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

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

2 7.1 Step In Reviewing Factors and Multiples Figure out each product. What do you notice? Write the multiplication expression that is missing. How did you decide what to write? What do you know about factors and multiples? Look at the diagram on the right. Write 0 in the first box. What numbers could you write in the second box so that the relationship is true? What are some other numbers that you could write in the second box? Step Up I looked for factors that I could double and halve. 1 x 30 is the same as x Write numbers to complete these. is a multiple of is a factor of 5 is a multiple of is a factor of is a multiple of is a factor of is a multiple of is a factor of d. is a multiple of is a factor of 9 e. is a multiple of is a factor of f. is a multiple of is a factor of 5 15

3 7.1. Complete these to show pairs of possible factors. 0 is the same as 5 is the same as 70 is the same as d. is the same as e. 0 is the same as Step Ahead f. 0 is the same as Write at least three numbers to match each label. One is done for you. Numbers 1 to 100 g. 7 is the same as h. is the same as factors 3 factors factors

4 7. Step In Reviewing Strategies to Multiply One- and Two-Digit Numbers Owen is planning a party. He buys bags of potato chips. There are 1 small packets of chips inside each bag. POTATO CHIPS How many small packets of chips has he bought? PL E How did you figure out the total? I can break 1 into factors. x 1 is the same as x 9 x. Owen then buys 5 packs of apple juice. There are juice boxes in each pack. How many boxes did he buy? M I know that 10 x = 0. Half of 0 = 10. SA I could also double one factor and halve the other. 5 x is the same as 10 x 1. Owen needs at least 70 granola bars. How many boxes should he buy? 1. Write the total cost. Show your thinking. Buy tickets $5 $ 15 Buy 7 tickets $35 $ Step Up

5 7.. Write the products. Show your thinking. 5 = 7 = 5 = Step Ahead Write the missing number in each algorithm. d = 3. Write the anwers that you can figure out in your head. 35 = 5 1 = 0 9 = e = f. 5 = g. 3 5 = d. 7 = h. 5 9 = H T O H T O H T O

6 7.3 Step In Using the Associative Property to Multiply Two-Digit Numbers (Double and Halve) 15 I want to lay turf in an area that measures 1 yd by 15 yd. How many square yards of turf will I need? 1 Look at this array. How could you figure out the number of square yards without counting all the squares? There are 30 squares in rows = 10. You could also double and halve. Imagine the array above is cut in half and rearranged like this. Has the total number of squares changed? Label the new dimensions. Are these numbers easier to multiply in your head? How will 30 change if you doubled and halved it again? Step Up 1. Double one number and halve the other to make a problem that is easier to solve. Then write the product = 1 15 = 35 = 15

7 7.3. Double and halve twice to solve each of these = 13 1 = 3. Calculate the products. Show the steps you use. 5 = d = Step Ahead 5 = 5 1 = 1 = e. f = 1 55 = Loop the expression that you would not use the double-and-halve strategy to solve. Then explain your reasoning

8 7. Step In Using the Associative Property to Multiply Two-Digit Numbers (Use Factors) There are 15 small boxes inside each of these large boxes. Write a multiplication sentence you could use to figure out the total number of small boxes in all the large boxes. How would you calculate the total in your head? How would you multiply 3 5? Which factors would you multiply first? Why? What is the total number of small boxes? Step Up I used factors to make the multiplication easier. Rozene counted 3 pine trees in one square of this field. How could Rozene estimate the total number of trees in the whole field if there are the same number in each square? 1. Break one number into two factors to make it easier to multiply. Then complete the equation. 35 is the same as = 35 is the same as = 15 is the same as d. 5 is the same as = 5 is the same as = e is the same as = 15

9 7.. Break both numbers into two factors. Then write an equation showing the four factors in the order you would multiply them to figure out the product. 0 1 is the same as d. e. Step Ahead º 9 º º 3 15 is the same as 1 is the same as 1 5 is the same as 5 1 is the same as For each of these, write the product. Then write the different pairs of two-digit numbers that may have been factored to create these equations. = = = = = 5 9 = = 1 º 5 º

10 7.5 Step In Investigating Perfect Squares Look at this growing pattern. How many squares are in the first picture? How many squares have been added to make the second picture? Picture 1 Picture Picture 3 How many squares have been added to make the third picture? What do you think the fourth and fifth pictures will look like? How many squares will be added each time? Color squares to show your thinking. Then write the addition sentences to match. Picture Picture 5 Picture Picture What do you notice about the numbers being added each time? 10

11 Complete the addition sentences to describe each picture on page 10. Then write the related multiplication sentence. Step Up Picture 1 1 = 1 = 1 1 Picture = = Picture = = Picture = = Picture = =. Imagine there were two more pictures in the pattern from Question 1. Write the matching addition and multiplication sentences. Picture = = Picture 7 = = Step Ahead Complete the table This table shows a square number pattern. Picture (Input) Squares (Output) Write an equation to show the process for figuring out any square number. 11

12 7. Step In Solving Word Problems Involving Multiplication (Two-Digit Numbers) The Bay City Tigers need to buy 5 pairs of shorts. How could you figure out the total cost of the shorts? Abraham 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 1 team shirts and 1 pairs of shorts. What will be the total cost? Step Up = = = = 35 I will call the total cost of the shirts and shorts T. T = (35 + 7) x 1 1. Use the uniform prices above. The Cincinnati Chargers need to buy 1 complete uniforms. What is the total cost? $7 $35 $7 $13 Working Space $ 1

