverlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. Common Core State Standard 3.MD.8: Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. 24 MTB Grade 3 CCSS Teacher Notes

CCSS Activity 14 Part B To provide practice in modeling the distributive property by showing areas of rectangles, have students play an alternate version of Floor Tiler. The game begins the same way as the original version: A player spins two numbers and multiplies the numbers. In this version, however, the next step is different. After finding the product, the player draws an outline of a rectangle that has the same number of grid squares on the grid paper. For example, if a player spins 7 and 8, the player draws an outline of a rectangle that has an area of 56 squares. Then the player breaks apart the rectangle into two smaller rectangles and uses different colors to shade the two rectangles. Figure 5 shows a picture of an example: 7 8 = 56 7 5 + 7 3 =? 35 + 21 = 56 7 5 7 3 Figure 5: Two rectangles for the product 56 Once the player has colored the rectangles, that player writes a number sentence for each of the smaller rectangles. The other player writes a number sentence for the outlined rectangle, and the partners compare answers to see that, for example, 7 8 = 7 5 + 7 3. Common Core State Standard 3.MD.7: Relate area to the operations of multiplication and addition. Common Core State Standard 3.MD.7a: Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. Common Core State Standard 3.MD.7b: Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. Common Core State Standard 3.MD.7d: Recognize area as additive. Find areas of rectilinear figures by decomposing them into nonoverlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. MTB Grade 3 CCSS Teacher Notes 25

CCSS Activity 14 Student Master Name Date Finding the Area and Perimeter Part A Count the squares to find the area of each rectangle. Then draw a line to the multiplication sentence that models the area of the rectangle. Write the perimeter for each rectangle. 1. 2 7 = 14 Area Perimeter square cm cm 2. 5 6 = 30 Area Perimeter square cm cm 3. 3 6 = 18 Area Perimeter square cm cm 26 MTB Grade 3 CCSS Teacher Notes

CCSS Activity 14 Student Master (continued) Name Date Complete the multiplication sentences for the area of each figure. Then find the area and perimeter. 4. Multiplication sentence: 5 4 = Area square cm + square cm = square cm Perimeter cm 5. Area square cm + square cm = square cm Perimeter cm Part B Solve. 6. a. Mr. Barnhart is ordering carpet for his son s bedroom. The room is 8 feet by 10 feet. How much carpet does Mr. Barnhart need to buy? Area of the room Mr. Barnhart needs to buy square feet square feet of carpet. b. Mr. Barnhart also wants to put some trim around the base of his son s room. How much trim should he buy? Explain your answer. feet MTB Grade 3 CCSS Teacher Notes 27

CCSS Activity 14 Student Master (continued) Name Date 7. Maya is planning a garden. She is allowed to use 8 square feet of her yard. a. Could she use the area shown below? Why or why not? 4 ft 2 ft b. Draw a picture of what her garden could look like on the centimeter grid below: c. Maya wants to put a fence around her garden so her dog does not dig in it. Using your picture in Part b, how many feet of fencing should she buy? Explain your answer. 28 MTB Grade 3 CCSS Teacher Notes

CCSS Activity 15 with Student Master In Unit 11, Lesson 7: Cipher Force!, students explore what happens when you add, subtract, multiply and divide by 0. The lesson also provides an opportunity to help students understand division as an unknown-factor problem. After students show how Conrad could use subtraction to solve a division problem (URG p. 89), explain that students can also think of a division problem as an unknown-factor problem. For example, to solve 15 3 =?, students could think: What number times 3 equals 15? To provide more practice in solving division problems by thinking of an unknown factor, have students complete CCSS Activity 15 Student Master, Multiplication/Division Fact Families. If necessary, do the first two problems as a class. For Question 1 (24 3 = ), remind students to think of fact families. Ask: What number times 3 equals 24? (8) For Question 2 (8 8 = ), ask: What number times 8 equals 8? (1) Common Core State Standard 3.OA.6: Understand division as an unknown-factor problem. For example, find 32 8 by finding the number that makes 32 when multiplied by 8. MTB Grade 3 CCSS Teacher Notes 29

CCSS Activity 15 Student Master Name Date Multiplication/Division Fact Families Use the related multiplication fact to solve each division problem. 1. 24 3 = Think: 3 = 24 2. 8 8 = Think: 8 = 8 3. 6 3 = Think: 3 = 6 4. 10 5 = Think: 5 = 10 5. 12 2 = Think: 2 = 12 6. 27 3 = Think: 3 = 27 7. 15 3 = Think: 3 = 15 8. 16 4 = Think: 4 = 16 9. 25 5 = Think: 5 = 25 10. 48 8 = Think: 8 = 48 11. 20 4 = Think: 4 = 20 12. 32 4 = Think: 4 = 32 30 MTB Grade 3 CCSS Teacher Notes

