Unit 5 Decimal Operations — Unit Plan

Title	Takeaways	Assessment
Lesson 1 Decimal Numbers	—	What Does It Represent? (1 problem) The large square represents 1. What fraction does the shaded portion represent? Write the fraction in decimal notation. The large square represents 1. Shade the diagram to represent 0.7. Show Solution $\frac{28}{100}$ 0.28 Sample response:
Section F Check Foundations Checkpoint		Problem 1 The large square represents 1. What number is represented by the shaded parts? Write your answer both as a fraction and as a decimal. Show Solution $\frac{55}{100}$ or 0.55 Problem 2 Estimate the location of the following numbers on the number line: 0.43 0.3 0.09 1.2 1.02 Show Solution Problem 3 Choose 4 different decimals to complete the comparison statements. Use the number line if it is helpful. 6.52 6.4 6.39 6.53 6.6 ________ is greater than ________. ________ is less than ________. Show Solution Sample responses: 6.6 is greater than 6.53. 6.53 is greater than 6.52. 6.52 is greater than 6.4,. 6.4 is greater than 6.39. 6.39 is less than 6.4. 6.4 is less than 6.52. 6.52 is less than 6.53. 6.53 is less than 6.6.

Lesson 1 Using Decimals in a Shopping Context	—	Cooldown Candidates for Review (3 problems) Problem 1 Candidate 1: G6 L01 Cooldown (Original) Pros: Comprehensive, tests both addition and multiplication strategies Cons: Very literacy-heavy, requires lengthy explanations 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. Problem 2 Candidate 2: G6 L01 PP1 - Mai's Money Pros: Simple, multiple choice, low literacy burden, tests add/subtract with money Cons: Only tests one operation, no explanation required Mai had $14.50. She spent $4.35 at the gift shop and $5.25 at the arcade. How much money does Mai have left? A. $9.60 B. $10.60 C. $4.90 D. $5.90 Show Solution C. $4.90 Problem 3 Candidate 3: G6 L01 PP3 - Tickets Pros: Tests estimation, addition, subtraction, real-world context Cons: 3 parts may be too much for a cooldown Tickets to a show cost $5.50 for adults and $4.25 for students. A family is purchasing 2 adult tickets and 3 student tickets. Estimate the total cost. What is the exact cost? If the family pays $25, what is the exact amount of change they should receive? Show Solution $24 ( $6 +6+4+4+4=24$ ) $23.75 ( $5.50+5.50+4.25+4.25+4.25=23.75$ ) $1.25 ( $25.00-23.75=1.25$ )
Lesson 2 Using Diagrams to Represent Addition and Subtraction	—	Composing Base-Ten Units (2 problems) Problem 1 Mai added $0.08 + 0.13$ using base-ten blocks. Here is what she started with: Base-ten diagram showing 1 tenth (tall rectangle) in the tenths column and 11 hundredths (small squares arranged in rows of 5, 5, and 1) in the hundredths column. Which diagram shows what the blocks look like after composing? A. B. C. D. A.A B.B C.C D.D Show Solution A 10 of the hundredths squares can be composed into 1 tenth rectangle. Starting with 1 tenth and 11 hundredths, composing 10 hundredths into 1 tenth gives 2 tenths and 1 hundredth, which equals 0.21. Problem 2 Add $0.6 + 0.38$ . Show your work. Find the sum. Show Solution 0.98 Sample work: Students should align the decimal points so that tenths are added to tenths and hundredths are added to hundredths.
Lesson 3 Adding and Subtracting Decimals with Few Non-Zero Digits	Trailing zeros after a decimal point do not change a number's value (e.g., 34.560 = 34.56) Line up place values vertically when adding or subtracting decimals You may need to 'regroup' (carry or borrow) just like with whole numbers	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	For numbers with many digits, vertical calculation is more efficient than base-ten diagrams Pad with trailing zeros so both numbers have the same number of decimal places (2.4 → 2.4000) Regroup across multiple place values when subtracting	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.

Lesson 5 Using Fractions to Multiply Decimals	Decimals can be written as fractions with denominators of 10, 100, 1000, etc. To multiply decimals, rewrite them as fractions, multiply, then convert back The number of decimal places in the product equals the total decimal places in the factors	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 8 Calculating Products of Decimals	To multiply decimals: multiply the digits as whole numbers, then place the decimal point Count the total decimal places in both factors to know where the decimal goes in the product Example: 1.25 x 0.7 -> compute 125 x 7 = 875, then shift 3 decimal places -> 0.875	Calculate This! (1 problem) Calculate $(1.6) \boldcdot (0.215)$ . Show your reasoning. Show Solution 0.344. Sample reasoning:

Lesson 10 Using Partial Quotients	Division can be done in parts by subtracting groups from the dividend Partial quotients uses place value: start with the largest chunks you can Add up all the partial quotients to get the final answer	Dividing by 11 (1 problem) Calculate $4,235 \div 11$ using any method. Show Solution 385. Sample reasoning:
Lesson 12 Dividing Numbers that Result in a Decimal	Long division works even when the quotient is not a whole number When there is a remainder, add a decimal point and zeros to the dividend to keep dividing Place the decimal point in the quotient directly above the decimal in the dividend	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	Multiplying both dividend and divisor by the same power of 10 doesn't change the quotient Use this to turn decimal divisors into whole numbers before dividing Example: 4.5 / 0.3 = 45 / 3 = 15 (multiply both by 10)	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:
Unit 5 Assessment Unit 5 Assessment - Decimal Operations		Problem 1 Find the product: $(0.061) \boldcdot (0.43)$ Show Solution 0.02623 Problem 2 Find the difference: Show Solution 0.5692 Problem 3 For part of a science experiment, Andre adds 0.25 milliliters of food coloring to 12.3 milliliters of water. How many milliliters does the mixture contain? A.12.05 B.12.325 C.12.55✓ D.14.8 Show Solution C Problem 4 Four runners are training for long races. Noah ran 5.123 miles, Andre ran 6.34 miles, Jada ran 7.1 miles, and Diego ran 8 miles. What is the total running distance of the four runners? Compared to Noah, how much farther did Jada run? Show Solution 26.563 miles 1.977 miles Problem 5 One way to compute a 15% tip for a bill is to multiply it by 0.15. A restaurant bill was $42.40. Calculate the tip. Explain or show your reasoning. Show Solution $6.36. Sample reasoning: I multiplied 42.40 by 0.1 to get 4.24 and then found half of that to get $(0.05) \boldcdot (42.40) = 2.12$ . Then I added the two answers to get $6.36. Problem 6 A woodworker wants to cut a board that is 8.225 feet long into 5 equal-length pieces. How long will each piece be? A. 0.1645 foot B. 1.645 feet C. 4.1125 feet D. 41.125 feet Show Solution 1.645 feet Problem 7 The list below shows the cost of the same candle at two different stores. Store ABC sells 6 of these candles for $12.00. Store XYZ sells 8 of these candles for $14.00. Which store sells the candle for a lower unit rate? Explain how you determined your answer. Problem 8 A diagram of a rectangular flag, with a shaded section, is shown below. What is the area, in square centimeters, of the shaded section of the flag? Show your work. Answer: ______ square centimeters Problem 9 A tutoring company charges $25.00 per hour to tutor a student. How many hours of tutoring would cost $62.50? A. $2\frac{1}{2}$ B. $3\frac{1}{2}$ C. $37\frac{1}{2}$ D. $87\frac{1}{2}$ Show Solution A