5th Grade iReady Math Review pt. 1 PDF

# Understanding of Place Value ## Name: 1. The decimal grid in each model represents 1 whole. Shade each model to show the decimal number below the model. - 0.5 - 0.05 Complete the comparison statements. - 0.05 is **one-tenth** of 0.5. - 0.5 is **ten** times the value of 0.05. Complete...

# Understanding of Place Value ## Name: 1. The decimal grid in each model represents 1 whole. Shade each model to show the decimal number below the model. - 0.5 - 0.05 Complete the comparison statements. - 0.05 is **one-tenth** of 0.5. - 0.5 is **ten** times the value of 0.05. Complete the equations. - 0.5 ÷ **10** = 0.05 - 0.05 × **10** = 0.5 ## Draw a number line from 0 to 2. Then draw and label points at 2 and 0.2. Use the number line to explain why 2 is 10 times the value of 0.2. - The number line shows that 2 is 10 times greater than 0.2. Complete the equations to show the relationship between 2 and 0.2. - 0.2 × **10** = 2 - 2 ÷ **10** = 0.2 ## Which type of model do you like best? Explain why. # Understanding Powers of 10 ## Name: Multiply or divide. 1. 6 × 10 = **60** 2. 0.6 ÷ 10 = **0.06** 3. 6 ÷ 10² = **0.06** 4. 0.6 × 10² = **60** 5. 6 ÷ 10^-1 = **60** 6. 60 ÷ 10¹ = **6** 7. 0.3 × 10 = **3** 8. 0.3 × 10² = **30** 9. 0.3 × 10³ = **300** 10. 0.03 × 10² = **3** 11. 0.003 × 10² = **0.3** 12. 0.03 × 10³ = **30** 13. 72 ÷ 10 = **7.2** 14. 0.72 × 10² = **72** 15. 7,200 ÷ 10³ = **7.2** 16. 20 ÷ 10² = **0.2** 17. 0.9 × 10³ = **900** 18. 0.001 × 10² = **0.1** 19. 54 ÷ 10 = **5.4** 20. 150 ÷ 10³ = **0.15** 21. 0.46 × 10³ = **460** ## What strategies did you use to solve the problems? Explain. # Reading a Decimal in Word Form ## Name: What is the word form of each decimal? 1. 0.2 = **two tenths** 2. 0.02 = **two hundredths** 3. 0.002 = **two thousandths** 4. 0.12 = **twelve hundredths** 5. 0.012 = **twelve thousandths** 6. 0.102 = **one hundred two thousandths** 7. 1.002 = **one and two thousandths** 8. 9.4 = **nine and four tenths** 9. 90.04 = **ninety and four hundredths** 10. 0.94 = **ninety-four hundredths** 11. 500.2 = **five hundred and two tenths** 12. 8.008 = **eight and eight thousandths** 13. 700.06 = **seven hundred and six hundredths** 14. 6.335 = **six and three hundred thirty-five thousandths** 15. 3,000.001 = **three thousand and one thousandth** ## What strategies did you use to help you read the decimals? Explain. # Writing a Decimal in Standard Form ## Name: What decimal represents each number? 1. one and six tenths = **1.6** 2. eight and eleven hundredths = **8.11** 3. 6 × 1 + 5 × 1/10 = **6.5** 4. thirteen and thirteen thousandths = **13.013** 5. 2 × 10 + 7 × 1/10 + 3 × 1/100 = **20.73** 6. 4 × 1 + 1 × 1/100 + 9 × 1/1000 = **4.019** 7. five hundred twelve thousandths = **0.512** 8. 8 × 100 + 2 × 1/10 + 8 × 1/1000 = **800.208** 9. 2 × 1 + 4 × 1/100 = **2.04** 10. forty-two and forty-one hundredths = **42.41** 11. 7 × 100 + 2 × 10 + 3 × 1 + 6 × 1/10 = **723.6** 12. twelve and sixty-eight thousandths = **12.068** 13. 