CCSS Activity 16 with Student Master In Unit 12, Lesson 6, Focus on Word Problems (Student Guide, p. 176), students use addition and subtraction to solve word problems. Question 5 asks students to choose a jar of pennies based on place-value clues. Extend the problem to review rounding. Ask students the following question: If Beverly put all of the pennies in 1 jar, would you say the jar has about 700 pennies or 800 pennies? (700 pennies) To provide more practice in rounding numbers to 10 and 100, have students complete CCSS Activity 16 Student Master, Rounding Whole Numbers Part 2. Common Core State Standard 3.NBT.1: Use place value understanding to round whole numbers to the nearest 10 or 100. MTB Grade 3 CCSS Teacher Notes 31

CCSS Activity 16 Student Master Name Date Rounding Whole Numbers Part 2 Round to the nearest 100 or 10 to describe how many pennies are in each jar. Circle the rounded number. 1. 5. There are about 300 or 400 pencils in the jar. 2. There are about 290 or 300 paper clips in the jar. 6. There are about 400 or 500 buttons in the jar. 3. There are about 830 or 840 pennies in the jar. 7. There are about 900 or 1,000 beads in the jar. 4. There are about 1,200 or 1,100 stickers in the jar. There are about 620 or 630 candies in the jar. 32 MTB Grade 3 CCSS Teacher Notes

CCSS Activity 17 with Student Master In Unit 13, Lesson 2, What s 1?, students represent fractions using pattern blocks. The following activity introduces another model for students to use to represent fractions the number line. Before the activity, prepare a long strip of paper (or cardstock) that will model the unit whole. After students have completed Student Guide, p. 184, draw a number line on the board showing labels for 0 and 1, and explain that 1 is the unit whole. The distance from 0 to 1 should be the same length as the paper strip. See Figure 6 below. 0 Figure 6: A number line from 0 to 1 with a paper strip modeling the unit whole 1 (unit whole) Use the paper strip to model the unit whole. Start a discussion about representing fractions on a number line. Begin by asking: If we cut this unit whole in half, how many pieces do we have? (2) Cut the strip in half, and tape the pieces onto the number line. Explain that students can count by ½s to label the number line. 0 ½ one half Figure 7: Two halves with ½ and 2 labeled on the number line 1 (unit whole) 2 2 two halves MTB Grade 3 CCSS Teacher Notes 33

CCSS Activity 17 (continued) If we cut the two halves in half, how many pieces do we have? (4) Cut the two halves in half, and tape the pieces onto the number line. Together with the class, count by ¼s as you label the number line ¼, 24, ¾, and 44. Draw tick marks for ¼ and ¾ as students count those fractions. 0 ¼ one fourth ½ 24 two fourths" ¾ three fourths" 1 (unit whole) 22 44 four fourths Now that the fourths are represented on the number line, encourage students to use the number line to find equivalent fractions. Ask: What fraction is equivalent to ½? ( 24 ) What fractions are equivalent to 1? ( 22, 44 ) What are some other fractions that are equivalent to 1? ( 33, 666, 99999 99999 ) To provide more practice in representing fractions on a number line, have students complete CCSS Activity 17 Student Master, Fractions on a Number Line. Common Core State Standard 3.NF.2: Understand a fraction as a number on the number line; represent fractions on a number line diagram. Common Core State Standard 3.NF.2a: Represent a fraction b 1 on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size b 1 and that the endpoint of the part based at 0 locates the number b 1 on the number line. Common Core State Standard 3.NF.2b: Represent a fraction b a on a number line diagram by marking off a lengths b 1 from 0. Recognize that the resulting interval has size b a and that its endpoint locates the number b a on the number line. Common Core State Standard 3.NF.3a: Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. Common Core State Standard 3.NF.3b: Recognize and generate simple equivalent fractions, (e.g., 1 2 = 2 4, 4 6 = 2 3 ). Explain why the fractions are equivalent, e.g., by using a visual fraction model. Common Core State Standard 3.NF.3c: Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3 1 ; recognize that 6 1 = 6; locate 4 4 and 1 at the same point of a number line diagram. 34 MTB Grade 3 CCSS Teacher Notes

CCSS Activity 17 Student Master Name Date Fractions on a Number Line Count by ⅓s, ¼s, or ⅕s. Fill in the missing fractions. 1. ⅓ ⅓ ⅓ 0 2. ⅕ ⅕ ⅕ ⅕ ⅕ 1, or (unit whole) 0 1, or 3. ¼ ¼ ¼ ¼ 0 1, or MTB Grade 3 CCSS Teacher Notes 35

CCSS Activity 18 with Student Master In Unit 13, Lesson 4, Fraction Games, students compare and order fractions using one-half as a benchmark. Extend the lesson to help students relate fractions to measurements on a ruler. Have students complete CCSS Activity 18 Student Master, Fractions on a Ruler. For Questions 1-3, students measure the length of an object to the nearest ¼ inch and then fill in the missing fractions on a ruler. Question 4 asks students to explain similarities and differences between a ruler and a number line. After students have filled in the missing fractions, ask them to locate the following fractions on the number line to review recognizing equivalent fractions and fractions that are equivalent to whole numbers. 24 ( ½ ) 44 (1) 2 44 (3) 1 44 (2) Common Core State Standard 3.NF.2: Understand a fraction as a number on the number line; represent fractions on a number line diagram. Common Core State Standard 3.NF.2a: Represent a fraction b 1 on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size b 1 and that the endpoint of the part based at 0 locates the number b 1 on the number line. Common Core State Standard 3.NF.2b: Represent a fraction b a on a number line diagram by marking off a lengths b 1 from 0. Recognize that the resulting interval has size b a and that its endpoint locates the number b a on the number line. Common Core State Standard 3.NF.3: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Common Core State Standard 3.NF.3a: Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. Common Core State Standard 3.NF.3c: Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3 1 ; recognize that 6 1 = 6; locate 4 4 and 1 at the same point of a number line diagram. Common Core State Standard 3.MD.4: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units whole numbers, halves, or quarters. 36 MTB Grade 3 CCSS Teacher Notes

CCSS Activity 18 Student Master Name Fractions on a Ruler Date Measure each object to the nearest ¼ inch. Then skip-count by ¼s to fill in the missing fractions on the number line. 1. 2. Length inches ¼ 1 1 ¼ 1¾ Length inches ¼ ½ 1 1½ 2 3. Length inches 1 ¼ 1¾ 2 ¼ 2 ¾ 3 ¼ MTB Grade 3 CCSS Teacher Notes 37

CCSS Activity 18 Student Master (continued) Name Date 4. Length inches 2 ¼ 3 3 ¼ 3 ¾ 5. How are a ruler and a number line the same? How are they different? 38 MTB Grade 3 CCSS Teacher Notes

CCSS Activity 19 with Student Master In Unit 14, Lesson 4: Make Your Own Survey, students gather survey data about other classmates. They collect, organize, and graph the data using bar graphs. Extend the lesson to provide practice in making picture graphs. After students have completed the lesson, distribute CCSS Activity 19 Student Master, Showing Data on a Picture Graph, which shows sample hair color data from Student Guide, page 206 (shown below). Hair Color Number of Students Dark brown 9 Light brown 3 Blonde 5 Black 2 Golden 5 Have students make a picture graph for the data. Remind students that they first need to decide what picture to use to show the data. Then they will need to decide on the key: How many students will each picture represent? Common Core State Standard 3.MD.3: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step how many more and how many less problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. MTB Grade 3 CCSS Teacher Notes 39

CCSS Activity 19 Student Master Name Date Showing Data on a Picture Graph Make a picture graph to show the data in the table. Hair Color Number of Students Dark brown 9 Light brown 3 Blonde 5 Black 2 Golden 5 Hair Color HAIR COLOR Number of Students Dark brown Light brown Blonde Black Golden Key: = students 40 MTB Grade 3 CCSS Teacher Notes

CCSS Activity 20 In Unit 15, Lesson 1, Decimal Fractions, students connect decimals to common fractions. They complete the Tenths Helper chart by writing tenths fractions and their equivalent decimals. This lesson also provides an opportunity for students to recognize whole numbers as fractions. After students have completed the chart, explain that fractions can also be used to show division. For example, the fraction 1 10 can be read as one tenth or one divided by ten. Have students use their Tenths Helper charts and calculators to see the connection between fractions and division. For example, for the fraction 1 10, have students key in [1] [ ] [10] [=] on their calculators. The display shows the matching decimal, 0.1. Have students do this for a few of the fractions on the chart, such as 2 10, 5 10, and 9 10. Ask the following questions: What patterns did you find? ( 2 10 = 0.2; 5 10 = 0.5; 9 10 = 0.9; When you divide a number by 10, you get a decimal with that number in the tenths place.) What happens when you key in 10 10 as a division problem? (You get 1.) What is 10 divided by 10? (1) Next, write the following fractions on the board: 3 1 5 1 What do these fractions have in common? (They all have 1 on the bottom; they have 1 for a denominator) Have students key in these fractions as division problems on their calculators. What happens when you divide by 1? (When you divide a number by 1, the answer is that number.) What is 12 divided by 1? (12) Since fractions can also be used to show division, what whole number would be the same as the fraction 12 1? (12) 8 1 10 1 Give students more practice by having them express whole numbers as fractions. Examples: 6 = 6 1 ; 15 = 15 1 ; 230 = 230 1 ; 1,000 = 1000 1 Common Core State Standard 3.NF.3c: Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3 1 ; recognize that 6 1 = 6; locate 4 4 and 1 at the same point of a number line diagram. MTB Grade 3 CCSS Teacher Notes 41

