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Common Core Grade 5 Math (Worksheets, Homework, Lesson Plans)

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The following lesson plans and worksheets are from the New York State Education Department Common Core-aligned educational resources. The Lesson Plans and Worksheets are divided into six modules.

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Grade 5 Homework, Lesson Plans And Worksheets

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Curriculum  /  Math  /  5th Grade  /  Unit 6: Multiplication and Division of Decimals  /  Lesson 24

Multiplication and Division of Decimals

Lesson 24 of 24

Criteria for Success

Tips for teachers, anchor tasks.

Problem Set

Target Task

Additional practice.

Solve real-world problems involving measurement conversions.

Common Core Standards

Core standards.

The core standards covered in this lesson

Measurement and Data

5.MD.A.1 — Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

Foundational Standards

The foundational standards covered in this lesson

4.MD.A.1 — Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), …

4.MD.A.2 — Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

The essential concepts students need to demonstrate or understand to achieve the lesson objective

• Make sense of a three-act task and persevere in solving it (MP.1).
• Solve multi-step word problems involving measurement conversions (MP.4).
• Assess the reasonableness of a solution by rounding to estimate or by checking a solution using multiplication (MP.1).

Suggestions for teachers to help them teach this lesson

Lesson Materials

• Grade 5 MCAS Reference Sheet (1 per student) — Teachers in different states will need to find and use their own state's reference sheet

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

Act 1: Watch the video  The Fish Tank (Act 1) .

a.   What do you notice? What do you wonder?

b.   How long will it take to fill the fish tank? Make an estimate.

Guiding Questions

The Fish Tank by Graham Fletcher is made available on  Questioning My Metacognition  under the CC BY-SA 4.0 license. Accessed Sept. 23, 2019, 1 a.m..

Act 2: Use the following information to solve:

• It takes 10 seconds to fill 1 cup.
• The dimensions of the fish tank are:

• A quart is 58 cubic inches.

Act 3: Watch the video The Fish Tank (Act 3)  to see how long it took to fill the fish tank. Was your answer reasonable? Why or why not?

Act 4: If you doubled all of the dimensions of the fish tank, how long would it take to fill it?

Unlock the answer keys for this lesson's problem set and extra practice problems to save time and support student learning.

Discussion of Problem Set

• How did you solve #5?
• How did you solve #7? How did you convert from cups to gallons? What is a cup expressed as a fraction of a gallon? How did you figure that out?
• How did you solve #11? How is this problem similar to problems in previous units related to volume? How is it different?
• How did you solve #13? How is this problem similar to problems in previous units related to line plots? How is it different?

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Owen lives 1.2 kilometers from school. Lucia lives 0.86 kilometers from school. Ignacio lives 90 meters from school. If Owen, Lucia, and Ignacio all walk to and from school, how far, in kilometers, did they all walk in total?

Manouel is driving to visit his brother. He listens to a podcast on the way that is 57 minutes long. The drive to his brother’s house is  $$1\tfrac{3}{4}$$ hours long. How much longer, in minutes, is the drive than the podcast?

Student Response

An example response to the Target Task at the level of detail expected of the students.

The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Extra Practice Problems

Answer keys for Problem Sets and Extra Practice Problems are available with a Fishtank Plus subscription.

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Topic A: Multiplying Decimals

Multiply a single-digit whole number by a decimal in cases that involve basic facts. Estimate the product of a single-digit whole number and a decimal by rounding numbers to their largest place.

Multiply a single-digit whole number by a decimal.

Construct viable arguments and critique the reasoning of others regarding the placement of the decimal point in computations that involve multiplying a single-digit whole number by a decimal.

Multiply a multi-digit whole number by a decimal.

Multiply a decimal by a decimal in cases that involve basic facts. Estimate the product of two decimals by rounding numbers to their largest place.

Multiply a decimal by a decimal.

Multiply with decimals in all cases, reasoning about the placement of the decimal point.

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Topic B: Dividing Decimals

Divide a decimal by a single-digit whole number in cases that involve basic facts. Estimate quotients of decimal dividends and single-digit whole number divisors by rounding numbers to compatible numbers.

Divide a decimal by a single-digit whole number.

Divide a decimal by a single-digit whole number that requires decomposition in the smallest place.

Divide a decimal by a two-digit whole number.

Divide a decimal by a two-digit whole number that requires decomposition in the smallest place.

Divide a whole number or a decimal by 1 tenth or 1 hundredth.

Divide a whole number or a decimal by a decimal in cases that involve basic facts. Estimate quotients with decimal divisors by rounding numbers to compatible numbers.

Divide a whole number or a decimal by a decimal.

Divide with decimals in all cases, reasoning about the placement of the decimal point.

Topic C: Decimal Expressions and Real-World Problems

Solve real-world problems that require interpretation of the remainder involving all possible cases, including further decomposition into a decimal.

Solve real-world problems involving multiplication and division with decimals.