3 × 1,000 + 6 × 100 + 3 × 10 + 7 × 1/10 + 2 × 1/100 + 8 × 1/1000 = **3637.28** 14. nine hundred fifty-six and four hundred twenty-seven thousandths = **956.427** ## How was writing decimals for numbers in word form different from numbers in expanded form? # Comparing Decimals ## Name: Write the symbol <, =, or > in each comparison statement. 1. 0.02 **>** 0.002 2. 0.05 **<** 0.5 3. 0.74 **<** 0.84 4. 0.74 **>** 0.084 5. 1.2 **<** 1.25 6. 5.130 **=** 5.13 7. 3.201 **>** 3.099 8. 0.159 **<** 1.590 9. 8.269 **>** 8.268 10. 4.60 **>** 4.060 11. 302.026 **>** 300.226 12. 0.237 **>** 0.223 13. 3.033 **<** 3.303 14. 9.074 **<** 9.47 15. 6.129 **<** 6.19 16. 567.45 **>** 564.75 17. 78.967 **>** 78.957 18. 5.346 **<** 5.4 19. 12.112 **<** 12.121 20. 26.2 **=** 26.200 21. 100.32 **>** 100.232 ## What strategies did you use to solve the problems? Explain. # Rounding Decimals ## Name: Round each decimal to the nearest tenth. 1. 0.32 = **0.3** 2. 3.87 = **3.9** 3. 0.709 = **0.7** 4. 12.75 = **12.8** 5. 12.745 = **12.7** 6. 645.059 = **645.1** Round each decimal to the nearest hundredth. 7. 1.079 = **1.08** 8. 0.854 = **0.85** 9. 0.709 = **0.71** 10. 12.745 = **12.75** 11. 645.059 = **645.06** 12. 50.501 = **50.50** Round each decimal to the nearest whole number. 13. 1.47 = **1** 14. 12.5 = **13** 15. 200.051 = **200** ## Write two different decimals that are the same value when rounded to the nearest tenth. Explain why the rounded values are the same. - 1.14 and 1.16 are the same value when rounded to the nearest tenth, because both decimals fall within the range of 1.1 to 1.2. ## Round 1.299 to the nearest tenth and to the nearest hundredth. Explain why the rounded values are the equivalent. - 1.299 rounds to 1.3 to the nearest tenth, and 1.30 to the nearest hundredth. The rounded values are equivalent because 1.3 and 1.30 represent the same number. # Multiplying Multi-Digit Whole Numbers ## Name: Estimate. Circle all the problems with products between 3,000 and 9,000. Then find the exact products of only the problems you circled. 1. 132 × <b>34</b> = **4,488** 2. 247 × <b>15</b> = **3,705** 3. 145 × 23 4. <b>308</b> × <b>12</b> = **3,696** 5. 158 × 41 6. 364 × <b>32</b> = **11,648** 7. 400 × <b>29</b> = **11,600** 8. 254 × <b>17</b> = **4,318** 9. 187 × 42 10. 216 × <b>12</b> = **2,592** 11. 323 × <b>18</b> = **5,814** 12. 194 × 26 13. <b>317</b> × <b>14</b> = **4,438** 14. 385 × 31 15. 285 × 27 ## What strategies did you use to solve the problems? Explain. # Multiplying with the Standard Algorithm ## Name: The answers are mixed up at the bottom of the page. Cross out the answers as you complete the problems. 1. 580 × 30 = **17,400** 2. 3,104 × 18 = **55,872** 3. 1,482 × 38 = **56,316** 4. 1,085 × 17 = **18,445** 5. 1,236 × 55 = **67,980** 6. 1,625 × 18 = **29,250** 7. 2,105 × 13 = **27,365** 8. 1,788 × 15 = **26,820** 9. 2,500 × 19 = **47,500** 10. 648 × 32 = **20,736** 11. 2,409 × 23 = **55,407** 12. 306 × 62 = **18,972** 13. 2,417 × 24 = **58,008** 14. 650 × 35 = **22,750** 15. 