This pdf cover the following topics: representing Decimals and Place value Graph Decimals on a Number Line Comparing and ordering Decimals decimal operations
1. DECIMALS PRACTICE BOOKLET TABLE OF CONTENTS SKILL 1: Representing Decimals and Place Value .........................................................................3 SKILL 2: Graph Decimals on a Number Line ................................................................................5 SKILL 3: Comparing Decimals .......................................................................................................7 SKILL 4: Ordering Decimals...........................................................................................................9 SKILL 5: Decimal Addition ..........................................................................................................11 SKILL 6: Decimal Subtraction .............................................................................................................. 12 SKILL 7: Estimate Decimal Sums and Differences ........................................................................... 13 SKILL 8: Unit 2 Review 1 .............................................................................................................14 SKILL 9: Decimal Multiplication by Whole Numbers .................................................................15 SKILL 10: Decimal Multiplication by Tenths ...............................................................................17 SKILL 11: Decimal Multiplication by Hundredths .......................................................................19 SKILL 12: Decimal Multiplication and Area Model .....................................................................21 SKILL 13: Decimal Multiplication by Power of 10 ......................................................................23 SKILL 14: Estimate Decimal Products..........................................................................................24 SKILL 15: Unit 2 Review 2 ...........................................................................................................25 SKILL16: Decimal Division with Whole Numbers ......................................................................26 SKILL17: Decimal Division by Tenths .........................................................................................28 SKILL18: Decimal Division by Hundredths .................................................................................30 SKILL 19: Decimal Division and Area Model ..............................................................................32 SKILL 20: Decimal Division by Power of 10 ...............................................................................34 SKILL 21: Estimate Decimal Quotients ........................................................................................36 SKILL 22: Unit 2 Review 3 ...........................................................................................................37 SKILL 23: Impact of Multiply/Divide by 0 & above ....................................................................38 SKILL 24: Decimal Word Problems .............................................................................................40 SKILL 25: Unit 2 Review 4 ...........................................................................................................43 SELECTED ANSWERS ...............................................................................................................44 EXTENSION ACTIVITIES ..........................................................................................................48 Mr. Walz 6th Grade Math Page 1
2. HOW TO USE THIS UNIT BOOKLET This Unit 2 – Decimals Practice Booklet contains the worksheet practice sets that need to be completed throughout the unit. 1) Read through the notes and examples for each skill also using your entrance tasks as a reference. 2) Complete the first practice set ON ANOTHER SHEET OF PAPER WITH THE APPROPRIATE HEADING copying each problem and showing ALL WORK. 3) When finished, self correct the selected answers using the back of this booklet. Once the practice set is complete and corrected, turn into Mr. Walz and then you can test on that skill. a. If you meet standard (pass) on that skill, move on to the next skill. b. If you do not meet standard (do not pass), complete practice set #2 for that skill before you can retest. i. It is key to practice doing each skill correctly and showing all work since that is the only way to meet the standard. 4) Extension activities are available in the back of this booklet for students to apply these skills in real-world situations and creative explorations. Students can complete these activities at any point when they are ahead of the skill that the class is working on. HOW FINAL GRADE IS CALCULATED 1) Student grades are based on the percentage of skills passed (the total number of Washington State Math Standards met). There are 25 skills in Unit 2 that need to be passed. These 25 skills will be added to the previous skills from other units. a. Example: Student A tried 25 skills but only met standard on 19. The final grade would be 76% (19 ÷ 25). APPROPRIATE HEADING SKILL/PRACTICE SET NAME STANDARD NUMBER PERIOD DATE 1) 2) 3) Make sure to copy each problem on to your paper and SHOW ALL WORK!!! Mr. Walz 6th Grade Math Page 2
3. SKILL 1: Representing Decimals and Place Value Standard 4.2.A OBJECTIVE: Represent decimals through thousandths. DECIMALS represent parts of a whole number and are referred to as rational numbers. Place value is the value of where a digit is in a decimal number. Standard form is the usual way to write a decimal, such as 3.52. Word form is writing the decimals in words, such as three and fifty-two hundredths. EXAMPLE A: Name the place value of the underlined digit. 14.234 3 is in the hundredths place value EXAMPLE B: Write the decimal is word form. 14.234 Fourteen and two hundred thirty-four thousandths EXAMPLE C: Write the decimal is standard form. Nine and fifteen hundredths ***HINTS: The decimal point is represented by the word AND. Treat the decimal part as its own number and add the place value of the final digit.*** ----------------------------------------------------------------------------------------------------------------------------- ------------ SKILL 1: PRACTICE SET #1 Name the place value of the underlined digit 1) 3.45 2) 56.789 3) 332.7 4) 17.768 5) 5.67 6) 8.745 Write the decimal is word form. 7) 2.3 8) 18.76 9) 20.657 10) 1.85 Write the decimal is standard form. 11) five and thirty-five hundredths 12) ten and three tenths 13) one hundred fifteen and fifteen thousandths 14) fifty-two and eight tenths 15) two hundred seventy and seventy-six hundredths 16) one and two tenths Mr. Walz 6th Grade Math Page 3
4. SKILL 1: PRACTICE SET #2 Name the place value of the underlined digit 1) 45.6 2) 87.34 3) 324.56 4) 2.329 5) 64.389 6) 8.34 Write the decimal is word form. 7) 4.7 8) 22.89 9) 45.329 10) 0.27 Write the decimal is standard form. 11) sixty-seven and one hundred three thousandths 12) seven and twenty-five hundredths 13) two hundred ten and thirty-six hundredths 14) ten and five tenths 15) two and three hundred forty-eight thousandths 16) seventy-two and two tenths SKILL 1: PRACTICE SET #3 Name the place value of the underlined digit 1) 56.23 2) 72.198 3) 2.43 4) 4.876 5) 332.87 6) 94.1 Write the decimal is word form. 7) 5.89 8) 37.65 9) 2.768 10) 46.1 Write the decimal is standard form. 11) twenty-five and one tenth 12) thirty and sixty-two hundredths 13) twenty-four and one hundred nineteen thousandths 14) ninety-nine and nine hundredths 15) five and eight tenths 16) thirteen and thirteen thousandths Mr. Walz 6th Grade Math Page 4
5. SKILL 2: Graph Decimals on a Number Line Standard 4.2.A OBJECTIVE: Represent decimals on a number line. A number line shows you a "picture view" of what a number is. You can visually see where your numbers are, and what other numbers are nearby. EXAMPLE: Place 3.2 and 5.67 on a number line. 1) Figure out the whole numbers that are above and below the decimals numbers given. a. 3.2 is between 3 and 4; 5.67 is between 5 and 6 2) Draw a line with arrows on the ends to indicate that it goes on forever. 3) Make little marks to indicate where the whole numbers are and label them (make sure there are enough spaces to show all the numbers that you are given to graph) 4) Put a dark circle on the decimal numbers that are given by estimating using benchmarks such as one-half. a. 3.2 is closer to 3; 5.67 is closer to 6 ***The trick with decimals is to make sure they are correctly between the whole numbers and estimate which number they would be the closest to. Also, remember from before, you do not need to start at 0. Just show a few numbers greater and less than the numbers you need to graph. *** SKILL 2: PRACTICE SET #1 Draw a number line for each problem and place the numbers on it. 1) Graph 5.3 2) Graph 3.8 3) Graph 9.75 4) Graph 11.12 5) Graph 14.9 6) Graph 4.45 7) Graph 19.02 8) Graph 23.8 9) Graph 34.5 and 36.1 10) Graph 87.98 and 88.23 11) Graph 67.4 and 67.9 12) Graph 9.23 and 11.5 Mr. Walz 6th Grade Math Page 5
