SAMPLE PAGES STUDENT JOURNAL SENIOR AUTHORS PROGRAM CONSULTANTS PROGRAM EDITORS. contributing authors. James Burnett Calvin Irons

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1 SAMPLE PAGES SENIOR AUTHORS James Burnett Calvin Irons PROGRAM CONSULTANTS Diana Lambdin Frank Lester, Jr. Kit Norris contributing authors Debi DePaul Peter Stowasser Allan Turton PROGRAM EDITORS James Burnett Beth Lewis Donna Richards STUDENT JOURNAL

2 7.1 Using the Partial-Products Strategy to Multiply (Two-Digit Numbers) Emma is painting the concrete floor of a playground. She needs to know the area of the playground to figure out how much paint to buy. The dimensions are shown to the right. Estimate the area of the playground. Would it be more or less than 100 sq yards? How could you figure out the exact area? Mary drew this grid to help. She split 2 into tens and ones then multipled 20 and. How could you use this strategy to figure out 3 2? Step Up 20 Area is Length is 2 yards Width is yards sq yards You can split a rectangle into parts to find the partial products. 1. Write the dimensions around the grid. Color the tens part blue and the ones part yellow. Write the product for each part then add the products to figure out the area of the grid. SAMPLE 17 Area 10 7 sq units 2 Area sq units 152 ORIGO Stepping Stones 7.1

3 2. Color the tens part red and the ones part blue. Then write each product. Add the two partial products and write the total. 3 7 c. 3 d. Step Ahead LEToE 3 3 PLETo SAMP 70SAMPLE MP SAM Write the dimensions of a rectangle that will give a product close to but not exactly 30. Then write the multiplication sentences to match. ORIGO Stepping Stones

4 7.2 Using the Partial-Products Strategy to Multiply (Three-Digit Numbers) Compare these dimensions of two paper strips. Which strip has the greater area? How do you know? How could you figure out the exact area of each strip? Look at this diagram LE How has the rectangle been split? What does each of the red numbers represent? resent? How could you use the diagram to figure out the total area of Strip A? How could you figure out the exact area of Strip B? Step Up STRIP A Width in Length 17 in STRIP B Width 7 in Length in You can split a rectangle into parts to find the partial products. I would add the areas of the smaller rectangles. That's The total area is 70 sq inches. SAMPLE E 1. Figure out ousou each partial product. Then add to figure out the total ORIGO Stepping Stones 7.2

5 2. Write the dimensions around the rectangle. Figure out each partial product. Then add to figure out the total. c. Step Ahead E= LE= tsam AMP MPLE Split the rectangle to show Then write number sentences to figure out the total are Area ORIGO Stepping Stones

6 7.3 Reinforcing the Partial-Products Strategy for Multiplication (Three-Digit Numbers) These marbles are numbered from 0 to 9. Imagine you pick four marbles without looking Write four possible numbers in these boxes. Look at the expression you wrote. How could you figure out the product? Draw lines to split the blue rectangle to show the hundreds, tens, and ones. Label the dimensions of each part. Then write each partial product to figure out the total. What are some other multiplication sentences nces that you could figure out strategy?mple using this strategy? Working Space Step Up undrs 1. Choose four different numbers from the marbles above. Use these numbers to write an expression. Then split the rectangle into hundreds, tens, and ones to help you figure out the product. undrsampsamp MPLE E 15 ORIGO Stepping Stones 7.3

7 2. Choose more numbers from the marbles on page 15. Complete these to figure out the products. 3. Complete each number sentence. Then write the total of the partial products = = 3 = 300 = 70 = = 37 c = 5 3 = SAMPLE AM Step Ahead Write these digits in the spaces below to create an expression that will give the greatest possible product. Use each digit once only. Then write the product ORIGO Stepping Stones

8 7. Using the Partial-Products Strategy to Multiply (Four-Digit Numbers) Jamal is planning a summer vacation. He buys three package deals to the Grand Canyon. Estimate the total amount that he will pay. Do you think it will be more or less than $5,000? GRAND CANYON VACATION PACKAGES $1,9 How could you figure out the exact cost? Lora drew this diagram to help her thinking. 3 1, ,000 = 3,000 How did she split the rectangle? PL = Complete the number sentences to show each partial product. Then add the partial 3 0 = products to find the total. 3 9 = Compare the parts of the rectangle in the diagram to each partial product. Color the part of the rectangle that shows Step Up SAMPLE 1. Figure out each partial product. Then write the total of the four products. 2,5 2,000 = 100 = 20 = 2, = 15 ORIGO Stepping Stones 7.