13 7.. Solve these word problems. Show your thinking. Sweaters cost $7 each. This is $15 more than the price of a cap. 5 of these caps were sold at one game. What was the total amount made in sales from caps? A stadium parking lot has 3 rows. There are spaces in each row. 00 spaces are reserved for staff. How many spaces are there for supporters? Sports bags cost $9 each. If this price was reduced by $3, how much would be saved when buying bags? Step Ahead $ d. A club has $500 to spend. It buys 5 footballs at $9 each and 3 helmets at $75 each. How much money is left over? $ $ Write a word problem to match this equation. Then figure out the product. 13 = spaces 13

14 7.7 Step In Subtracting Common Fractions (Number Line Model) Terek 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 of the box left over. POPCORN How much popcorn did Terek 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? Grace 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 = =

15 7.7. Use this number line to help you write the differences = = 0 17 = 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 = e. 15 Difference 11 1 = 1 1 f. 1 1 = 1 5 Difference 3 = Complete each equation so that the difference is between and 3. Use the number lines on pages 1 and 15 to help you. 3 d. = 1 1 Difference 3 = = 5 = 0 = d. = Working Space 15

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

17 7.. Calculate the difference. Draw jumps on the number line to show your thinking = 1 3 = 3. Calculate the difference. Show your thinking. d = = = e = f = 10 = Step Ahead Write the missing numbers on this trail

18 7.9 Step In Calculating the Difference between Mixed Numbers (Decomposing Whole Numbers) Morgan has two pet lizards. One is 3 7 inches long and the other is 1 How could you figure out the difference between their lengths? inches long. Yara 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? = = 5 The difference is 1 5 inches Step Up 1. Calculate the difference. Draw jumps on the number line to show your thinking. 3 5 =

19 7.9. Calculate the difference. Draw jumps on the number line to show your thinking = = Calculate the difference. Show your thinking. 7 1 = d. = = e = f = = 5 3 Step Ahead Look at these related equations. + = + = = = Each sentence describes the same two parts ( and ) that make a total (). Write the related equations for the equation shown = 3 19

20 7.10 Step In Solving Word Problems Involving Mixed Numbers and Common Fractions Abel used a watering can and poured 3 3 water onto his seedlings which were in a garden bed that was 5 3 can had 3 Step Up quarts of feet long. Afterward, the watering 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? Two identical cakes were baked for a big party. Each cake was cut into twelfths. Halfway through the party, 3 1 of one cake had been eaten. The other cake had pieces missing and 5 people were standing near it. How much cake was still left? 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 1 10 kilograms. The total weight of the cats is kilograms. How much does Boxy weigh? A builder cut 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? A bucket held 3 1 gallons of water. 1 1 gallons were used for watering lettuce and 1 gallon was used for carrots. How much water was left? kg gal d. Lily visited her dad. It took 1 hours to get there. It usually takes 1 3 hours. How much later than usual did she arrive? in hr 170

21 7.10. Solve these problems. Show your thinking. Wendell cut 5 oranges into sixths for a picni Afterward, there was only of an orange left. How many oranges and part oranges were eaten? A baker used sticks of licorice and had sticks left so she ate 1 of a stick. How many sticks did the baker have at the start? Mom had 7 3 yards of fabric rolled up. She cut off yards for a quilt she was making. Some squares on that quilt were 1 yard long on each side. She also cut yards off the roll to make a second quilt. How much fabric was left on the roll? Step Ahead oranges Write a subtraction word story that involves mixed numbers and common fractions. sticks yd 171

22 7.11 Step In Solving Word Problems Involving Dot Plots Two friends are training for a triathlon. The dot plots below show the distances they ran. Running Distance (Alicia) Running Distance (William) Miles How many times did each person go running? Who ran the greatest distance in one run? What was the most common distance that each person ran? Miles Who ran the greater total distance? What is the difference between the total distances that each person ran? How did you figure out the answer? Step Up 1. Your teacher will give you a support page. Draw on the dot plot below to show the distance that Riku cycled each day. Cycling Distance (Riku) Miles 17

23 7.11. Your teacher will give you a support page. Draw on the dot plot below to show the distance that Fernando cycled each day. Cycling Distance (Fernando) Refer to the dot plots in Questions 1 and to answer these questions. How many times did each person go cycling? Who cycled the greatest distance in one ride? What distance did Riku cycle most often? miles d. What is the difference between greatest distances each person cycled? Step Ahead Miles mile Refer to the dot plot in Question. Figure out the total distance Fernando cycled. Show your working. miles 173

24 7.1 Step In Introducing Stem-and-Leaf Plots This stem-and-leaf plot shows the number of points that Henry scored in his last 1 basketball games. His highest score was 31 points. What are some other scores that he has recorded? How do you know? What is the lowest score that he recorded? What score did he record more than once? Stem The stem shows the digits in the tens place. The leaf shows the digits in the ones place. So, in the stem-and-leaf plot above, 3 1 means 31. Read the scores in each row from left to right. What do you notice? The scores are ordered from least to greatest. Henry scored 1 points in his last game of the season. Write this score in the plot. 0 3 Points Scored Leaf Key 3 1 means 31 Step Up 1. Athena plays on the same team as Henry. Write her scores in order from least to greatest. Cross out each score as you write it. Points Scored

25 7.1. Record Athena's scores from Question 1 in this stem-and-leaf plot. Stem Points Scored Leaf Refer to the stem-and-leaf plot above to answer these questions. What was Athena's lowest score? points Which score was recorded more than once? points How many times did she score more than 15 points? times d. How many times did she score fewer than 10 points? times e. What is the difference between her highest and lowest scores? Step Ahead Use the stem-and-leaf plots on pages 17 and 175. Figure out the difference between the total points scored by Henry and Athen Show your working. points points 175