Solve Equations and Inequalities (Grade 6)

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Lesson Plans and Worksheets for Grade 6
Lesson Plans and Worksheets for all Grades

Examples, solutions, videos, and lessons to help Grade 6 students understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

Common Core: 6.EE.5

Suggested Learning Targets

• I can understand that solving an equation or inequality is like answering a question.
• I can use substitution to determine whether a given number in a specified set makes an equation true.
• I can use substitution to determine whether a given number in a specified set makes an inequality true.
• I can recognize solving an equation or inequality as a process of answering "which values from a specified set, if any, make the equation or inequality true?".
• I can use the solution to an equation or inequality to prove that the answer is correct.
• I can use substitution to determine whether a given number in a specified set makes an equation or inequality true.
Solving equations through substitution example 1
Lux is installing tiles on a bathroom floor. She has large and small tiles. The large tiles have an area of 5 square feet and the small tiles have an area of 2 square feet. The total area of the floor is 40 square feet.
If L is the number of large tiles used, and S is the number of small tiles used, we can write the following equation.
5L + 2S = 40
Which of these combinations of tiles is exactly enough to cover the whole bathroom floor? Select all that apply.
6 large tiles and 5 small tiles
6 large tiles and 6 small tiles
7 large tiles and 5 small tiles
10 large tiles and 4 small tiles
Solving equations through substitution example 2
Mario started the day with 5 fire flowers. He used some, and now he only has 3 left. If u is the number of flowers he used, we can write the following equation.
5 - u = 3
How many fire flowers did Mario use?

Solving equations through substitution
Example:
Joey is training for a hot dog eating contest. The person who eats the most hot dogs in 10 minutes is the winner.
If r is the number of hot dogs Joey can eat in a minute, and N is the total number of hot dogs he eats in the contest, we can write the following equation.
N/10 = r
If Joey can eat 6 4/5 hot dogs per minute, how many hot dogs does he eat during the 10 minute contest?
65 hot dogs
56 hot dogs
68 hot dogs
45 hot dogs
Solving inequalities through substitution
Example:
Nidalee is about to play a game at a county fair. Dinner plates are mounted on a wall, and the goal is to break as many as possible by throwing a spear. Nidalee gets unlimited throws, but there is a 1 minute limit. For each plate she breaks, Nidalee receives 2 tokens. It costs 5 tokens to play the game. For Nidalee to gain tokens, the following inequality must be true. (P is the number of plates Nidalee breaks.)
2 • P - 5 > 0
In which situation(s) will Nidalee gain tokens>
Mark all that apply.
She breaks 1 plate.
She breaks 2 plates.
She breaks 3 plates.
She breaks 6 plates.
Activities:

1) Given the expression 72 = 6(n + 5)
What is the value of n? Use what you know about equations to explain why your answer is correct.

2) Given n = 459 ÷ 9
What is the value of n? Is the value of f in the equation 4 × f = 252 greater or less than the value of n? Use what you know about algebra to explain why your answer is correct.

3) Tell if you agree or disagree with the value of the variable for each equation.
a) 56y = 8. y = 7
Explain why you agree or disagree.

b) 83 = 2 × f. f = 41
Explain why you agree or disagree.

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