TEXAS PAGES SENIOR AUTHORS James Burnett Calvin Irons PROGRAM CONSULTANTS Diana Lambdin Frank Lester, Jr. Kit Norris contributing authors Beth Lewis Peter Stowasser Allan Turton STUDENT JOURNAL
9.1 Step In Identifying Nearby Multiples of Ten Where is 72 located on this number line? How do you know? Step Up 0 100 Which ten is closest? How do you know? Which ten is closest? How far away is 47 from the closest ten? Where is 47 on the number line? Imagine you placed a ball on this special number line. 40 50 60 How could the ball help you decide which ten is closest to 54? 1. For each number, write the ten that is closest. 30 40 50 32 36 c. 43 d. 47 e. 49 200
9.1 2. Write the ten that is closest. You can draw lines to help. 10 20 30 13 14 c. 21 d. 29 e. 31 3. Write how far away each number is from the nearest ten. You can draw lines to help you. f. 60 70 80 64 68 c. 73 80 90 100 79 g. 86 h. 76 88 d. i. 91 e. j. 79 94 Step Ahead Write two two-digit numbers that do not have a 0 or a 5. Then complete the sentences. Use the number lines above to help. The distance to the nearest ten is. The distance to the nearest ten is. 201
9.2 Step In Estimating Answers (Adding within 100) Imagine you had $80. Could you buy both items? How do you know? How could you estimate the total cost? $48 $25 What is another way you could estimate the total cost? How could you estimate the total cost of these two items? Step Up 48 is close to 50 so I just think 50 + 25. 1. Write a number sentence to show how you could estimate the total cost. $17 +20 +5 0 10 20 30 40 50 60 70 80 These amounts are each close to $15, so I just think $15 + $15. 75 $14 see $38 + $26 see $45 + $19 think $ 40 + $ 26 think $ + $ 202
9.2 2. Estimate the cost of each purchase. Then write an addition sentence to show your thinking. Blocks and Play house is about $ Sports car and Tea set is about $ Toy and Bed is about $ Bowl and Collar is about $ 3. Imagine you had the amount in the wallet. Color a to show if you could buy both games. $55 yes no Toy Mania Blocks $35 Play house $39 Tea set $18 Sports car $25 Puppy Palace Bed $45 Toy $17 Bowl $12 Collar $29 $18 $39 Step Ahead Imagine you have $60 and buy two toys. Loop the two toys that would give you the least amount of change. $35 $18 $35 $28 $35 203
9.3 Step In Estimating Answers (Subtracting within 100) Imagine you cut off 39 cm from this piece of wood. What is an easy way to estimate the length of the piece left over? What happens if the piece of wood is 45 cm long and you cut off a length that is 16 cm? How would you estimate 45 16? Step Up see think 75 cm 39 is close to 40 so I just think 75-40. 16 is close to 15, so I can just think 45-15. 1. Write a subtraction sentence to show how you could estimate the amount left over. 57 29 57 30 see think 85 48 c. see 65 37 d. see 71 49 think think 204 160615
9.3 2. Estimate the difference between these lengths. Then write a number sentence to show your thinking. 29 cm 54 cm The difference is about cm. 96 cm The difference is about cm. c. 46 cm 85 cm The difference is about cm. d. 52 cm The difference is about cm. e. The difference is about 26 cm cm. 38 cm 19 cm 72 cm Step Ahead Estimate the length of the piece of wood that will be left over after all of these lengths have been cut off. 1 length of 26 cm 95 cm 1 length of 18 cm 1 length of 34 cm Left over length of wood is about cm. 160615 205
9.4 Step In Using the Associative Property of Addition with Three One- and Two-Digit Numbers Imagine you threw three small beanbags onto this target. If each beanbag lands in the red circle, what total scores might you record? How could you figure out the totals? 24 32 7 5 Imagine two beanbags land in blue and one beanbag lands in red. How could you figure out the total scores you could record? Why are 18 and 32 called friendly pairs? What other numbers make friendly pairs? Step Up I chose 7, 9, and 3. Then I added in this order, 7 + 3 + 9 because 7 + 3 makes 10 which is easy. I could add friendly pairs of numbers like 18 and 32 first. 9 3 18 46 Imagine three beanbags land in different pink parts of this target. Write addition sentences to show four possible total scores. 6 + 4 + 8 = 15 40 8 4 6 2 10 45 206