962 × 44 = **42,328** # Using Estimation and Area Model to Divide ## Name: Check each answer by multiplying the divisor by the quotient. If the answer is incorrect, cross out the answer and write the correct answer. | Division Problems | Student Answers | Check | |---|---|---| | 516 ÷ 12 | 48 <strikethrough> 43 </strikethrough> | 12 × 48 = 576 | | 837 ÷ 31 | 27 | | 351 ÷ 13 | 57 | | 918 ÷ 54 | 22 | | 896 ÷ 32 | 23 | | 1,482 ÷ 78 | 14 | | 1,012 ÷ 11 | 82 | | 1,344 ÷ 56 | 24 | ## Explain how you could know that the answers to two of the problems are incorrect without multiplying. - You could tell that the answer to 837 ÷ 31 is incorrect because 837 is closer to 900 than 800. - You could tell that the answer to 1,482 ÷ 78 is incorrect because 1,482 is closer to 1,500 than 1,400. # Using Area Models and Partial Quotients to Divide ## Name: Estimate. Circle all the problems that will have quotients greater than 30. Then find the exact quotients of only the problems you circled. 1. 540 ÷ <b>12</b> = **45** 2. 798 ÷ <b>38</b> = **21** 3. 429 ÷ <b>11</b> = **39** 4. 931 ÷ 19 5. 925 ÷ <b>25 ** = **37** 6. 390 ÷ 15 7. 1,071 ÷ <b>51</b> = **21** 8. 1,326 ÷ <b>13</b> = **102** 9. 1,856 ÷ 32 10. 2,952 ÷ <b>72</b> = **41** 11. 1,869 ÷ 89 12. 1,798 ÷ <b>29</b> = **62** ## Select a problem you did not circle. Describe two different ways you could use estimation to tell the quotient is not greater than 30. - 1798 ÷ 29 - If you estimate 1,798 as being close to 1,800 and 29 as being close to 30, the quotient should be close to 60, which is larger than 30. - If you estimate using compatible numbers, you can multiply 29 x 30, which is equal to 870, and 29 x 40, which is equal to 1,160. 1,798 lies between these two numbers, so the quotient would be between 30 and 40, and less than 30. # Adding Decimals ## Name: Circle all the problems with sums less than 5. Then find the exact sums of only the problems you circled. 1. 0.24 + <b>4.25</b> = **4.49** 2. <b>4.8</b> + <b>0.16</b> = **4.96** 3. 2.31 + 2.075 4. 2.31 + 2.7 5. 0.909 + <b>4.09</b> = **5.009** 6. 3.99 + 1.109 7. 2.675 + <b>2.325</b> = **5** 8. 3.775 + 0.225 9. 2.06 + <b>2.933</b> = **4.993** 10. 2.6 + 2.933 11. 1.809 + <b>3.091</b> = **4.9** 12. 3.01 + 1.991 13. 1.83 + 3.1 + 0.1 14. 0.012 + <b>3.79</b> + <b>1.101</b> = **4.903** 15. 2.6 + 2.04 + 0.099 ## What strategies did you use to solve the problems? # Subtracting Decimals to Hundredths ## Name: The answers are mixed up at the bottom of the page. Cross out the answers as you complete the problems. 1. 7.5 – 1.2 = **6.3** 2. 10.75 – 4.13 = **6.62** 3. 20.2 – 14.8 = **5.4** 4. 6.12 – 0.7 = **5.42** 5. 41.5 – 33.25 = **8.25** 6. 15.9 – 8.92 = **6.98** 7. 105.53 – 99.28 = **6.25** 8. 9.46 – 3.68 = **5.78** 9. 74 – 65.9 = **8.1** 10. 5.05 – 0.56 = **4.49** 11. 31.27 – 23.67 = **7.6** 12. 256.4 – 248.38 = **8.02** 13. 12 – 4.39 = **7.61** 14. 1,280.01 – 1,272.77 = **7.24** 15. 