6. SKILL 2: PRACTICE SET #2 Draw a number line for each problem and place the numbers on it. 1) Graph 10.6 2) Graph 4.2 3) Graph 8.41 4) Graph 17.67 5) Graph 22.7 6) Graph 35.8 7) Graph 21.07 8) Graph 65.48 9) Graph 102.5 and 104.1 10) Graph 9.97 and 11.23 11) Graph 78.6 and 79.1 12) Graph 24.7 and 25.3 SKILL 2: PRACTICE SET #3 Draw a number line for each problem and place the numbers on it. 1) Graph 4.12 2) Graph 6.47 3) Graph 11.95 4) Graph 5.7 5) Graph 19.46 6) Graph 42.13 7) Graph 73.8 8) Graph 73.2 9) Graph 2.34 and 4.8 10) Graph 16.34 and 18.13 11) Graph 82.5 and 84.1 12) Graph 35.8 and 36.3 Mr. Walz 6th Grade Math Page 6
7. SKILL 3: Comparing Decimals Standard 6.1.A OBJECTIVE: Compare non-negative decimals using the number line, lists, and the symbols <, >, or =. ----------------------------------------------------------------------------------------------------------------------------- ---------- SKILL 3: PRACTICE SET #1 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) Mr. Walz 6th Grade Math Page 7
8. SKILL 3: PRACTICE SET #2 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) SKILL 3: PRACTICE SET #3 2) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) Mr. Walz 6th Grade Math Page 8
9. SKILL 4: Ordering Decimals Standard 6.1.A OBJECTIVE: Order non-negative decimals using the number line/lists. Another method to order decimals is to graph them on a number line. Here is the example above using the number line method. 4.0073 4.73 4 4.073 3 4 5 6 The order from least to greatest is 4, 4.0073, 4.073, 4.73 ***Read the directions carefully to make sure you are listing them in the order that is asked SKILL 4: PRACTICE SET #1 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) Mr. Walz 6th Grade Math Page 9
10. 13) 14) SKILL 4: PRACTICE SET #2 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) SKILL 4: PRACTICE SET #3 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) Mr. Walz 6th Grade Math Page 10
11. SKILL 5: Decimal Addition Standard 5.2.F OBJECTIVE: Fluently and accurately add decimals 1. Line up the decimal points 2. Add digits in the same place value position (think addition of whole numbers) 3. Decimal drops straight down to final answer. Find the sum. SKILL 5: PRACTICE SET #1 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) SKILL 5: PRACTICE SET #2 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) SKILL 5: PRACTICE SET #3 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) Mr. Walz 6th Grade Math Page 11
12. SKILL 6: Decimal Subtraction Standard 5.2.F OBJECTIVE: Fluently and accurately subtract decimals 1. Line up the decimal points 2. Subtract digits in the same place value position (think subtraction of whole numbers) 3. Decimal drops straight down to final answer. Find the difference. SKILL 6: PRACTICE SET #1 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) SKILL 6: PRACTICE SET #2 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) SKILL 6: PRACTICE SET #3 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) Mr. Walz 6th Grade Math Page 12
13. SKILL 7: Estimate Decimal Sums and Differences Standard 5.2.G OBJECTIVE: Estimate sums and differences of decimals to approximate solutions to problems and determine reasonableness of answers. ***HINT: Add or subtract the whole numbers together and ignore the decimal portion to estimate. Estimation is used to check the reasonableness of your final answer. It is used in word problems too.*** Estimate each sum or difference using front-end estimation. Since it’s an estimation there should be no exact answer given. SKILL 7: PRACTICE SET #1 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) SKILL #7: PRACTICE SET #2 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) SKILL #7: PRACTICE SET #3 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) Mr. Walz 6th Grade Math Page 13
14. SKILL 8: Unit 2 Review 1 This is a review of all the standards you have worked on so far this year. Use your entrance tasks to help if needed. SKILL 8: PRACTICE SET #1 1) Simplify. 2) Graph 8.21 on a number line 3) Evaluate. 20 1.2 12.4 x 13.4; x 7.89 4) Graph 11.67 on a number line 5) Simplify. 6) Evaluate. 5 3 4.23 y 8.4; y 19.23 7) Simplify. 8) Evaluate. 4.3 2.5 9.45 12.12 a; a 4.87 Multiply. 145 9 10) Multiply. 23 16 SKILL 8: PRACTICE SET #2 1) Simplify. 2) Graph 14.32 on a number line 3) Evaluate. 14.23 34.58 x 6.7; x 9.4 4) Graph 0.45 on a number line 5) Simplify. 6) Evaluate. 6.7 2 3 45.34 t; t 32.89 7) Simplify. 8) Evaluate. 5.7 4.3 2.19 16.3 b c; b 4.32; c 9.78 9) Multiply. 10) Multiply. 21 45 56 32 SKILL 8: PRACTICE SET #3 1) Simplify. 2) Graph 54.7 on a number line 3) Evaluate. 57.68 32.91 x 2.4; x 11.23 4) Graph 2.2 on a number line 5) Simplify. 6) Evaluate. 15.2 2 4 6.43 c; c 13.4 7) Simplify. 8) Evaluate. 12.8 4.5 6.8 t 4.3 5.9; t 19.2 9) Multiply. 10) Multiply. 243 7 62 48 Mr. Walz 6th Grade Math Page 14
15. SKILL 9: Decimal Multiplication by Whole Numbers Standard 6.1.F OBJECTIVE: Fluently and accurately multiply non-negative decimals. 1. Set-up multiplication problem ignoring all the decimal points. 2. Complete long multiplication (Unit 1; Skill 3). 3. Count the number of decimals digits (those to the right of the decimal point) in both numbers. 4. Move decimals that many places to the left in final answer (you made need to add zeroes to complete this). EXAMPLE A: Calculate 0.0005 × 8. EXAMPLE B: Calculate 47.4 × 45. Mr. Walz 6th Grade Math Page 15
16. SKILL 9: PRACTICE SET #1 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) SKILL 9: PRACTICE SET #2 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) SKILL 9: PRACTICE SET #3 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) Mr. Walz 6th Grade Math Page 16
17. SKILL 10: Decimal Multiplication by Tenths Standard 6.1.F OBJECTIVE: Fluently and accurately multiply non-negative decimals. 1. Set-up multiplication problem ignoring all the decimal points. 2. Complete long multiplication (Unit 1; Skill 3). 3. Count the number of decimals digits (those to the right of the decimal point) in both numbers. 4. Move decimals that many places to the left in final answer (you made need to add zeroes to complete this). EXAMPLE A: Calculate 0.8 × 0.9. EXAMPLE B: Calculate 0.78 × 0.5. EXAMPLE C: SKILL 10: PRACTICE SET #1 1) 2) 3) Mr. Walz 6th Grade Math Page 17
18. 4) 5) 6) 7) 8) 9) 10) 11) 12) 0.8 × 0.9 SKILL 10: PRACTICE SET #2 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) SKILL 10: PRACTICE SET #3 1) 2) 3) 4) 5) 6) 7) 8) 9) Mr. Walz 6th Grade Math Page 18
19. SKILL 11: Decimal Multiplication by Hundredths Standard 6.1.F OBJECTIVE: Fluently and accurately multiply non-negative decimals. 1. Set-up multiplication problem ignoring all the decimal points. 2. Complete long multiplication (Unit 1; Skill 3). 3. Count the number of decimals digits (those to the right of the decimal point) in both numbers. 4. Move decimals that many places to the left in final answer (you made need to add zeroes to complete this). EXAMPLE A: Calculate 3.24 × 0.67. EXAMPLE B: Calculate 2.731 × 0.32 2.731 3 decimal places 0.32 2 decimal places 5462 81930 0.87392 5 decimal places in the answer Thus, the final answer is 0.87392 SKILL 11: PRACTICE SET #1 1) 2) 3) 4) 5) 6) Mr. Walz 6th Grade Math Page 19
20. 7) 8) 9) 10) 11) 12) SKILL 11: PRACTICE SET #2 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) SKILL 11: PRACTICE SET #3 1) 2) 3) 4) 5) 6) 7) 8) 9) Mr. Walz 6th Grade Math Page 20
21. SKILL 12: Decimal Multiplication and Area Model Standard 6.1.B OBJECTIVE: Represent multiplication decimals using area models and the number line, and connect each representation to the related equation.. EXAMPLE A: 3 x 0.2 1) 0.2 represents 2 bars out of 10 2) 3 x 0.2 represents 2 bars shaded 3 times 3) So, 3 x 0.2 = 0.6 because, with 3 groups of 0.2, six-tenths of a whole (0.6) is shaded. EXAMPLE B: 0.2 x 0.3 1) Represent the number 0.2 (2 bars shaded out of 10) 2) Cut 0.2 into tenths (ten equal parts) 3) Shade three of the tenths to show 0.3 4) Since each small square is 0.01 of the whole and six of the small squares are marked, the diagonally marked section represents 0.06, so 0.3 x 0.2 = 0.06. SKILL 12: PRACTICE SET #1 Complete the problems using the area model already provided. 0.4 0.3 2) 0 .2 0 . 5 Copy and complete the area model to represent each problem. 0 .7 0 .6 4) 0.1 0.5 0 .4 2 6) 0 .5 0 . 6 MULTIPLY DECIMALS USING ANY WAY YOU HAVE LEARNED. 0.45 3 8) 0.5 0.12 9) 10) 0 .8 2 0 .2 4 Mr. Walz 6th Grade Math Page 21
22. 11) 0.6 0.75 12) 0 .9 5 SKILL 12: PRACTICE SET #2 Complete the problems using the area model already provided. 0 .9 0 . 7 2) 0.4 0.5 Copy and complete the area model to represent each problem. 0 .2 0 . 3 4) 0 .1 0 .8 0 .3 3 6) 0 .5 0 . 3 MULTIPLY DECIMALS USING ANY WAY YOU HAVE LEARNED. 0.62 3 8) 0.7 0.26 0.9 4 10) 0 .1 7 11) 0.5 0.34 12) 0.43 6 SKILL 12: PRACTICE SET #3 Complete the problems using the area model already provided. 0 .2 0 . 3 2) 0 .3 0 .3 MULTIPLY DECIMALS USING ANY WAY YOU HAVE LEARNED. 3) 4) 0.7 0.4 0 .1 0 .2 5) 0.2 4 6) 0.5 0.9 0.25 5 8) 0.3 1.4 0.8 0.39 10) 0.4 7 Mr. Walz 6th Grade Math Page 22
23. SKILL 13: Decimal Multiplication by Power of 10 Standard 6.1.E OBJECTIVE:Multiply decimals by 1000, 100, 10, 1, 0.1, 0.01, & 0.001. If you are multiplying by 10, 100 or 1000… then move the decimal to the RIGHT the same number as there are zeroes. If you are multiplying by 0.1, 0.01, or 0.001… then move the decimal to the LEFT the same number as there are zeroes. WHAT HAPPENED TO EXAMPLE ANSWER THE DECIMAL? EXAMPLE A: 2.1 x 10 21 moved one place right 2.1 x 100 210 moved two places right 2.1 x 1000 2100 moved three places right 2.1 x 0.1 .21 moved one place left 2.1 x 0.01 .021 moved two places left 2.1 x 0.001 .0021 moved three places left Multiply using the rules for powers of 10. SKILL 13: PRACTICE SET #1 1) 2) 3) 4) 5) 6) 7) 8) 9.4 0.1 9) 2.4 0.01 10) 0.4 0.1 11) 96.23 0.001 12) 137 0.01 13) 0.697 0.1 14) SKILL 13: PRACTICE SET #2 1) 82.3 100 2) 0.31 10 3) 8.3 0.1 4) 724.3 0.001 5) 0.812 1000 6) 12.5 0.01 7) 3.9 0.1 8) 0.75 10 9) 19.34 0.01 10) 12 100 11) 214.2 0.001 12) 4.32 1000 13) 0.845 100 14) 31.4 0.1 SKILL 13: PRACTICE SET #3 13.2 0.1 2) 16.8 10 3) 1.5 100 19.43 1000 5) 4.2 0.01 6) 0.5 0.001 7) 8) 9) 0.92 100 0.3 1000 7.1 0.01 Mr. Walz 6th Grade Math Page 23
24. SKILL 14: Estimate Decimal Products Standard 6.1.C OBJECTIVE: Estimate products of decimals. EXAMPLE: 8.345 x 4.983 8.345 rounds to 8; 4.983 rounds to 5 Rounding the factors gives 8 x 5 = 40 Therefore, a good estimate of the product of the decimal numbers 8.345 and 4.983 is 40. ***HINT: Use the tenths digit to round your whole number. If it is 4 or less, keep the whole number the same. If it is 5 or above, increase the whole number by 1. Estimation is used to check the reasonableness of your final answer. It is used in word problems too.*** Estimate each product using rounding. Since it’s an estimation there should be no exact answer given. SKILL 14: PRACTICE SET #1 1) 7.63 x 9.98 2) 2.33 x 4 3) 3.1259 x 49.8783 4) 1.69 x9 5) 6) 7) 8) 9) 10) 11) 12) 13) SKILL 14: PRACTICE SET #2 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) SKILL 14: PRACTICE SET #3 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) Mr. Walz 6th Grade Math Page 24
25. SKILL 15: Unit 2 Review 2 This is a review of all the standards you have worked on so far this year. Use your entrance tasks to help if needed. SKILL 15: PRACTICE SET #1 1) Simplify. 2) Compare. 3) Evaluate. 2.3 0.7 1.2 45.67 45.76 3x; x 4.3 4) Compare. 5) Simplify. 6) Evaluate. 0.253 0.243 5.2 5 7.34 y 4.3; y 0.4 7) Simplify. 8) Evaluate. (8.12 3.23) 100 12.12a; a 0.001 9) Divide. 9 333 10) Divide. 360 15 SKILL 15: PRACTICE SET #2 1) Simplify. 2) Compare. 3) Evaluate. 1.4 0.6 4.7 0.59 0.594 5x; x 12.3 4) Compare. 5) Simplify. 6) Evaluate. 0.358 0.321 21.6 9 6.43 y 4.8; y 3.2 7) Simplify. 8) Evaluate. (10.4 3.76) 0.001 42.34a; a 100 9) Divide. 10) Divide. 12 576 504 8 SKILL 15: PRACTICE SET #3 1) Simplify. 2) Compare. 3) Evaluate. 7.5 1.3 2.59 2.6 2.60 1.4 x; x 0.34 4) Compare. 5) Simplify. 6) Evaluate. 1.45 1.32 7.2 4 4.65 y 0.03; y 253.7 7) Simplify. 8) Evaluate. (21.4 19.24) 0.1 0.0843a; a 1000 9) Divide. 10) Divide. 5 5380 990 22 Mr. Walz 6th Grade Math Page 25
26. SKILL16: Decimal Division with Whole Numbers Standard 6.1.F OBJECTIVE: Fluently and accurately divide non-negative decimals. 1. Set-up division problem. 2. Complete long division (Unit 1; Skill 4). 3. Place the decimal in the quotient above the decimal in the dividend (move it straight up into the answer) EXAMPLE A: EXAMPLE B: Mr. Walz 6th Grade Math Page 26
28. SKILL17: Decimal Division by Tenths Standard 6.1.F OBJECTIVE: Fluently and accurately divide non-negative decimals. 1. Set-up division problem. 2. Move decimal one place to the right in the divisor and dividend. 3. Place decimal straight above in quotient. 4. Complete long division (Unit 1; Skill 4). EXAMPLE A: EXAMPLE B: Move the decimals in both the numbers to the right the same number of times. Complete long division. Mr. Walz 6th Grade Math Page 28
30. SKILL18: Decimal Division by Hundredths Standard 6.1.F OBJECTIVE: Fluently and accurately divide non-negative decimals. 1. Set-up division problem. 2. Move decimal two places to the right in the divisor and dividend. 3. Place decimal straight above in quotient. 4. Complete long division (Unit 1; Skill 4). EXAMPLE A: SKILL 18: PRACTICE SET #1 1) 2) 3) 4) 1.44 0.03 5) 1.96 0.04 6) 0.06 0.06 0.42 0.07 8) 0.0325 0.25 9) 0.9 0.02 10) 0.0184 0.08 11) 12) 0.882 0.14 Mr. Walz 6th Grade Math Page 30