CCSS Activity 21 In Unit 15, Lesson 3, Decimal Hex, students play a game in which they compare two decimal fractions or a decimal and a common fraction. To provide practice in expressing whole numbers as fractions, write the following fractions on the board so that they look like extra spaces on the Decimal Hex game board: 4 3 21 6 Explain that these fractions all represent whole numbers that are on the game board. Ask volunteers to identify the whole number represented by each fraction. Remind students that they can think of the fractions as division problems. 4 = 4 4 = 1 3 = 3 3 = 1 21 = 2 1 = 2 6 = 6 6 = 1 Have students play a modified version of the game that will give them practice expressing a fraction as a whole number. Have students look at the Decimal Hex game board. If one of their cubes lands on the 1 space in the middle of the board, they must call out a fraction equivalent to 1; for example: 5 5. If one of their cubes lands on the 2 space, they must call out a fraction equivalent to 2; for example, 2 1. Once they call out the equivalent fraction, they get an extra spin. Common Core State Standard 3.NF.3c: Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3 1 ; recognize that 6 1 = 6; locate 4 4 and 1 at the same point of a number line diagram. 42 MTB Grade 3 CCSS Teacher Notes

CCSS Activity 22 In Unit 16, Lesson 4, Elixir of Youth, students read a story about two detectives who use multiplication to solve problems involving volume. For example, the two detectives know that a vase holds 50 buckets, and each bucket holds 5 gallons. So to find out how much liquid the vase can hold, they multiply 50 5 gallons, or 250 gallons. After students read through this part of the story on Adventure Book page 103 (Unit Resource Guide page 72), quickly review multiplying by multiples of 10. Write 50 5 on the board, and ask students to describe how the detectives solved the problem. Some might remember the pattern for multiplying a number by ten: multiply the related fact and then write a zero at the end of the number. Ask a volunteer to show how to solve the problem using base-ten pieces. If necessary, help the student illustrate the following reasoning: 5 50 = 5 5 tens = 25 tens So, 5 50 = 250 Then, as students continue reading the story, encourage them to point out other problems that involve multiplying by multiples of 10. (For example, the questions for Adventure Book page 110 on Unit Resource Guide page 74 involve multiplying 2, 5, and 12 by 20.) 3.NBT.3: Multiply one-digit whole numbers by multiples of 10 in the range 10 90 (e.g., 9 80, 5 60) using strategies based on place value and properties of operations. MTB Grade 3 CCSS Teacher Notes 43

CCSS Activity 23 In Unit 17, Lesson 1, Geoboard Fractions, students represent fractions on geoboards by dividing a rectangle into equal-area parts. They also measure the area of these parts, and understand that the fractional parts of a whole must have equal areas but can have different shapes. As students work on Student Guide, p. 252, encourage them to connect multiplication and addition to the concept of area. Using a transparency of Centimeter Grid Paper, lead a discussion of how multiplication and addition relate to area. After students have made the rectangle shown at the top of the page, ask them the following questions: What is the area of this rectangle? (8 squares) What multiplication sentence describes the area of this rectangle? (4 2 = 8) What addition sentence could describe the area of this rectangle? (2 + 2 + 2 + 2 = 8; 4 + 4 = 8) As students discuss the questions above, model the addition and multiplication. 2 2 2 2 2 4 2 + 2 + 2 + 2 = 8 4 2 = 8 Encourage students to see that the area of a rectangle can be found by multiplying the side lengths of the rectangle. Using the transparency, draw a few larger rectangles on the overhead and label the side lengths. Suggestions: 6-by-8; 7-by-9; and so on. Have half of the students find the area by multiplying the side lengths. Have the other half find the area by counting the squares. Students will see that multiplying the side lengths results in the same area, and it is faster! Student Guide - page 252 Common Core State Standard 3.MD.7: Relate area to the operations of multiplication and addition. Common Core State Standard 3.MD.7a: Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. Common Core State Standard 3.MD.7b: Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. 44 MTB Grade 3 CCSS Teacher Notes