Unit 5 Arithmetic In Base Ten — Unit Plan

Title	Takeaways	Assessment
Lesson 1 Using Decimals in a Shopping Context	—	How Did You Compute with Decimals? (1 problem) Reflect on how you made calculations when planning a menu. How did you add dollar amounts that were not whole numbers? Use the numbers $5.89 and $1.45 to show or explain your strategy. How did you multiply dollar amounts that were not whole numbers? Suppose you are computing the cost of 4 pounds of beef at $5.89 per pound. Use this example to explain or show your strategy. Show Solution Sample response: I would add the dollars and cents separately, and then combine the sums at the end. $5 + 1$ is 6 and $89 + 45$ is 134, so it’s $6 plus $1.34, which is $7.34. Sample response: I would round the $5.89 to $5.90 to make it easier to multiply. Then, I would find 4 times $5, which is $20, and 4 times $0.90, which is $3.60. The two products added together is $23.60. The exact cost would be 4 cents less than $23.60, because $5.89 is 1 cent less than $5.90, and 4 times 1 cent is 4 cents. So, the total cost would be $23.56.
Lesson 2 Using Diagrams to Represent Addition and Subtraction	—	Why or Why Not? (1 problem) Does adding 0.025 and 0.17 give a sum of 0.042? Explain or show your reasoning. If you choose to use a diagram, you can use the following representations of base-ten units. 1 large square labeled "one." 1 medium rectangle labeled “zero point one, or tenth.” 1 medium square labeled “ 0 point 0 one, or hundredth.” 1 tiny rectangle labeled “0 point 0 0 1, or thousandth.” 1 tiny square labeled “0 point 0 0 0 1, or ten-thousandth.” Show Solution No. Sample reasoning: The number 0.17 is greater than 0.042, so 0.042 cannot be the sum of 0.17 and another decimal. A diagram showing 1 medium rectangle (1 tenth), 9 medium squares (9 hundredths), and 5 small rectangles (5 thousandths). $0.025 + 0.17 = 0.02 + 0.005 + 0.1 + 0.07 = 0.125 + 0.07 = 0.195$ . Calculation with numbers should show the decimal points lining up and a sum of 0.195.
Lesson 3 Adding and Subtracting Decimals with Few Non-Zero Digits	—	Calculate the Difference (1 problem) Find the value of each expression and show your reasoning. $1.56 + 0.083$ $0.2 - 0.05$ Show Solution 1.643. Sample reasoning: Six hundredths and 8 hundredths make 14 hundredths, or 1 tenth and 4 hundredths. The sum has 1 one, 6 tenths, 4 hundredths, and 3 thousandths. 0.15. Sample reasoning:
Lesson 4 Adding and Subtracting Decimals with Many Non-Zero Digits	—	How Much Farther? (1 problem) A runner has run 1.192 kilometers of a 10-kilometer race. How much farther does she need to run to finish the race? Show your reasoning. Show Solution 8.808 kilometers. Sample reasoning: $9.999 - 1.192 = 8.807$ . Adding 0.001 to 8.807 gives 8.808.
Section A Check Section A Checkpoint		Problem 1 Which calculation shows a correct way to find $31.076 + 4.85$ ? A. B. C. D. ✓ Show Solution D Problem 2 a. b. Show Solution 98.963 2.958

