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Common Core for Grade 6

More Lessons for Grade 6

Examples, solutions, videos, and lessons to help Grade 6 students learn to use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

A. Make tables of equivalent ratios relating quantities with whole- number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios

B. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

**C. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.**

D. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Common Core: 6.RP.3c

### Suggested Learning Targets

Component Skills from Previous Grades

Using ratios to solve percent problems (Common Core Standard 6.RP.3c)

**6.RP.3.c - Find Percent of a Quantity**

How to find the percent of a quantity, explains that percent means a rate per 100 and uses a ratio table to find the missing part?

Example:

Cool Treats sold 120 milkshakes today. 40% of the milkshakes were strawberry flavoured. How many strawberry milkshakes did Cool Treats sell?

**6.RP.3.c - Solve Percent Problems Finding the Whole**

How to find the whole, when given a part and the percent and uses a ratio table to find the missing part?

Examples:

1. Cool Treats sold 120 milkshakes on Saturday. That is 40% of the milkshakes that it sold during the weekend. How many milkshakes did Cool Treats sell over the weekend?

2. Barbara hiked 7 miles from one point of a mountain to another point before stopping for a break. That is 27% of the entire trip. How many miles in Barbara's complete hike?

**How to solve percent problems using tape diagram?**

Example:

10% of 75 is what number?**Example:**

The label on a sweater says that it is 65% wool. To figure how much of the sweater is not wool, you need to do which of the following

A. multiply 65 by 0.1

B. Add 65 and 100

C. divide 100 by 65

D. subtract 65 from 100**Using a ratio table to solve percent problems**

Examples:

20% of 50 =

What % of 50 is 30?

20% of ___ = 40

Common Core for Grade 6

More Lessons for Grade 6

Examples, solutions, videos, and lessons to help Grade 6 students learn to use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

A. Make tables of equivalent ratios relating quantities with whole- number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios

B. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

D. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Common Core: 6.RP.3c

- I can demonstrate how a percent is a ratio of a number to 100.
- I can find a percent of a number as a rate per 100.
- I can solve real-world problems involving finding the whole, given a part and a percent
- I can solve problems involving unit pricing and speed.
- I can find a percent of a given quantity involving finding the whole, given a part and the percent.

Component Skills from Previous Grades

6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | 6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. | 6.RP.3a Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. |
6.RP.3b Solve unit rate problems including those involving unit pricing and constant speed. |

Using ratios to solve percent problems (Common Core Standard 6.RP.3c)

How to find the percent of a quantity, explains that percent means a rate per 100 and uses a ratio table to find the missing part?

Example:

Cool Treats sold 120 milkshakes today. 40% of the milkshakes were strawberry flavoured. How many strawberry milkshakes did Cool Treats sell?

How to find the whole, when given a part and the percent and uses a ratio table to find the missing part?

Examples:

1. Cool Treats sold 120 milkshakes on Saturday. That is 40% of the milkshakes that it sold during the weekend. How many milkshakes did Cool Treats sell over the weekend?

2. Barbara hiked 7 miles from one point of a mountain to another point before stopping for a break. That is 27% of the entire trip. How many miles in Barbara's complete hike?

Example:

10% of 75 is what number?

The label on a sweater says that it is 65% wool. To figure how much of the sweater is not wool, you need to do which of the following

A. multiply 65 by 0.1

B. Add 65 and 100

C. divide 100 by 65

D. subtract 65 from 100

Examples:

20% of 50 =

What % of 50 is 30?

20% of ___ = 40

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