500.2 – 494.94 = **5.26** # Using Estimation with Decimals ## Name: Solve the problems: 1. Lori needs at least 12 liters of water to fill a water cooler. She has a container with 4.55 liters of water, a container with 3.25 liters of water, and a container with 4.85 liters of water. Does she have enough water? Use estimation only to decide. Explain why you are confident in your estimate. - By rounding the capacity of each container to the nearest whole number, we find 4.55 rounds to 5, 3.25 rounds to 3, and 4.85 rounds to 5. Adding these estimates together, we get 5 + 3 + 5 = 13 liters. Lori has more than enough water. 2. Nia wants the total weight of her luggage to be no more than 50 kilograms. She has three suitcases that weigh 15.8 kilograms, 17.42 kilograms, and 16.28 kilograms. Is the total weight within the limit? Use only estimation to decide. Explain how you know your estimate gives you the correct answer. - By rounding the weights of each suitcase to the nearest whole number, we get 16, 17 and 16. Adding these three numbers together, we get 16 + 17 +16 = 49 kilograms. 49 kilograms is less than 50, so the total weight is within the limit. Because we rounded each weight down, the actual total weight must be less than 49. 3. Omar measures one machine part with length 4.392 centimeters and another part with length 6.82 centimeters. What is the difference in length? Use estimation to check your answer for reasonableness. - 4.392 rounds to 4 and .6.82 rounds to 7. The difference in length is approximately 7-4 = 3 centimeters. # Using Estimation with Decimals Continued ## Name: 4. Kyle wants to buy a hat for $5.75, a T-shirt for $7.65, and a keychain for $3.15. He has $16. Does he have enough money? Use estimation only to decide. Explain why you are confident in your estimate. - Rounding all prices up to the nearest dollar, we get $6 + $8 + $4 = $18. Kyle does not have enough money. 5. For his hiking club, Ricardo is making a container of trail mix with 3.5 kilograms of nuts. He has 1.78 kilograms of peanuts and 0.625 kilograms of almonds. The rest of the nuts will be cashews. How many kilograms of cashews does he need? Use estimation to check your answer for reasonableness. - Rounding up the weights of the peanuts and almonds gives us 2 kg + 1 kg = 3 kg of peanuts and almonds. Subtracting from the total 3.5 kg, we estimate that he needs approximately .5 kg of cashews. 6. Suppose you want to be sure that the total cost of three items does not go over a certain amount. How can you use estimation only to solve the problem? - Round up the cost of each item to the nearest dollar or ten cents. Then add the rounded prices together. If the sum is less than the total allowed amount, you know that you have enough money. # Multiplying a Decimal by a Whole Number ## Name: Multiply. 1. 3 × 0.2 = **0.6** 2. 3 × 0.03 = **0.09** 3. 3 × 0.23 = **0.69** 4. 4 × 0.08 = **0.32** 5. 4 × 1.1 = **4.4** 6. 4 × 1.18 = **4.72** 7. 6 × 0.07 = **0.42** 8. 6 × 1.1 = **6.6** 9. 6 × 1.17 = **7.02** 10. 21 × 0.05 = **1.05** 11. 21 × 1.05 = **22.05** 12. 21 × 2.05 = **43.05** 13. 9 × 3.25 = **29.25** 14. 5 × 0.87 = **4.35** 15. 11 × 3.68 = **40.48** 16. 16 × 6.4 = **102.4** 17. 7 × 6.89 = **48.23** 18. 