Add, Subtract, and Multiply Decimals Bookstore

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1 Add, Subtract, and Multiply Decimals SUGGESTED LEARNING STRATEGIES: Think/Pair/Share, Create Representations, Quickwrite, Debriefing Mrs. Grace s middle school class operates a bookstore before school and during lunch. Juan and Isabel are in charge of ordering supplies and selling items. The table below lists the items they sell and the price per item. ACTIVITY 2.6 Item Price Price in Dollars Pencils 25 Notebook Paper $1.32 Ink Pens 43 Markers $2.35 Erasers Mrs. Grace asked Juan and Isabel to rewrite the price chart so that each price is written in dollars. Complete the chart. 2. Kalen buys two pencils, an ink pen, and a box of markers. What will they cost? WRITING MATH When writing amounts of money, dollar or cents signs can be used. Sixty-five cents can be written as 65 or $0.65. Writing sixty-five cents as 0.65 or $0.65 is incorrect. To add or subtract decimals: 1. Line up the decimal points. 2. Use zeros as placeholders if needed. 3. Elan purchases a pack of notebook paper and an eraser. What will they cost? 4. Who spent more on their purchases, Kalen or Elan? How much more? Explain how you arrived at your answer. 5. Alena has $5.00 to spend at the bookstore and would like to buy a box of markers, 2 erasers, 1 pencil, and a pack of notebook paper. Does she have enough money? If yes, does she have any money left over? Explain. 3. Add or subtract. 4. Place the decimal point in the answer under the decimal points in the problem. 6. Joey wants to buy 20 pencils but he may not have enough money. He can use repeated addition or multiplication to see what they cost. Which operation is more efficient? Why? Unit 2 Operations with Numbers 97

2 ACTIVITY 2.6 Add, Subtract, and Multiply Decimals SUGGESTED LEARNING STRATEGIES: Think/Pair/Share, Create Representations To investigate how to multiply decimals by whole numbers, let a grid represent one whole. The model shown below represents two wholes, or 2. The grid represents one whole, or 1. One tenth, or 0.1, can be represented by one row or one column of the grid. 7. Explore multiplying 0.7 times 2. a. Shade each grid above to represent 0.7. b. Find the value of the total shaded area. Think of an equivalent fraction when you need help with decimal multiplication =? = = = =? = = 0.24 c. Shade the grids below with the value you found in Part b by completely filling one grid before moving to the next. d. Write the value of the shaded area as a decimal. e. Complete this number sentence = 8. Study the products in the box to the right. What do you think the product of will be? 4 8 = = = = SpringBoard Mathematics with Meaning Level 1

3 Add, Subtract, and Multiply Decimals ACTIVITY 2.6 SUGGESTED LEARNING STRATEGIES: Discussion Group, Quickwrite, Think/Pair/Share, Create Representations 9. How do the number of decimal places in the products in Questions 7 and 8 compare to the number of decimal places in the factors? 10. Write a rule for multiplying a whole number and a decimal number. Be sure to include instructions for placing the decimal point. Find each product How much it will cost Joey to buy 20 pencils at the bookstore? At the end of February, Mrs. Grace asks Juan and Isabel to estimate the monthly income from selling items in the bookstore. 15. Juan and Isabel decided to estimate by rounding. They rounded the prices of the items to the nearest tenth of a dollar and rounded the numbers of items sold to the nearest ten. Help them fill in their chart. MATH TERMS Income is the amount of money earned from selling a product or service. Item Price in Dollars Rounded Price Items Sold Pencils 32 Paper 17 Pens 16 Markers 8 Erasers 27 Rounded Items Sold 16. What is the estimated total income from selling school supplies during the month of February? Estimated Income To round, look at the digit to the right of the place that you are rounding. If that digit is 5, 6, 7, 8, or 9, add 1 to the place you are rounding; if that digit is 0, 1, 2, 3, or 4, the digit you are rounding remains the same. 17. Mrs. Grace then asked them to calculate how close their estimate is to the actual total. a. Find the exact income for each item in the table. b. Find the exact amount of money collected during February. c. How close is the estimate to the actual total? Unit 2 Operations with Numbers 99

4 ACTIVITY 2.6 Add, Subtract, and Multiply Decimals SUGGESTED LEARNING STRATEGIES: Use Manipulatives, Think/ Pair/Share, Self Revision/Peer Revision, Predict and Confirm Mrs. Grace has decided to carpet the bookstore floor. She asked Isabel and Juan to measure the rectangular room. Their measurements are shown below. 3.2 ft 4.7 ft 18. Predict what the area of the carpeted area will be. Investigate some ideas about multiplying decimal numbers to help Isabel and Juan find the exact area of the bookstore! The area of a rectangle is A = l w. 19. You can use a model to find the product of 0.7 and a. The entire grid represents 1. What does each small square represent? 0.7 b. In the model, shade 0.3 in one color and 0.7 in another color. Complete. 20. The number of one-hundredths shaded with both colors is. This shows that the product of 0.7 and 0.3 is. A number sentence for this is. 21. How does the number of decimal places in the product compare to the number of decimal places in the factors? 100 SpringBoard Mathematics with Meaning Level 1

5 Add, Subtract, and Multiply Decimals ACTIVITY 2.6 SUGGESTED LEARNING STRATEGIES: Self Revision/Peer Revision, Look for a Pattern, Group Presentation, Create Representations, Think/Pair/Share, Predict and Confirm 22. Find each product. a b c Write a rule for multiplying two decimal numbers. Remember to include instructions for placing the decimal point. You can think aloud to make sense of a product. For = 0.24, imagine the decimals as fractions: = 24 and think 100 aloud this way: Four-tenths times six tenths is twenty-four hundredths. 24. Remember that the floor of the bookstore measures 3.2 ft by 4.7 ft. What is the area of the floor in square feet? Estimating is often helpful to check whether a product is reasonable. One method of estimating is front-end estimation. 25. Find each product. Use front-end estimation to check your answer. a b MATH TERMS In front-end estimation the front-end digits (the leftmost digits) are used for computation. The other digits become zeros. 26. Find the product of 0.02 and 0.7. a. How many decimal places are needed in the answer? b. You will need to use zeros as placeholders. Where will you place them in the product? How do you know? c. Write the product. Find each product Unit 2 Operations with Numbers 101

6 ACTIVITY 2.6 Add, Subtract, and Multiply Decimals SUGGESTED LEARNING STRATEGIES: Quickwrite, Work Backward 29. Mike multiplied and found as the product. He counted 6 decimal places in the factors, so he knew that there should be 6 decimal places in his answer. Then he used front end estimation to check his answer for reasonableness and saw that his answer should be close to 2. Now he thinks that he made a mistake. Help Mike find his mistake. Explain your thinking. CHECK YOUR UNDERSTANDING Write your answers on notebook paper. Show your work. 1. Mark went to the movies one Saturday. After buying his ticket, he had $7.00 left over. Does he have enough money to buy a small popcorn and large water? If yes, how much change will he receive? If no, how much more money does he need to make his purchase? Popcorn Bottled Water Small $3.75 $2.50 Medium $4.50 $3.00 Large $5.25 $ The relay team competed in the county track meet. Their clocked times were: 14.6 sec, 15.2 sec, 16.1 sec, and 14.2 sec. Compute the amount of time that it took the team to complete the race. 3. Keisha would like to buy five pairs of socks that cost $3.95 a pair. How much will she spend buying socks not including any taxes? 4. Samson purchased the following items at the grocery store. Estimate his final bill, not including taxes. Explain your process. 3 kg. of bananas at 49 per kg. 1 package of almonds at $4.99 each 2 packages of wheat crackers at $2.39 each 5 cans of cat food at 35 each 2 tomatoes at $1.19 each 5. Kevin helped the coach prepare the soccer field for Tuesday s game. The field measures meters by 82.3 meters. What is the area of the playing field in square meters? 6. Find the product of 3.25 and Maria multiplied 0.8 by 0.5 and got a product of 0.4. Is she correct? Explain. 8. MATHEMATICAL REFLECTION Will the product of a whole number and a decimal number less than one ever be larger than the whole number? Give examples to support your answer. 102 SpringBoard Mathematics with Meaning Level 1