Day 5 Decimals and Percentages

Transcription

1 Day 5 Decimals and Percentages What mathematical justification can you give for the rules we teach in dealing with decimals? 1. Which decimal fraction is larger 0.34 or 0.7? 2. Line up the decimal points to add or subtract decimals 3. Multiply as whole numbers and the sum of the number of decimal places in the factors is the number of decimal places in the answer. 4. Divisor and dividend is first multiplied by the same power of ten so the divisor is a natural number. Division is then performed as for natural numbers. The decimal point is placed in the quotient above its new position.

2 Day 5 Decimals and Percentages P a g e 2 Students Understanding of Tenths A) An animal at the zoo eats pounds of food each day. How many days will it take this animal to eat pounds of food? (, 8) (, ) (, 6) (, 6) (, ) (, 6 ) B) How many tens in 356? a) 3 b) 5 c) 6 d) 35 e) 35.6

3 Day 5 Decimals and Percentages P a g e 3 I. Decimal Activities

4 Day 5 Decimals and Percentages P a g e 4 7-tenths hundredths 9-tenths and 8-hundredths 50-hundredths

5 Day 5 Decimals and Percentages P a g e 5 Decimal Grids 1. Use the grid to find three numbers between 0.07 and Explain how you know the numbers are between these two numbers. 2. Circle the smaller number: and Explain how to use the grids below to support your answer.

6 Day 5 Decimals and Percentages P a g e 6 3. Determine if the sentences are true or false. Use the grids to show support for each answer. a) b) 88 8

7 Day 5 Decimals and Percentages P a g e 7 c) 8 8 d)

8 Day 5 Decimals and Percentages P a g e 8 Using Mental Images of Decimals Imagine each number on decimal grids. Name each number, then write them in order from smallest to largest. 8 Name three decimals less than one but greater than. Describe what they would look like on a 10x10 grid. How do you know that they are greater than? Imagine each number on a 10x10 grid. Which number is the smallest? How do you know? 6 Name three decimals equal to. Describe what they would look like in a 10x10 grid. How do you know that they are equal to? 6 8

9 Day 5 Decimals and Percentages P a g e 9 Addition and Subtraction of Decimals with 10x10 Grids Solve each problem using the grid. Record the problem with symbols showing the final answer. Problem Estimate Picture Symbols than one or less than one? 37-hundredths and 3-tenths more than onehalf or less than one-half? than one or less than one?

10 Day 5 Decimals and Percentages P a g e 10 Problem Estimate Picture Symbols 15-hundredths minus 7-hundredths than onehalf or less than one-half? than one or less than one? than onehalf or less than one-half? than one or less than one?

11 Day 5 Decimals and Percentages P a g e 11 Problem Estimate Picture Symbols 99-hundredths 88-hundredths than onehalf or less than one-half? than one or less than one? 57-hundredths minus 3-tenths than onehalf or less than one-half? than one or less than one?

12 Day 5 Decimals and Percentages P a g e 12 II. Building Meaning for Percentages using Grids, Number Lines, Fraction Equivalencies, and Unit Rate Which square has a larger portion shaded? Which square has a larger portion shaded?

13 Day 5 Decimals and Percentages P a g e 13 Grid A Grid B

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18 Day 5 Decimals and Percentages P a g e 18 III. What I Used To Do A sofa originally costs $800. The sofa is discounted 40% off. What is the sale price? 40% of 800 is y There are 56 girls in the 8 th -grade honors math class. This accounts for 70% of the class. How many students are taking 8 th -grade honors math? 70% of k is 56 There are 50 middle school teachers in a staff development. 18 of them are 6 th -grade teachers. What percent of the teachers teach 6 th - grade? x% of 50 is 18

19 Day 5 Decimals and Percentages P a g e 19 IV. What Dan Does What is 35% of 800? V. What Singapore Math Does

20 Day 5 Decimals and Percentages P a g e 20 VI. Percentage Problems: Solving with Sketches and Diagrams A At a clearance sale, the price of a VCR was discounted 40%. The discounted price was $375. What was the original price? B The price of a large chocolate bar was increased by 20%. It now costs $1.50. What did it cost before the increase? C In a certain town, 16% of the population lives in apartment buildings. If 2800 people live in apartments, what is the town s population? D A telethon for a local charity raised $45,000. This was a 125% of the goal. What was the goal? E Sandra sold 40% more Campfire Girls cookies than her sister. Together they solved $408 worth. How much did each girl sell? F A length of string that is 180-cm long is cut into 3 pieces. The second piece is 25% longer than the first. The third piece is 25% shorter than the first. How long is each piece?

21 Day 5 Decimals and Percentages P a g e 21 G Jane paid $17.49 for a book, including tax. If the sales tax is 6%, what was the price without the tax? H If 5 gallons of a mixture with a 30% concentration of ammonia is added to 20 gallons of water, what is the concentration of ammonia? I The population of Multnomah County is 20% of the population of Oregon. Also, 65% of the population of Multnomah County is within the Portland city limits. What percent of the Oregon population is in Multnomah County within the Portland city limits? J A car is sold with a $1000 rebate and a 15% discount. Which gives a better discount: (a) rebate and then discount the price after the rebate, (b) discount the price and then rebate?