5.NBT.B.7 5.OA.A.1 5.OA.A.2

Write and evaluate numerical expressions involving multiplication and division with decimals.

Topic D: Measurement Conversion and Real-World Problems

Express measurements in a whole number of larger units or mixed units in terms of a smaller unit.

Express measurements in a fractional or decimal number of larger units in terms of a smaller unit.

Express measurements in a whole number of smaller units in terms of a larger unit.

Express measurements in a fractional or decimal number of smaller units in terms of a larger unit.

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Eureka Math Grade 5 Module 4 Lesson 24 Answer Key

Engage ny eureka math 5th grade module 4 lesson 24 answer key, eureka math grade 5 module 4 lesson 24 problem set answer key.

Question 1. A vial contains 20 mL of medicine. If each dose is \(\frac{1}{8}\) of the vial, how many mL is each dose? Express your answer as a decimal.

Answer: Each dose has a 2.5 ml dose.

Explanation: Here, a vial contains 20 mL of medicine, and if each dose is \(\frac{1}{8}\) of the vial, so each dose has \(\frac{1}{8}\) × 20 ml which is \(\frac{5}{2}\). So each dose has a 2.5 ml dose.

Question 2. A container holds 0.7 liters of oil and vinegar. \(\frac{3}{4}\) of the mixture is vinegar. How many liters of vinegar are in the container? Express your answer as both a fraction and a decimal.

Answer: The number of liters of vinegar is in the container is \(\frac{21}{40}\) liters. And in decimals it is 0.75 × 0.7 = 0.525 liters.

Explanation: Here, a container holds 0.7 liters of oil and vinegar and \(\frac{3}{4}\) of the mixture is vinegar, so the number of liters of vinegar is in the container is \(\frac{3}{4}\) × 0.7 = \(\frac{3}{4}\) × \(\frac{7}{10}\) = \(\frac{21}{40}\) liters. and in decimals it is 0.75 × 0.7 = 0.525 liters.

Question 3. Andres completed a 5-km race in 13.5 minutes. His sister’s time was 1\(\frac{1}{2}\) times longer than his time. How long, in minutes, did it take his sister to run the race?

Answer: His sister to run the race in 20.25 minutes.

Explanation: Here, Andres completed a 5-km race in 13.5 minutes, and his sister’s time was 1\(\frac{1}{2}\) times longer than his time. So his sister run the race in \(\frac{1}{2}\) of 13.5 which is 0.5 × 13.5 = 6.75. And his sister to run the race in 13.5 + 6.75 which is 20.25 minutes.

Question 4. A clothing factory uses 1,275.2 meters of cloth a week to make shirts. How much cloth is needed to make 3\(\frac{3}{5}\) times as many shirts?

Answer: The cloth needed is 4,509.72 meters.

Explanation: Here, a clothing factory uses 1,275.2 meters of cloth a week to make shirts which is, and the cloth needed to make shirts are 1,275.2 of 3\(\frac{3}{5}\) which is 1,275.2 × \(\frac{18}{5}\) = 4,509.72 meters.

Question 5. There are \(\frac{3}{4}\) as many boys as girls in a class of fifth-graders. If there are 35 students in the class, how many are girls?

Answer: The number of girls is 20 students.

Explanation: Given that there are \(\frac{3}{4}\) as many boys as girls in a class of fifth-graders and there are 35 students in the class, so the number of girls is, as the total of 7 units are the same as 35 students and for 1 unit it will be 35 ÷ 7 which is 5 students. So the number of girls is 4 × 5 = 20 students and the number of boys is 3 × 5 = 15 students.

Question 6. Ciro purchased a concert ticket for $56. The cost of the ticket was \(\frac{4}{5}\) the cost of his dinner. The cost of his hotel was 2\(\frac{1}{2}\) times as much as his ticket. How much did Ciro spend altogether for the concert ticket, hotel, and dinner?

Answer: Ciro spends altogether for the concert ticket, hotel, and dinner is $266.

Explanation: Given that Ciro purchased a concert ticket for $56 and the cost of the ticket was \(\frac{4}{5}\) the cost of his dinner is, for 4 units it is 56, so for 1 unit it will be \(\frac{56}{4}\) which is 14, and for dinner, it is 5 × 14 = 70. The cost of his hotel was 2\(\frac{1}{2}\) times as much as his ticket, so 2.5 × 56 which is 140. So altogether it will be 140 + 70 + 56 which is 266. Ciro spends altogether for the concert ticket, hotel, and dinner is $266.

Eureka Math Grade 5 Module 4 Lesson 24 Exit Ticket Answer Key

Question 1. An artist builds a sculpture out of metal and wood that weighs 14.9 kilograms. \(\frac{3}{4}\) of this weight is metal, and the rest is wood. How much does the wood part of the sculpture weigh?

Answer: The wooden part is 3.725 kilograms.