9.4 Imagine two beanbags land in purple and one beanbag lands in yellow. Write addition sentences to show four possible total scores. c. Imagine two beanbags land in orange and one beanbag lands in pink. Write addition sentences to show four possible total scores. Step Ahead Anya threw three beanbags onto this target and scored a total of 55. Where did the beanbags land? 40 25 7 8 35 20 45 14 5 2 3 5 6 4 26 15 Write addition sentences to show three different possible solutions. 35 10 5 1 9 6 40 15 Answers will vary. This is one example. 207
9.5 Step In Using the Associative Property of Addition with Four One- and Two-Digit Numbers Imagine you had to build a fence around this garden. How many meters of fencing would you need? How could you figure out the total? 2 m 8 m 7 m How could you use the same thinking to add these numbers? Step Up I added 8 + 2 first because that s 10. Then 9 + 7 is 16 and 10 + 16 is 26. 7 m 8 m 4 m 1. Figure out the total length of all the sides without measuring. Write an addition sentence to show your thinking. 4 m 7 m 9 m 9 m 6 m 6 m 5 m 12 m 6 m 8 m 208
9.5 2. Write an addition sentence to show how you find the total length of all the sides. 17 m 9 m 21 m 18 m 12 m 7 m 13 m c. 31 m d. 8 m Step Ahead 23 m 26 m Ethan figured out that he would need 90 meters of fencing to fence this whole property. Write the missing lengths. There is more than one possible answer. 20 m 17 m 22 m 25 m 5 m 19 m m 25 m m Working Space 120815 209
9.6 Step In Solving Word Problems What does this clipboard show? What is a standing jump? What are some different word problems you can make using these numbers? Think about each word problem that was shared. Standing Jumps Jumps Kevin Owen 82 cm Abigail Elena How did you decide if the problem involved addition or subtraction? Is it possible to use addition to solve subtraction problems? Explain your thinking. Step Up How much farther did Kevin jump than Blake? Who jumped 10 cm less than Abigail? 75 cm Blake Connor 68 cm 68 Sara cm 65 cm Sophie 65 cm 1. Color the beside the number sentences that show the thinking you could use to solve each problem. There is more than one possible way of thinking. Benjamin jumped 77 cm. Rozene jumped 59 cm. What is the difference? 77 59 = Hailey jumped 87 cm. This was 20 cm more than Owen. How far did Owen jump? 87 + 20 = 77 + 59 = 78 20 = 95 77 = 20 + = 87 59 + = 77 87 20 = 210
9.6 2. Write a number sentence to show how you solve each problem. You can use the number line to help. Juliana jumped 75 cm. Cary jumped 17 cm less than Julian How far did Cary jump? Abraham jumped 58 cm. This was 15 cm less than Jennifer. How far did Jennifer jump? c. d. e. 40 50 60 70 80 Rodrigo jumped 75 cm. This was 17 cm more than Betty. How far did Betty jump? Yuma jumped 23 cm farther than Nin Nina jumped 49 cm. How far did Yuma jump? Jose jumped 19 cm less than Ruth. Ruth jumped 56 cm. How far did Jose jump? Step Ahead Lewis jumped 82 cm. This was 15 cm more than Kyle but 7 cm less than Fion Use the number line to figure out the length of each jump. Kyle cm Fiona cm 40 50 60 70 80 90 100 211
9.7 Step In Identifying One-Half, One-Fourth, and One-Eighth (Length Model) Describe how these two strips of paper have been folded. What do you know about this strip of paper? Color the strip of paper above to show one-eighth. Step Up The strip of paper is folded into eighths. There are eight parts of equal length. 1. Color one part of each strip. Then write the fraction that is shaded. c. 212
9.7 2. Draw lines to connect each fraction strip to its fraction name. Cross out the fraction strips that do not have a match. one-half Step Ahead one-fourth one-eighth Solve this problem. You can draw a picture to help your thinking. Two friends each buy a stick of licorice. They notice that the two sticks of licorice are the same length. Brian eats one-half of his piece and Frida eats one-eighth of her piece. Who ate more licorice? 213
9.8 Step In Identifying Examples and Non-Examples of One-Half, One-Fourth, and One-Eighth (Length Model) Which strip of paper shows one-eighth shaded? How do you know? Does this strip of paper show one-fourth shaded? How do you know? How could you prove your thinking? Step Up I think that 4 shaded parts should be about the same length as the whole strip. 1. Color one part in each strip. Then loop the strips that show one-half shaded. 214