32 × 5.12 = **163.84** ## How did you know where to put the decimal point in problem 6? - The decimal point in problem 6 goes two places from the right because the number to be multiplied by 4 contains two digits after the decimal, # Multiplying Decimals Less Than 1 ## Name: Multiply. 1. 0.5 × 3 = **1.5** 2. 0.5 × 0.3 = **0.15** 3. 0.5 × 0.03 = **0.015** 4. 6 × 0.2 = **1.2** 5. 0.6 × 0.2 = **0.12** 6. 0.06 × 0.2 = **0.012** 7. 0.8 × 0.1 = **0.08** 8. 0.8 × 0.2 = **0.16** 9. 0.8 × 0.3 = **0.24** 10. 0.4 × 0.02 = **0.008** 11. 0.4 × 0.04 = **0.016** 12. 0.4 × 0.12 = **0.048** 13. 0.3 × 0.4 = **0.12** 14. 0.6 × 0.4 = **0.24** 15. 0.6 × 0.8 = **0.48** 16. 0.01 × 0.5 = **0.005** 17. 0.05 × 0.5 = **0.025** 18. 0.25 × 0.5 = **0.125** ## Describe a pattern you noticed when you were completing the problem set. - The number of decimal places in the product is equal to the total number of decimal places in the two numbers being multiplied. # Multiplying with Decimals Greater Than 1 ## Name: The answers are mixed up at the bottom of the page. Cross out the answers as you complete the problems. 1. 0.3 × 1.2 = **0.36** 2. 1.2 × 0.4 = **0.48** 3. 1.2 × 1.1 = **1.32** 4. 0.3 × 12.1 = **3.63** 5. 4.4 × 1.1 = **4.84** 6. 0.02 × 1.8 = **0.036** 7. 7.1 × 5.1 = **36.21** 8. 6.6 × 0.02 = **0.132** 9. 2.4 × 4.8 = **11.52** 10. 9.2 × 5.24 = **48.208** 11. 1.2 × 1.24 = **1.488** 12. 8.4 × 6.2 = **52.08** 13. 4.2 × 3.21 = **13.482** 14. 4.25 × 8.5 = **36.125** 15. 1.9 × 2.78 = **5.282** # Dividing a Decimal by a Whole Number ## Name: Multiply to check if the student's answer is reasonable. If not, cross out the answer and write the correct quotient. | Division Problems | Student Answers | Check | |---|---|---| | 0.88 ÷ 11 | <strikethrough> 0.8 </strikethrough> 0.08 | 11 × 0.08 = 0.88 | | 5.6 ÷ 8 | <strikethrough> 0.07 </strikethrough> 0.7 | 8 × 0.7 = 5.6 | | 7.2 ÷ 9 | 0.8 | 9 × 0.8 = 7.2 | | 25.35 ÷ 5 | 5.7 | 5 × 5.7 = 28.5 | | 21.7 ÷ 7 | 3.1 | 7 × 3.1 = 21.7 | | 14.4 ÷ 12 | <strikethrough> 0.12 </strikethrough> 1.2 | 12 × 1.2 = 14.4 | | 96.16 ÷ 8 | 12.2 | 8 × 12.2 = 97.6 | | 60.18 ÷ 2 | 30.9 | 2 × 30.9 = 61.8 | ## Can an answer be incorrect even if it looks reasonable? Explain. - Yes, an answer can be incorrect even if it looks reasonable. For example, if you are dividing 0.88 by 11 and get an answer of 0.8, it might seem reasonable because 0.8 is close to 1, and 11 is close to 10. However, the correct answer is 0.08. # Dividing by Hundredths ## Name: Divide. 1. 1 ÷ 0.25 = **4** 2. 4 ÷ 0.25 = **16** 3. 3.75 ÷ 0.25 = **15** 4. 6.5 ÷ 0.25 = **26** 5. 1.8 ÷ 9 = **0.2** 6. 1.8 ÷ 0.9 = **2** 7. 1.8 ÷ 0.09 = **20** 8. 225 ÷ 75 = **3** 9. 22.5 ÷ 7.5 = **3** 10. 2.25 ÷ 0.75 = **3** 11. 0.36 ÷ 0.06 = **6** 12. 6.36 ÷ 0.06 = **106** 13. 36.36 ÷ 0.06 = **606** 14. 9 ÷ 2.25 = **4** 15.13.5 ÷ 2.25 = **6** ## Describe a pattern you noticed when you were completing the problem set. - The number of places you move the decimal point to the right in the dividend is equal to the number of decimal places in the divisor.