Explanation: Given that an artist builds a sculpture out of metal and wood that weighs 14.9 kilograms and \(\frac{3}{4}\) of this weight is metal, and the rest is wood. So the weight of the sculpture is, as metal part is \(\frac{3}{4}\) × 14.9 which is 11.175 kilograms and the wooden part is 14.9 – 11.175 = 3.725 kilograms.

Question 2. On a boat tour, there are half as many children as there are adults. There are 30 people on the tour. How many children are there?

Answer: The number of children is 10 children.

Explanation: The total number of people is 30 and a half as many children as there are adults which means the number of children is \(\frac{1}{2}\). Let the number of adults be X and the equation is X + X \(\frac{1}{2}\) = 30, now we will multiply both side by 2. So 2X + X = 60, 3X = 60 X = 20. So the number of children is \(\frac{1}{2}\) × 20 = 10 children.

Eureka Math Grade 5 Module 4 Lesson 24 Homework Answer Key

Question 1. Jesse takes his dog and cat for their annual vet visit. Jesse’s dog weighs 23 pounds. The vet tells him his cat’s weight is \(\frac{5}{8}\) as much as his dog’s weight. How much does his cat weigh?

Answer: The weight of the cat is 14.375 pounds.

Explanation: Given that Jesse takes his dog and cat for their annual vet visit and Jesse’s dog weighs 23 pounds and the vet tells him his cat’s weight is \(\frac{5}{8}\) as much as his dog’s weight. So the weight of the cat is 23 × \(\frac{5}{8}\) which is 23 × 0.625 = 14.375 pounds.

Question 2. An image of a snowflake is 1.8 centimeters wide. If the actual snowflake is \(\frac{1}{8}\) the size of the image, what is the width of the actual snowflake? Express your answer as a decimal.

Answer: The width of the actual snowflake is 0.225 cm.

Explanation: Given that the image of a snowflake is 1.8 centimeters wide and the actual snowflake is \(\frac{1}{8}\) the size of the image, and the width of the actual snowflake is 1.8 × \(\frac{1}{8}\) which is 0.225 cm.

Question 3. A community bike ride offers a short 5.7-mile ride for children and families. The short ride is followed by a long ride, 5\(\frac{2}{3}\) times as long as the short ride, for adults. If a woman bikes the short ride with her children and then the long ride with her friends, how many miles does she ride altogether?

Answer: The adult ride and children ride altogether 38.019 miles.

Explanation: As a community bike ride offers a short 5.7-mile ride for children and families and the short ride is followed by a long ride, 5\(\frac{2}{3}\) times as long as the short ride, for adults. So if a woman bikes the short ride with her children and then the long ride with her friends, so the adult ride is  5.7 ×  5\(\frac{2}{3}\) which is 5.7 × 5.67 = 32.319. Now we will add the adult ride and children ride altogether, which is 5.7 + 32.319 = 38.019 miles.

Question 4. Sal bought a house for $78,524.60. Twelve years later he sold the house for 2\(\frac{3}{4}\) times as much. What was the sale price of the house?

Answer: The sale price of the house is $ 215,942.65.

Explanation: Here, Sal bought a house for $78,524.60 and twelve years later he sold the house for 2\(\frac{3}{4}\) times as much. So the sale price of the house is 2\(\frac{3}{4}\) × 78,524.60 which is 2.75 × 78,524.60 = $ 215,942.65.

Question 5. In the fifth grade at Lenape Elementary School, there are \(\frac{4}{5}\) as many students who do not wear glasses as those who do wear glasses. If there are 60 students who wear glasses, how many students are in the fifth grade?

Answer: The number of students are in fifth grade is 300 students.

Explanation: Given that there are \(\frac{4}{5}\) as many students who do not wear glasses as those who do wear glasses and the total number of students are equal with one or \(\frac{5}{5}\) which means the proportion of user who wear glasses is \(\frac{5}{5}\) – \(\frac{4}{5}\) which is \(\frac{1}{5}\) and from the information we can process (\(\frac{4}{5}\) ÷ \(\frac{5}{5}\)) × 60 on solving we will get the result as 240. So it means the total number of students in the class is accumulation between students without glasses is 240 + 60 = 300 students.

Question 6. At a factory, a mechanic earns $17.25 an hour. The president of the company earns 6\(\frac{2}{3}\) times as much for each hour he works. The janitor at the same company earns \(\frac{3}{5}\) as much as the mechanic. How much does the company pay for all three employees’ wages for one hour of work?

Answer: The company pay for all three employees wages for one hour of work is $142.60.

Explanation: Given that a factory, a mechanic earns $17.25 an hour and the president of the company earns 6\(\frac{2}{3}\) times as much for each hour he works, so presidents wage is 6\(\frac{2}{3}\) × $17.25 which is $115. And the janitor at the same company earns \(\frac{3}{5}\) as much as the mechanic, so janitor wage is \(\frac{3}{5}\) × $17.25 which is $10.35. So the company pay for all three employees wages for one hour of work is $17.25 + $115 + $10.35 which is $142.60.

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