9.8 2. Color one part in each strip. Then loop the strips that show one-fourth shaded. 3. Color one part in each strip. Then loop the strips that show one-eighth shaded. Step Ahead Write 'Yes' or 'No' to answer the question. Then fill the strip with ones blocks to test your prediction. Do you think that one-eighth of this strip is shaded? 215
9.9 Step In Counting By Halves, Fourths, and Eighths Beyond One Whole (Length Model) This strip of paper is folded into two-halves. One-half is shaded. What do you notice about this strip of paper? How many halves are now shaded? How many halves are in one whole? Two strips of paper are placed side by side. Each strip shows one whole and each strip has been folded into halves. How many halves are now shaded? Step Up four-halves Two-halves are now shaded. There are twohalves in one whole. 1. Continue the pattern above. Color parts to show each fraction. five-halves c. six-halves 216
9.9 2. Each strip is one whole. Color parts to show each fraction. one-fourth two-fourths c. three-fourths d. four-fourths e. five-fourths f. g. h. six-fourths seven-fourths eight-fourths Step Ahead Count by eighths. Write the fractions that you would say. one-eighth two-eighths -eighths -eighths -eighths -eighths -eighths -eighths -eighths 217
10 9. Step In Identifying and Comparing Amounts of Money Look at these coins. What is the name of each coin? How much is each coin worth? PL E Sometimes these types of coins show different pictures. Why do they show different pictures? What different pictures have you seen? What other coins from our country have you seen? What value do they have? The total is. c. 218. The total is. d. The total is The total is. 1. Figure out the total for each group of coins. SA Step Up M What is the total value of all the coins shown above? How could you figure it out easily? The total value of the coins is 82. This amount can be recorded as $0.82.
9. 10 2. Write each amount. Then loop the greater amount in each pair. $ 0. or $ PL E 0. $ 0. or M 0. SA $ Step Ahead Reece has 5 coins in his pocket. Cruz has 2 coins in his pocket. The value of Cruz s money is more than Reece s money. Draw the coins that each boy might have in his pocket. 1 5 10 Reece s coins Cruz s coins 25 219
11 9. Step In Determining the Value of a Collection of Coins What is the total value of these coins? PL E Write an addition sentence to show the order that you added the coins. How did you decide the order to add the coins? Step Up 1. Write the missing numbers. 220 4 dimes is 2 quarters is 2 nickels is 3 dimes is 3 pennies is 1 nickel is The total is The total is SA M How could you show a total value of 90 cents? What coins would you add to the collection above?
9. 11 2. Write each amount. 0. $ 0. PL E $ 3. Read the story. Write the missing numbers. Angelo had 2 quarters, 1 dime, and 3 nickels in his wallet. cents, which can be written as $ He had 0.. M Angelo gave his sister a dime. Then he found a quarter on the sidewalk. cents, which can be written as $ 0.. SA Now Angelo has Step Ahead Terri has 4 coins in her pocket. The total is greater than 40 cents but less than 60 cents. Draw two different pictures to show the coins she might have in her pocket. 1 5 10 25 221
12 9. Step In Working with Cents Imagine you had these coins and you wanted to buy this banan Which coins would you use to pay the exact amount for the banana? 42 Which coins could you use to pay for the banana and get some change? 34 Step Up PL E Which coins would you use to pay for the apple? Why? 1. Write or draw two different ways to pay for each fruit using nickels, dimes, and quarters. Use exact amounts because no change will be given. 5 10 25 45 each SA M 25 10 10 30 each c. 85 each d. 222 70 each
9.12 2. Draw nickels, dimes, and quarters to pay for each item. Use amounts that will give you just a few cents change. 5 10 25 $0.57 $0.88 c. $0.69 e. f. $0.73 d. $0.92 $0.27 Step Ahead Kinu has two quarters, three dimes, and two nickels. If she traded all the money for pennies, how many pennies would she have? If she traded all the money for nickels, how many nickels would she have? 223