9 2. Label the dimensions for each part and write number sentences to figure out each partial product. Then add the partial products to figure out the total. 3 2,17 c. 1, ,20 E= = SAM AMPL MPLE Step Ahead Color the part of the rectangle yellow that shows 20. Color the part of the rectangle blue that shows 500. Color the part of the rectangle red that shows 3,000. 3, ORIGO Stepping Stones

10 7.5 Reinforcing the Partial-Products Strategy for Multiplication (Four-Digit Numbers) What multiplication expression could you write to match this diagram? 3 2, Write the expression in the boxes below. How could you figure out the product? What number sentences would you write? Step Up Record your thinking in the working space. 1. Write the multiplication expressions to match. Then use the working space to figure out each product. SAMPL MPLE Working Space 1, , Working Space 10 ORIGO Stepping Stones 7.5

11 2. Write the expressions to match. Then use the working space to figure out each product. 7 1, , Working Space 3. Figure out each product. thinking.ple Show your thinking. 2,25 = Step Ahead SAMPLEWo 2,503 = SAMPLE Aran figured out 3 3,05. He added these partial products. Describe his mistake in words. 9,000 1, , 1 5 ORIGO Stepping Stones

12 7. Using the Partial-Products Strategy to Multiply (Two Two-Digit Numbers) New turf is being laid in a playground. This diagram shows the dimensions of the playground. Estimate the amount of turf needed. 3 yd How could you figure out the exact amount of turf to order? Jose drew this diagram. What does his diagram show? How did he split the rectangle? What does each red number represent? ent? What is the unknown value? How do you know? How could you figure out the total area of the playground? Step Up I know 0 x 3 is 0. 0 x 30 is ten times more, so about 1,200 sq yards of turf will be needed. 1. Figure out each partial product. Then write the total of the four products. 0 SAMPLE M 3 27 yd 00 20? = = 20 = 20 = ORIGO Stepping Stones 7.

13 2. Write a multiplication sentence to show each part. Then write the total of the four partial products = LE LE MPL 30 5 Step Ahead 2 2 Write the dimensions around the rectangle. Write a multiplication sentence to show each part. Then add the partial products to figure out the total. LEE PLE SAMPLE ORIGO Stepping Stones 7. 13

14 7.7 Reinforcing the Partial-Products Strategy for Multiplication (Two Two-Digit Numbers) Mia split this rectangle into partial products to help figure out the total. What multiplication sentence is she trying to figure out? 30 Color the part blue that shows 30. Color the part yellow that shows 2 0. Color the part red that shows How could you figure out the total? Write each partial product in the working space. Then add the partial products to find the total. Step Up What does the last part show? 0 1. Write the dimensions around the rectangle. Write a multiplication sentence for each part. Then add the four partial products to find the total. 2 Working Space SAMPLE E ORIGO Stepping Stones 7.7

15 2. Write the dimensions around the rectangle. Figure out the product for each part. Then add the four partial products to find the total Figure out each product. Show your thinking = 3 27 = 1 29 = PLE PLc. Step Ahead 2 1 = ens ensa SAMPLEM Write a number sentence for the missing partial product. Then write the total. c = 1 3 = = = 1, = = = 0 10 = 0 = = 30 = ORIGO Stepping Stones

16 7. Solving Multi-Step Word Problems Involving Multiplication The Bay City Tigers need to buy 25 pairs of shorts. How could you figure out the total cost of the shorts? Alex wrote the partial products to figure out the total. What is the total cost of the shorts? How do you know? The Mountain Warriors need to buy team shirts and pairs of shorts. What will be the total cost? Step Up = = = = 0 I will call the total cost of the shirts and shorts T. T = (5 + 3) x SAMPLE 1. Use the uniform prices above. The Cincinnati Chargers need to buy 1 complete uniforms. What is the total cost? $72 $5 $3 $ $5 Working Space $ 1 ORIGO Stepping Stones 7.

17 2. Solve these word problems. Show your thinking. Sweaters cost $39 each. This is $15 more than the price of a cap. Over the season, 725 caps were sold. What was the total sales from caps? A stadium parking lot has 3 rows. There are 2 spaces in each row. 200 spaces are reserved for staff. How many spaces are there for supporters? c. Sports bags cost $29 each. If this price was reduced by $3, how much would be saved when buying 2 bags? Step Ahead quatis $ $ Write a word problem to match this equation. Then figure out the product. d. A team of 1 players bought boots for $3 and socks for $9. What was the total cost for the team? SAMPL MPLE 2 13 = $ spaces ORIGO Stepping Stones 7. 17

18 7.9 Subtracting Common Fractions (Number Line Model) Logan went to the movies and bought a small box of popcorn. At the start of the movie, the box was 7 full. At the end of the movie, there was 2 of the box left over. POPCORN How much popcorn did Logan eat during the movie? What equation could you write? When you subtract fractions what happens to the numerator? What happens to the denominator? How could you show the difference on this number line? Layla and her friend bought a box of popcorn to share. They each ate 3 of the popcorn in the box. How much popcorn was left over? How could you figure out the amount? Step Up 11 7 = 13 = 9 1. Draw and label jumps to match each equation. 0 0 = 0 1 SAM 0SAMPLE P 1 c. 1 = ORIGO Stepping Stones 7.9