Lesson 5 Using Fractions to Multiply Decimals	—	Explaining and Calculating Products (1 problem) Use what you know about decimals or fractions to explain why $(0.2) \boldcdot (0.002)= 0.0004$ . A rectangular plot of land is 0.4 kilometer long and 0.07 kilometer wide. What is its area in square kilometers? Show Solution Sample response: 0.2 is $\frac{2}{10}$ , and 0.002 is $\frac{2}{1,000}$ . Multiplying the two we have: $\frac{2}{10} \boldcdot \frac{2}{1,000} = \frac{4}{10,000}$ , which is 0.0004. 0.028 square kilometers, because $(0.4) \boldcdot (0.07)=0.028$
Lesson 6 Methods for Multiplying Decimals	—	A Product of Two Decimals (1 problem) Explain or show how you would find the value of $(1.35) \boldcdot (4.2)$ if you know that $135 \boldcdot 42 = 5{,}670$ . Show Solution Sample responses: $135 = (1.35) \boldcdot 100$ and $42 = (4.2) \boldcdot 10$ , so $135 \boldcdot 42$ is $100 \boldcdot 10$ , or 1,000, times $(1.35) \boldcdot (4.2)$ . This means $(1.35) \boldcdot (4.2)$ is $5,670 \div 1,000$ , which is 5.67. $(1.35) \boldcdot (4.2) = \frac{135}{100} \boldcdot \frac{42}{10} = \frac{135 \boldcdot 42}{10 \boldcdot 100} = \frac{5,670}{1,000}$ , which is 5.67.
Lesson 7 Using Diagrams to Represent Multiplication	—	Find the Product (1 problem) Find the value of $(4.2) \boldcdot (1.6)$ by drawing an area diagram or using another method. Show your reasoning. Show Solution 6.72. Sample reasoning: The sum of the areas of the sub-rectangles is $4 + 0.2 + 2.4 + 0.12 = 6.72$ .
Lesson 8 Calculating Products of Decimals	—	Calculate This! (1 problem) Calculate $(1.6) \boldcdot (0.215)$ . Show your reasoning. Show Solution 0.344. Sample reasoning:
Section B Check Section B Checkpoint		Problem 1 A rectangular wall is 7.2 meters long and is 3.8 meters in height. What is its area in square meters? Show your reasoning. Show Solution 27.36 square meters. Sample reasoning: $(7.2) \boldcdot (3.8) = \frac{72}{10} \boldcdot \frac{38}{10} = \frac{2,736}{100} = 27.36$ Problem 2 Find the product of 64 and 9. Explain how you can use the value of $64 \boldcdot 9$ to find the value of $(6.4) \boldcdot (0.009)$ . Show Solution 576 Sample responses: There is 1 decimal place in 6.4 and 3 decimal places in 0.009, so the product will have 4 decimal places. I can move the digits in 576 to the right 4 places to get 0.0576. 64 is $10 \boldcdot (6.4)$ , and 9 is $1,000 \boldcdot (0.009)$ , so the product of 64 and 9 is 10,000 times the product of 6.4 and 0.009. Dividing 576 by 10,000 gives 0.0576.

Lesson 9 Using Base-Ten Diagrams to Divide	—	Putting 33 into 4 Groups (1 problem) To find $33 \div 4$ , Clare drew a diagram and thought about how to put the tens and ones into 4 equal-size groups. There aren’t enough tens or ones to put into 4 groups. What can Clare do to find the quotient? Explain or show your reasoning. What is the value of $33 \div 4$ ? Show Solution Sample response: The 3 tens can be decomposed into 30 ones, making a total of 33 ones. Of these, 32 ones can be distributed into 4 groups, 8 ones in each. There is 1 one left. This can be decomposed into 10 tenths and distributed into 4 groups, 2 tenths in each group. There are 2 tenths left. These can be decomposed into 20 hundredths and then distributed into 4 groups, 5 hundredths in each group. 8.25
Lesson 10 Using Partial Quotients	—	Dividing by 11 (1 problem) Calculate $4,235 \div 11$ using any method. Show Solution 385. Sample reasoning:
Lesson 11 Using Long Division	—	Dividing by 5 (1 problem) Use long division to find the value of $1{,}875 \div 5$ . Then check your answer by multiplying it by 5. Show Solution 375.
Lesson 12 Dividing Numbers that Result in a Decimal	—	Calculating Quotients (1 problem) Use long division to find each quotient. Show your computation, and write your answer as a decimal. $43.5 \div 5$ $7 \div 8$ Show Solution 14.5 0.875
Lesson 13 Dividing a Decimal by a Decimal	—	The Quotient of Two Decimals (1 problem) Write two division expressions that have the same value as $36.8 \div 2.3$ . Find the value of $36.8 \div 2.3$ . Show your reasoning. Show Solution Sample responses: $3.68 \div 0.23$ and $368 \div 23$ . 16. Sample reasoning:
Section C Check Section C Checkpoint		Problem 1 Use long division to find the value of $78.9 \div 2$ . Show Solution 39.45 Problem 2 Write a division expression that has the same value as $1.2 \div 0.75$ and can be used to find the quotient. Find the value of $1.2 \div 0.75$ . Show your reasoning. Show Solution Sample responses: $120 \div 75$ or $1,200 \div 750$ 1.6 (or equivalent). Sample reasoning: $120 \div 75 = \frac{120}{75} = 1\frac{45}{75}$ , which is equal to $1\frac {9}{15}$ or $1\frac{3}{5}$ .

Lesson 14 Solving Problems Involving Decimals	—	Ribbon for Sharing (1 problem) Jada and Han are sharing a piece of ribbon that is 1.905 meters long for a craft project. Jada cuts 0.82 meter from one end of the ribbon and Han cuts 0.175 meter from the other end. Afterward, they split the ribbon that is left into equal-size pieces that are 0.13-meter long each. How many pieces will they have? Show your reasoning. Show Solution 7 pieces. Sample reasoning: Jada and Han cut a total of $0.82 + 0.175$ , or 0.995 meter, from the two ends. This leaves $1.905-0.995$ , or 0.91 meter. Dividing 0.91 by 0.13 gives 7.
Lesson 15 Making and Measuring Boxes	—	No cool-down
Unit 5 Assessment End-of-Unit Assessment