32. SKILL 19: Decimal Division and Area Model Standard 6.1.B OBJECTIVE: Represent division of decimals using area models and the number line, and connect each representation to the related equation.. EXAMPLE A: SKILL 19: PRACTICE SET #1 Complete the problems using the area model already provided. 1) 0.2 0.4 2) 0.12 0.3 Copy and complete the area model to represent each problem. 3) 4) 0.24 0.8 0.4 0.5 0.32 0.8 6) 0.45 0.9 MULTIPLY DECIMALS USING ANY WAY YOU HAVE LEARNED. 7) 0.45 0.3 8) 0.6 0.2 10) 0.2 4 0.8 2 0.55 0.5 12) 0.25 5 Mr. Walz 6th Grade Math Page 32
33. SKILL 19: PRACTICE SET #1 Complete the problems using the area model already provided. 1) 0.25 0.5 2) 0.2 0.2 Copy and complete the area model to represent each problem. 3) 4) 0.36 0.3 0.45 0.5 0.18 0.9 6) 0.49 0.7 MULTIPLY DECIMALS USING ANY WAY YOU HAVE LEARNED. 7) 0.28 0.2 8) 0.48 0.4 9) 10) 0.7 5 0.6 3 0.66 0.6 12) 0.1 2 SKILL 19: PRACTICE SET #1 Complete the problems using the area model already provided. 1) 0.18 0.2 2) 0.35 0.7 MULTIPLY DECIMALS USING ANY WAY YOU HAVE LEARNED. 3) 0.21 0.7 4) 0.8 0.5 0.3 3 6) 0.6 6 0.64 0.8 8) 0.72 0.8 Mr. Walz 6th Grade Math Page 33
34. SKILL 20: Decimal Division by Power of 10 Standard 6.1.E OBJECTIVE: Divide decimals by 1000, 100, 10, 1, 0.1, 0.01,and 0.001. If you are dividing by 10, 100 or 1000… then move the decimal to the LEFT the same number as there are zeroes. If you are dividing by 0.1, 0.01, or 0.001… then move the decimal to the RIGHT the same number as there are zeroes. EXAMPLE ANSWER WHAT HAPPENED TO THE DECIMAL? 4.2 ÷ 10 0.42 moved one place left EXAMPLE A: 94.56 100 4.2 ÷ 100 0.042 moved two places left Since it is divided by 100, move decimal point two places to the left. 4.2 ÷ 1000 0.0042 moved three places left 4.2 ÷ 0.1 42 moved one place right 94.56 0.9456 4.2 ÷ 0.01 420 moved two places right 4.2 ÷ 0.001 4200 moved three places right Divide using the rules for powers of 10. SKILL 20: PRACTICE SET #1 11.3 100 2) 78.43 10 3) 123 1000 19.32 1000 5) 24.3 10 6) 9.4 100 9 .4 0 .1 8) 0.98 .01 9) 1.23 .001 0.4 0.1 11) 8.45 0.001 12) 14.8 0.1 0.697 10 14) 34.56 0.01 15) SKILL 20: PRACTICE SET #2 1) 2) 3) 4) 5) 6) Mr. Walz 6th Grade Math Page 34
35. 7) 8) 9) 10) 11) 12) 13) 14) 15) SKILL 20: PRACTICE SET #3 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) Mr. Walz 6th Grade Math Page 35
36. SKILL 21: Estimate Decimal Quotients Standard 6.1.C OBJECTIVE: Estimate quotients of decimals. 1. Round the divisor (what goes outside the box or given second) to the nearest whole number. 2. Round the dividend (what goes inside the box or given first) to the nearest number that the divisor can go evenly into 3. Divide. EXAMPLE: 42.345 ÷ 5.12 5.12 is the divisor and round to 5 42.345 is the dividend and this rounds to 40 since 5 can evenly divide 40 Therefore, a good estimate is 40 ÷ 5 which is 8. ***HINT: It may seem that you have to round the dividend a lot. That is ok because you want to be able to divide evenly. Estimation is used to check the reasonableness of your final answer. It is used in word problems too.*** Estimate each quotient using rounding. Since it’s an estimation there should be no exact answer given. SKILL 21: PRACTICE SET #1 1) 103.4 ÷ 9.98 2) 17.6 ÷ 4 3) 65.78 ÷ 7.12 4) 11.23 ÷9 5) 54.34 ÷ 4.8 6) 99.34 ÷ 11.2 7) 10.3 ÷ 1.6 8) 31.3 ÷ 3.4 9) 64.3 ÷ 11.83 10) 0.43 ÷ 0.9 11) 46.8 ÷ 14.7 12) 109.3 ÷ 9.1 13) 18.491 ÷ 5.7 SKILL 21: PRACTICE SET #2 1) 96.2 ÷ 10.8 2) 22.5 ÷ 3.2 3) 44.3 ÷ 14.68 4) 67.5 ÷8 5) 13.24 ÷ 2.12 6) 46.8 ÷ 4.91 7) 44.2 ÷ 11.31 8) 54.6 ÷ 7.19 9) 121.8 ÷ 25 10) 4.3 ÷ 0.9 11) 6.4 ÷ 0.82 12) 115.72 ÷ 9.82 13) 27.3 ÷ 6.43 SKILL 21: PRACTICE SET #3 1) 76.9 ÷ 5.23 2) 31.8 ÷ 8.2 3) 96.5 ÷ 8 4) 13.5 ÷ 12.8 5) 74.1 ÷ 6.21 6) 82.9 ÷ 10.87 7) 105.3 ÷ 10 8) 73.1 ÷ 24.81 9) 53.7 ÷ 7.2 10) 31.98 ÷ 0.58 11) 4.82 ÷ 0.92 12) 92.4 ÷ 9.1 13) 23.1 ÷ 5.76 Mr. Walz 6th Grade Math Page 36
37. SKILL 22: Unit 2 Review 3 This is a review of all the standards you have worked on so far this year. Use your entrance tasks to help if needed. SKILL 22: PRACTICE SET #1 1) Simplify. 2) Order from least to greatest. 3) Evaluate. 0.24 0.4 1.4 5 45.67,45.64,45.6 y 0.08; y 1.304 4) Simplify. 5) Simplify. 6) Order from least to greatest. 6.36 1.2 1.46 0.4 0.3 0.2 0.78,0.65,0.68,0.69 7) Simplify. 8) Evaluate. (18.3 2.34) 1.2 14.4 x; x 0.9 9) Estimate. 13.45 18.123 10) Estimate. 12.234 9.89 SKILL 22: PRACTICE SET #2 1) Simplify. 2) Order from least to greatest. 3) Evaluate. 1.02 0.2 7.34 0.6,0.54,0.53 y 0.3; y 2.793 4) Simplify. 5) Simplify. 6) Order from least to greatest. 15.3 1.1 14.8 2.7 0.5 0.03 0.9,0.4,1.1,1.4 7) Simplify. 8) Evaluate. (4.6 8.23) 0.6 x 0.07; x 0.0161 9) Estimate. 72.3 1.52 10) Estimate. 16.78 3.1 SKILL 22: PRACTICE SET #3 1) Simplify. 2) Order from least to greatest. 3) Evaluate. 0.24 0.02 0.7 13 5.7,5.79,5.73 y 12; y 14.88 4) Simplify. 5) Simplify. 6) Order from least to greatest. 0.45 2.7 0.954 3.132 0.04 2.6 4.2,4.12,4.32 7) Simplify. 8) Evaluate. (9.7 6.28) 0.2 30.72 x; x 0.6 9) Estimate. 24.87 21.43 10) Estimate. 7 .6 5 . 9 Mr. Walz 6th Grade Math Page 37