19 2. Use this number line to help you write the differences = = 20 c = d. 3. Use what you know about subtracting fractions to calculate the difference between each pair of numbers.. Write the missing fraction in each equation Difference Step Ahead 10 = 23 9 e. 15 Difference 11 = 1 omples f = c. 5 Difference 3 = 2 Complete each equation so that the difference is between 2 and 3. Use the number lines on pages 1 and 19 to help you. 23 DifferencPL MPL23 c. d. 1 = 1 1 Difference SAMP MPLE PL = = 25 = c. 20 = d. 22 = Working Space ORIGO Stepping Stones

20 7.10 Calculating the Difference Between Mixed Numbers One bunch of bananas weighs 5 3 pounds. Another bunch weighs 3 2 pounds. How could you figure out the difference in mass between the two bunches? I would start with 5 3 When I add mixed numbers, I add the then take away 3 2 whole numbers and fractions separately in smaller jumps. One jump would be 3 and the next jump would be 2. then combine their totals. I think this will work for subtraction too. M How was addition used to calculate the difference on this number line? MP How could subtraction be used to find the difference? Step Up hinkis SAMPL MPLE 1. Calculate the difference. Draw jumps on the number line to show your thinking = = ORIGO Stepping Stones 7.10

21 2. Calculate the difference. Draw jumps on the number line to show your thinking = = 3. Calculate the difference. Show your thinking. c. 7 2 = = d. e = f. 2 = LE = SAMPLE 9AM 2E 10 = Step Ahead Write the missing numbers on this trail ORIGO Stepping Stones

22 7.11 Calculating the Difference Between Mixed Numbers (Decomposing Whole Numbers) Amos has two pet lizards. One is 3 7 inches long and the other is 1 How could you figure out the difference in their lengths? inches long. Maka figured it out like this. What did she do to make the subtraction easier? is the same as How could you use addition to help you calculate the difference? Look at the number lines below. What is the same about the two methods shown? What is different? = 1 7 = LE The difference is 1 5 inches LE SAM 1SA AMPLE 3 Step Up 1. Calculate the difference. Draw jumps on the number line to show your thinking = ORIGO Stepping Stones 7.11

23 2. Calculate the difference. Draw jumps on the number line to show your thinking = = Calculate the difference. Show your thinking. d = Step Ahead = Look at these related equations. Each sentence describes the same two parts ( and 2) that make a total (). Write the related equations for this. = PLEc. e. f M9 = LEc. LE3 LE LE10 10 = SAMPLE 1AM MMP AM AM 11 AM = = 2 + = 2 = = = 3 ORIGO Stepping Stones

24 7. Solving Word Problems Involving Mixed Numbers and Common Fractions Chang used a watering can and poured 3 3 quarts of water onto his seedlings which were in a garden bed that was 5 3 feet long. Afterward, the watering can had 3 quarts of water left in it. How much water was in the watering can at the start? How could you figure it out? Which information is important? Step Up Two identical cakes were baked for a big party. Each cake was cut into twelfths. Halfway through the party, 3 of one cake had been eaten. The other cake had pieces missing and 5 people were standing near it. How much cake was left over in total? Which operations will you use to figure it out? 1. Figure out the answer to each problem. Show your thinking. Bixy and Boxy are cats. Bixy weighs A bucket held gallons of water. 10 kilograms. The total weight of 1 1 the two cats is gallons was used on the lettuce then 1 10 kilograms. 2 gallon on the carrots. How M How much does Boxy weigh? much water was left in the bucket? kg c. The builder cut 2 7 inches off a length of lumber. The piece left was 5 3 inches long. How long was the piece of lumber at the start? SAMP AMPL A MPLE d. Luis visited his dad. It took 2 1 hr to get there when it usually takes 1 3 hr. How much later than usual did he arrive? gal in hr 17 ORIGO Stepping Stones 7.

25 2. Solve these problems. Show your thinking. Alisa cut 5 oranges into sixths for a picnic. Afterward, there was only of an orange left. How many oranges and part oranges were eaten? A baker used 3 7 sticks of licorice and had 1 5 sticks left so she ate of a stick. How many sticks did the baker have at the start? oranges sticks c. Mom had 7 2 yards of fabric rolled up. She cut L off 3 quilt she was making. Some squares on that quilt were yards for a e 1 each side. She also cut 2 yard long on yards off the roll to make a second quilt. How much fabric was left on the roll? yd Write a subtraction word story that involves mixed numbers and fraam common fractions. Step Ahead SAM AMPLE ORIGO Stepping Stones