In this Grade 5 lesson from Illustrative Mathematics Chapter 4, students apply the standard algorithm for multi-digit multiplication to solve real-world area problems involving the Great Garbage Patch and U.S. states, multiplying two- and three-digit numbers such as 452 × 600. Students also practice estimation to compare the area of states like New Mexico and Wyoming with the size of the Great Garbage Patch, reinforcing standard 5.NBT.B.5. The lesson connects multiplication of whole numbers to measurement concepts, including a review of kilometers and square kilometers.
Section 1
Evaluating Partial Quotient Strategies
When dividing with partial quotients, you can use different combinations of quotients to find the answer.
An efficient strategy uses fewer, larger partial quotients to solve the problem in fewer steps.
It is also critical to check for calculation errors in each step, such as incorrect subtraction or multiplication.
Section 2
Estimating Total Distance Using Multiplication
To find the total distance covered when repeating the same path multiple times, multiply the number of repetitions by the distance of a single path.
This skill involves using multiplication as a tool for solving real-world problems related to distance. By identifying the length of a single unit (like one lap or one trip) and the number of times that unit is repeated, you can calculate the total distance. This concept is the inverse of division, where you might know the total distance and need to find the number of trips. This skill reinforces the relationship between multiplication and division in practical scenarios.
Section 3
Estimating Area Ratios Using Division
To estimate how many times larger one area is than another, you can use division.
This is often expressed as a ratio:
This skill involves using division to compare the size of two different areas. By treating the larger area as the dividend and the smaller area as the divisor, you can find out approximately how many times bigger the first area is. This is useful for understanding the scale of large numbers, such as the area covered by pollution. Using estimation with rounded numbers can make the division easier and provide a clear comparison.
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Section 1
Evaluating Partial Quotient Strategies
When dividing with partial quotients, you can use different combinations of quotients to find the answer.
An efficient strategy uses fewer, larger partial quotients to solve the problem in fewer steps.
It is also critical to check for calculation errors in each step, such as incorrect subtraction or multiplication.
Section 2
Estimating Total Distance Using Multiplication
To find the total distance covered when repeating the same path multiple times, multiply the number of repetitions by the distance of a single path.
This skill involves using multiplication as a tool for solving real-world problems related to distance. By identifying the length of a single unit (like one lap or one trip) and the number of times that unit is repeated, you can calculate the total distance. This concept is the inverse of division, where you might know the total distance and need to find the number of trips. This skill reinforces the relationship between multiplication and division in practical scenarios.
Section 3
Estimating Area Ratios Using Division
To estimate how many times larger one area is than another, you can use division.
This is often expressed as a ratio:
This skill involves using division to compare the size of two different areas. By treating the larger area as the dividend and the smaller area as the divisor, you can find out approximately how many times bigger the first area is. This is useful for understanding the scale of large numbers, such as the area covered by pollution. Using estimation with rounded numbers can make the division easier and provide a clear comparison.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter