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Understand Equations and Their Solutions

Identify equations, determine whether values make them true, and understand what it means to solve an equation.

6.EE.B.5 Β· Equations & Inequalities
Level
Guided practice with vocabulary support

🟠 Level 0 β€” Extra Support

Sentence starters: β€œFirst, I…” Β· β€œThe answer is… because…” Β· β€œI know this because…”
W

Warm-Up

2 questions
Warm-Up 1
Which of these is an equation?
Vocabulary: An equation is a math sentence with an equal sign (=). It says two amounts are the same.
βœ“Correct! An equation always has an equal sign. It says the left side and the right side are the same value.
βœ—Not quite. Look for the equal sign (=). An equation says two sides are equal. The answer is B: 3 + 5 = 8.
Warm-Up 2
Is the number sentence 4 + 7 = 12 true or false?
Hint: Add the left side first. Does 4 + 7 equal 12?
βœ“Correct! 4 + 7 = 11, not 12. The equation is false.
βœ—Check again: 4 + 7 = 11, not 12. Since the sides are not equal, the equation is false.
P

Practice

5 questions
Practice 1
Is x = 6 a solution to the equation x + 4 = 10?
What is a solution? A solution is a value that makes the equation true. Replace x with 6 and check: does the left side equal the right side?
Try it: 6 + 4 = ?
Explain how you know:

Sentence frame: "When I replace x with ___, I get ___ + 4 = ___. Since ___ equals ___, the equation is ___."

βœ“Yes! Substituting 6: 6 + 4 = 10. Both sides equal 10, so x = 6 is a solution.
βœ—Substitute 6 for x: 6 + 4 = 10 βœ“. Both sides are equal, so x = 6 is a solution.
Practice 2
Which value of n makes the equation n βˆ’ 3 = 9 true?
Strategy: Try each answer. Replace n with the number, then subtract 3. Which one gives you 9?
Show your substitution work:

Sentence frame: "I substituted ___ for n. ___ minus 3 equals ___. Since ___ equals 9, the solution is n = ___."

βœ“Correct! 12 βˆ’ 3 = 9 βœ“. The value n = 12 makes the equation true.
βœ—Try substituting each value: 12 βˆ’ 3 = 9 βœ“. The answer is C, n = 12.
Practice 3
Sort each math sentence into the correct category.
Remember: An equation has an equal sign (=). An expression does not have an equal sign β€” it is just a math phrase.
5 + x = 12
3y + 7
18 = 2 Γ— 9
4a βˆ’ 1
m Γ· 3 = 6
10 + 2b
Equations
Expressions
βœ“All correct! Equations have equal signs. Expressions are math phrases without an equal sign.
βœ—Some items are in the wrong group. Remember: equations have an = sign, expressions do not. Try again!
Practice 4
Find the value that makes each equation true.
Strategy: Think about what number goes in the blank to make both sides equal. You can use mental math or work backward.
a. + 8 = 15
b. 20 βˆ’ = 15
c. 3 Γ— = 12

Sentence frame: "I know the answer is ___ because ___ and ___ equals ___."

βœ“All correct! 7 + 8 = 15, 20 βˆ’ 5 = 15, and 3 Γ— 4 = 12.
βœ—Some answers need another look. Check each equation: what number makes both sides equal?
Practice 5
Maya says that y = 5 is a solution to 3y = 20. Is she correct?
How to check: 3y means 3 times y. Replace y with 5, then multiply: 3 Γ— 5 = ?
Does your answer equal 20?
Explain Maya's error:

Sentence frame: "Maya's answer is not correct because 3 Γ— 5 = ___, not ___. The correct solution would be ___."

βœ“Correct! 3 Γ— 5 = 15, not 20. Maya is wrong β€” y = 5 is not a solution to 3y = 20.
βœ—Substitute: 3 Γ— 5 = 15 β‰  20. Maya is incorrect. The answer is B.
β˜…

Challenge

1 question
Challenge
Write an equation that has a solution of x = 8. Then explain how you know x = 8 makes your equation true.
Think about it: Start with x = 8. Can you build an equation like x + ___ = ___ or ___ Γ— x = ___ where 8 makes it true?
Your equation:
Explain why x = 8 is a solution:

Sentence frame: "My equation is ___. When I replace x with 8, I get ___. Since ___ = ___, x = 8 is a solution."