38. SKILL 23: Impact of Multiply/Divide by 0 & above Standard 6.1.G OBJECTIVE: Describe the effect of multiplying or dividing a number by one, by zero, by a number between zero and one, and by a number greater than one. MULTIPLICATION RULES EXAMPLE ANSWER 5x0 0 If you multiply any number by 0, then the product ALWAYS equals 0. 5x1 5 If you multiply any number by 1, then the product ALWAYS equals that number. If you multiply any number by a number LESS than 1 but GREATER than 0, then the 5 x 0.5 2.5 product ALWAYS equals a smaller number. If you multiply any number by a number GREATER than 1, then the product 5x2 10 ALWAYS equals a larger number. EXAMPLE A: Describe what happens when you multiply 9 times 0.3. The product will be a smaller number than 9. DIVISION RULES EXAMPLE ANSWER If you divide any number by 0, then the quotient ALWAYS equals no solution because 5÷0 No Solution you cannot divide by 0 ever. 5÷1 5 If you divide any number by 1, then the quotient ALWAYS equals that number. If you divide any number by a number LESS than 1 but GREATER than 0, then the 5 ÷ 0.5 10 quotient ALWAYS equals a larger number. If you divide any number by a number GREATER than 1, then the quotient ALWAYS 5÷2 2.5 equals a smaller number. EXAMPLE B: Describe what happens when you divide 9 by 1. The quotient will equal 9. Describe what happens in each of the following problem. Do not find the actual answer. SKILL 23: PRACTICE SET #1 1) 15 3 2) 25 0.25 3) 123 1 4) 12 0.76 5) 19 0 6) 9.4 1 7) 14 0 8) 7 .5 4 9) 18 0.2 10) 0.4 1 11) 8.45 5 12) 17 0 Mr. Walz 6th Grade Math Page 38
40. SKILL 24: Decimal Word Problems Standard 6.1.H OBJECTIVE: Solve single- and multi-step word problems involving operations with decimals and verify the solutions. -- List numbers given with label and what you are trying to answer 4. Answer – Separate your final answer and label appropriately; check its reasonableness Understanding: Pins cost $3.80; Gives $20; Change? Strategy: Subtraction “how much change” Solution: 20.00 – 3.80 16.20 Answer: $16.20 is the change Sam will get back Read each problem. Use the four problem solving steps to solve each problem. SKILL 24: PRACTICE SET #1 1) 2) 3) 4) Mr. Walz 6th Grade Math Page 40
41. 5) 6) SKILL 24: PRACTICE SET #2 1) 2) 3) 4) 5) 6) Mr. Walz 6th Grade Math Page 41
42. SKILL 24: PRACTICE SET #3 1) 2) 3) 4) 5) 6) Mr. Walz 6th Grade Math Page 42
43. SKILL 25: Unit 2 Review 4 This is a review of all the standards you have worked on so far this year. Use your entrance tasks to help if needed. SKILL 25: PRACTICE SET #1 1) 2) 3) 4) 5) 6) 7) 45.73 2 8) Estimate. 9) 10) Estimate. 12.4 8.75 18.65 2.7 SKILL 25: PRACTICE SET #2 1) 2) 3) 4) 5) 3.12 8 6) 7) 8) 9) Estimate. 58.6 34.9 10) Estimate. 97.6 10.24 SKILL 25: PRACTICE SET #3 1) 2) 3) 4) 5) 32.48 4 6) 7) 8) 9) Estimate. 24.76 21.98 10) Estimate. 53.1 4.87 Mr. Walz 6th Grade Math Page 43
44. ANSWER KEY – Answers to selected questions from each problem set. SKILL 1: Representing Decimals and Place Value Practice Set #1 Practice Set #2 Practice Set #3 3) tens 3) hundredths 3) tenths 6) hundredths 6) tenths 6) tenths 9) twenty and six hundred 9) forty-five and three 9) two and seven hundred fifty-seven thousandths hundred twenty-nine sixty-eight thousandths 12) 10.3 thousandths 12) 30.62 12) 7.25 SKILL 2: Graph Decimals on a Number Line No answers available for this skill. SKILL 3: Comparing Decimals Practice Set #1 Practice Set #2 Practice Set #3 3) < 3) < 3) > 6) = 6) < 6) = 9) < 9) > 9) < 12) < 12) < 12) < SKILL 4: Ordering Decimals Practice Set #1 Practice Set #2 Practice Set #3 3) 456.23, 456.37, 456.73, 3) 0.0002, 0.0012, 0.0022, 3) 1.06, 1.1, 1.3 465.32 0.0211 6) 2.2, 2.25, 3.1 6) 1.02, 1.25, 1.50, 1.52 6) 1.1, 1.90, 1.94 9) 6.5, 6.24, 6.20 9) 8.777, 8.77, 8.7, 8.07 9) 7.01, 6.93, 6.04 12) 8.7, 8.38, 8.15 12) 120.012, 12.12, 12.012, 12) 0.4, 0.1, 0.05 12.0012 SKILL 5: Decimal Addition Practice Set #1 Practice Set #2 Practice Set #3 3) 9.73 3) 138.8 3) 15.16 6) 10.435 6) 80.25 6) 84.07 9) 65.68 9) 9.41 9) 27.83 12) 41 12) 18.357 SKILL 6: Decimal Subtraction Practice Set #1 Practice Set #2 Practice Set #3 3) 0.0032 3) 17.8 3) 1.84 6) 182.745 6) 5.91 6) 6.93 9) 14.71 9) 6.91 9) 0.96 12) 12.3 12) 128.891 Mr. Walz 6th Grade Math Page 44
45. SKILL 7: Estimate Decimal Sums and Differences Practice Set #1 Practice Set #2 Practice Set #3 3) 9 3) 68 3) 823 6) 182 6) 38 6) 63 9) 65 9) 29 9) 3 12) 71 SKILL 8: Unit 2 Review 1 Practice Set #1 Practice Set #2 Practice Set #3 3) 21.29 3) 16.1 3) 8.83 6) 10.83 6) 12.45 6) 19.83 9) 1305 9) 945 9) 1701 SKILL 9: Decimal Multiplication by Whole Numbers Practice Set #1 Practice Set #2 Practice Set #3 3) 75.6 3) 4.024 3) 20.5 6) 4.8 6) 309 6) 42.24 9) 30.6 9) 283.8 9) 689.4 12) 1.7112 12) 59.5 SKILL 10: Decimal Multiplication by Tenths Practice Set #1 Practice Set #2 Practice Set #3 3) 3.696 3) 0.24 3) 0.32 6) 0.27 6) 0.603 6) 21.608 9) 0.098 9) 0.1842 9) 0.1788 12) 0.72 12) 0.1788 SKILL 11: Decimal Multiplication by Hundredths Practice Set #1 Practice Set #2 Practice Set #3 3) 0.0196 3) 0.0092 3) 0.022 6) 0.09708 6) 0.02108 6) 0.0162 9) 0.0042 9) 0.01152 9) 0.00648 12) 0.0104 12) 0.044892 SKILL 12: Decimal Multiplication and Area Model Practice Set #1 Practice Set #2 Practice Set #3 9) 1.6 9) 3.6 6) 0.45 12) 4.5 12) 2.58 9) 0.312 SKILL 13: Decimal Multiplication by Power of 10 Practice Set #1 Practice Set #2 Practice Set #3 3) 5200 3) 0.83 3) 150 6) 423 6) 0.125 6) 0.0005 9) 0.024 9) 0.1934 9) 0.071 12) 1.37 12) 4320 Mr. Walz 6th Grade Math Page 45
46. SKILL 14: Estimate Decimal Products Practice Set #1 Practice Set #2 Practice Set #3 3) 150 3) 0 3) 27 6) 3 6) 66 6) 96 9) 221 9) 0 9) 36 12) 14 12) 1 SKILL 15: Unit 2 Review 2 Practice Set #1 Practice Set #2 Practice Set #3 3) 12.9 3) 61.5 3) 0.476 6) 1.72 6) 15.36 6) 7.611 9) 37 9) 48 9) 1076 SKILL16: Decimal Division with Whole Numbers Practice Set #1 Practice Set #2 Practice Set #3 3) 0.9 3) 52.3 3) 0.057 6) 0.812 6) 491.8 6) 22.865 9) 1.5 9) 19.56 9) 64.3 12) 7.62 12) 0.024 12) 8.12 SKILL17: Decimal Division by Tenths Practice Set #1 Practice Set #2 Practice Set #3 3) 51.2 3) 0.36 3) 0.23 6) 97.3 6) 0.686 6) 25 9) 4.3 9) 71 9) 8.2 12) 4.5 12) 3 12) 18 SKILL18: Decimal Division by Hundredths Practice Set #1 Practice Set #2 Practice Set #3 3) 7.5 3) 61 3) 6 6) 1 6) 8.1 6) 6.2 9) 45 9) 8.7 9) 64 12) 6.3 12) 0.52 12) 41 SKILL 19: Decimal Division and Area Model Practice Set #1 Practice Set #2 Practice Set #3 9) 0.4 9) 0.2 3) 0.3 12) 0.05 12) 0.05 6) 0.1 SKILL 20: Decimal Division by Power of 10 Practice Set #1 Practice Set #2 Practice Set #3 3) 0.123 3) 0.1247 3) 5 6) 0.094 6) 0.08 6) 23 9) 1230 9) 0.0026 9) 35.91 12) 148 12) 0.913 12) 0.083 Mr. Walz 6th Grade Math Page 46
47. SKILL 21: Estimate Decimal Quotients Practice Set #1 Practice Set #2 Practice Set #3 3) 9 3) 3 3) 12 6) 9 6) 9 6) 8 9) 5 9) 5 9) 8 12) 12 12) 12 12) 10 SKILL 22: Unit 2 Review 3 Practice Set #1 Practice Set #2 Practice Set #3 3) 16.3 3) 9.31 3) 1.24 6) 0.65, 0.68, 0.69, 0.78 6) 0.4, 0.9, 1.1, 1.4 6) 4.12, 4.2, 4.32 9) 31 9) 73 9) 45 SKILL 23: Impact of Multiply/Divide by 0 & above Practice Set #1 Practice Set #2 Practice Set #3 3) same number 3) same number 3) smaller number 6) same number 6) same number 6) larger number 9) larger number 9) larger number 9) same number 12) zero 12) zero 12) larger number SKILL 24: Decimal Word Problems Practice Set #1 Practice Set #2 Practice Set #3 3) 64.32 3) 465.84 3) 332.9 6) 44.1 6) 173.75 6) 33.75 SKILL 25: Unit 2 Review 4 Practice Set #1 Practice Set #2 Practice Set #3 3) 0.26 3) 0.13 3) 0.96 6) 12.21 6) 159.9 6) 204.5 9) 4 9) 24 9) 3 Mr. Walz 6th Grade Math Page 47
48. Unit 2 Extension Activity #1 – Vocabulary Make a booklet, flashcards, or list of the following vocabulary words. Use your worksheets, the dictionary, or web resources to find the definitions. The vocabulary list must include a definition and example. Unit 2 Vocabulary list: Decimal Estimate > < = When you turn this in, make sure your name is on it. It will be returned to you for you to use as study guides. Unit 2 Extension Activity #2 – Decimal Brochure Design a brochure that explains the how to add, subtract, multiply and divide The brochure must include: Explanation of how to add, subtract, multiply and divide decimals. One example problem for each operation When you turn this in, make sure your name is on it. Mr. Walz 6th Grade Math Page 48
49. Unit 2 Extension Activity #3 – Comparing and Ordering Decimals Application Problems Mr. Walz 6th Grade Math Page 49
50. Unit 2 Extension Activity #4 – Decimal Logic Puzzle Unit 2 Extension Activity #5 – Decimal Magic Square Mr. Walz 6th Grade Math Page 50
51. Unit 2 Extension Activity #6 – Decimal Puzzle and Word Problems Mr. Walz 6th Grade Math Page 51
52. Unit 2 Extension Activity #7 – Decimal Application Problem Mr. Walz 6th Grade Math Page 52
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