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Common Core for Grade 7

Common Core for Mathematics

More Lessons for Grade 7

Examples, solutions, videos and lessons to help Grade 7 students learn how to solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

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For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation*.

Common Core: 7.EE.3

### Suggested Learning Targets

**Real World Problems**

Strategies:

• Draw pictures

• Write what you do and don't know.

• Break problems down into steps.

Example:

You want to center a couch against a wall in your house. The couch is 2.2 meters long and the wall is 4.8 meters long. How far from the end of the wall should the couch be?

**Percent Example:**

Strategy:

• Break the problem down into steps

The population of squirrels in a park is 90. Angelica, the park's chief ranger, believed the population will increase by 10% this year. By how much will the population increase? How many total squirrels will there be with this increase?

**Example with negative numbers**

You and 4 friends own a business. Together you decide to close the business and divide the cash, and debts, equally. The business has $26,000 in cash and $32,000 in debts. How much does each person gets?

Solving multi-step problems with positive and negative rational numbers in any form (7.EE.3)

In this lesson you will learn how to solve multi-step problems with whole numbers by creating diagrams.

Example:

You are redecorating your bedroom and want to place two posters on the wall. Your wall is 14 feet 3 inches long, and each poster is 42 inches across. How many inches away from the wall should you place each poster, if you want the distance between the posters and the distances from each poster to the nearest edge of the wall to be equal? Assess the reasonableness of answers using mental computation and estimation strategies. Example:

Kobe, A'mari and DJ are raising money for their football team to take a trip to San Diego. After one hour, Kobe collected $24.55 more than A'mari and DJ collected $15.60 less than Kobe. Altogether, the three boys collected $125.45. A'mari thinks that he collected about $30.00. Is A'mari's estimate reasonable? Multi-step word problems example 1

Joelle is working on a school report in a word processor. She wants to place a figure which is 13.09 centimeters wide so that it appears centered on the page. The width of the page is 21.59 centimeters. How much margin should she leave on the left so that the figure is centered? Multi-step word problems example 2

Jess recently started a business producing cosmetic products made from natural ingredients. She wants to advertise for products by distributing bags of samples in her neighborhood. She calculated that it takes for two minutes to prepare each bag. How many hours will it take to prepare 1200 bags of samples if she asks seven friends to help her with the work? Multi-step word problems example 3

Sandy is taking a cab in New York City. The taxi fare includes a base charge if $2.50 as soon as you enter the cab, plus an additional $2.50 per mile traveled. If Sandy starts off with a twenty dollar bill takes the cab for five miles and leaves a one dollar tip. How much money will she be left with?

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Common Core for Grade 7

Common Core for Mathematics

More Lessons for Grade 7

Common Core: 7.EE.3

- I can solve mathematical problems (two-step linear equations) posed with positive and negative rational numbers in any form.
- I can apply properties of operations to calculate two-step problems with numbers in any form.
- I can fluently solve multi-step, real-world problems posed with positive and negative rational numbers.
- I can apply properties of operations to calculate multi-step problems with numbers in any form.
- I can assess and justify the reasonableness of answers using mental computation and estimation strategies.

Strategies:

• Draw pictures

• Write what you do and don't know.

• Break problems down into steps.

Example:

You want to center a couch against a wall in your house. The couch is 2.2 meters long and the wall is 4.8 meters long. How far from the end of the wall should the couch be?

Strategy:

• Break the problem down into steps

The population of squirrels in a park is 90. Angelica, the park's chief ranger, believed the population will increase by 10% this year. By how much will the population increase? How many total squirrels will there be with this increase?

You and 4 friends own a business. Together you decide to close the business and divide the cash, and debts, equally. The business has $26,000 in cash and $32,000 in debts. How much does each person gets?

In this lesson you will learn how to solve multi-step problems with whole numbers by creating diagrams.

Example:

You are redecorating your bedroom and want to place two posters on the wall. Your wall is 14 feet 3 inches long, and each poster is 42 inches across. How many inches away from the wall should you place each poster, if you want the distance between the posters and the distances from each poster to the nearest edge of the wall to be equal? Assess the reasonableness of answers using mental computation and estimation strategies. Example:

Kobe, A'mari and DJ are raising money for their football team to take a trip to San Diego. After one hour, Kobe collected $24.55 more than A'mari and DJ collected $15.60 less than Kobe. Altogether, the three boys collected $125.45. A'mari thinks that he collected about $30.00. Is A'mari's estimate reasonable? Multi-step word problems example 1

Joelle is working on a school report in a word processor. She wants to place a figure which is 13.09 centimeters wide so that it appears centered on the page. The width of the page is 21.59 centimeters. How much margin should she leave on the left so that the figure is centered? Multi-step word problems example 2

Jess recently started a business producing cosmetic products made from natural ingredients. She wants to advertise for products by distributing bags of samples in her neighborhood. She calculated that it takes for two minutes to prepare each bag. How many hours will it take to prepare 1200 bags of samples if she asks seven friends to help her with the work? Multi-step word problems example 3

Sandy is taking a cab in New York City. The taxi fare includes a base charge if $2.50 as soon as you enter the cab, plus an additional $2.50 per mile traveled. If Sandy starts off with a twenty dollar bill takes the cab for five miles and leaves a one dollar tip. How much money will she be left with?

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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