Expanded Subtraction. Analyzing Data Using Subtraction

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Rudolf Taylor
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1 Expanded Subtraction Problem Solving: Analyzing Data Using Subtraction Expanded Subtraction How do we write and solve subtraction problems in expanded form? We learned how to use expanded addition to solve problems in Unit 1, Lesson 3. The expanded form is also used to solve subtraction problems. This is called expanded subtraction. Vocabulary expanded subtraction difference Look at how we model the subtraction problem Steps for Using Expanded Subtraction: Step 1 Write the numbers in expanded form. Step 2 Subtract the ones column. Write 3 in the ones column. Step 3 Subtract the tens column. Write 30 in the tens column. 98 apple 65 S Step 4 Combine and write the answer in standard form. The sum is = = 33 Remembering the steps of expanded addition will help us complete expanded subtraction problems. We write problems in expanded form to see the value of each digit in the problem. Unit 2 Lesson 2 77

2 Let s try solving a problem using expanded subtraction. As in addition, we combine the parts of our answer to write it in standard form. The answer in subtraction is called the difference. Example 1 Find the difference between 85 and 23 using expanded form. 85 apple 23 S 60 2 The difference is S 62 We can also use expanded form to subtract three-digit numbers. Example 2 Find the difference between 589 and 262 using expanded form. 589 apple 262 S The difference is S Unit 2 Lesson 2

3 Sometimes a number has digits that are zeros. When this happens in expanded subtraction, we need to use a placeholder. Example 3 Find the difference between 479 and 204 using expanded form. 479 apple 204 S S 275 Notice that there are 0 tens in 204. The 0 is written as a placeholder, and we subtract 70 0 in the tens place. The other digits are subtracted as usual. The difference is 275. Sometimes when we subtract, the amount of digits in each number is not the same. For example, we can subtract a two-digit number from a three-digit number. Example 4 Find the difference between 586 and 61 using expanded form. 586 apple 61 S S 525 There are no hundreds in 61, so we do not need to write a 0 in the hundreds place. The other digits are subtracted as usual. The difference is 525. Expanded subtractions helps us see place value. Apply Skills Turn to Interactive Text, page 54. Reinforce Understanding Use the mbook Study Guide to review lesson concepts. Unit 2 Lesson 2 79

4 Problem Solving: Analyzing Data Using Subtraction How do we find differences in data? We used bar graphs to display data. Now we will use subtraction to analyze data in a bar graph. We use subtraction to find the difference between two pieces of data. The difference represents an increase or a decrease. Look at the bar graph below. The graph displays the CD sales for the Scatter Plots from January through April. Number of CDs Sold 5,000 4,000 3,000 2,000 1,000 0 Hipster Records The Scatter Plots CDs Sold January April January February March April Month Suppose the Scatter Plots manager wants to know how many more CDs were sold in April than in January. We subtract the data in the graph to determine the difference in sales between the months. The graph shows that 1,000 CDs were sold in January. It also shows that 4,000 CDs were sold in April. We solve an extended subtraction fact to find the difference: 4,000 1,000 = 3,000. When we analyze data in a graph, it helps us to compare information by finding differences. The differences show an increase or decrease. The Scatter Plots sold 3,000 more CDs in April than January. Problem-Solving Activity Turn to Interactive Text, page 55. Reinforce Understanding Use the mbook Study Guide to review lesson concepts. 80 Unit 2 Lesson 2

5 Homework Activity 1 Find the difference using expanded form. Then write the answer in standard form. Model 76 apple 53 S S = 23 Activity apple apple 31 Use the bar graph to solve the problem apple apple apple apple 265 Month August July June May Hipster Records The Scatter Plots CDs Sold May August Number of CDs Sold 1. How many CDs did the Scatter Plots sell between May and August? 2. Compare the CD sales for May and June. What is the difference? 3. Compare the CD sales for July and August. What is the difference? 4. What were the total CD sales for May and June? July and August? Activity 3 Distributed Practice Add Unit 2 Lesson 2 81

Estimating Differences. Finding Distances on a Map

Estimating Differences. Finding Distances on a Map Estimating Differences Problem Solving: Finding Distances on a Map Estimating Differences How do we use rounding to estimate differences? Sometimes subtraction is like addition. There are times when we