Expression Equation Mastery Packet
Algebra Foundations
Expressions, Equations & Substitution
Unit 2 • Packet
Page 1 of 3
Name:
Date:
Period:
Score:
___ / 5
1. Write: Translate words into math symbols
2. Simplify: Distribute & combine like terms
3. Test: Substitute & check if statement is true
Part 1: Do Now Warm-Up
5 Questions • 8-10 Minutes
1. Write an algebraic expression for the verbal phrase: Skill: Writing
"Seven more than four times a number \(n\)"
Expression:
2. Write an algebraic equation for the sentence: Skill: Writing
"The difference between twice a number \(x\) and \(9\) is equal to \(21\)."
Equation:
3. Simplify the expression by combining like terms: Skill: Simplifying
\(8m + 5 - 3m + 9\)
Show Work & Final Answer:
4. Simplify the expression using the distributive property: Skill: Simplifying
\(4(3y + 2)\)
Show Work & Final Answer:
5. Substitute and check if the given value makes the equation true: Skill: Substitution
Is \(x = 5\) a solution to \(3x - 4 = 11\)?
Substitute \(x = 5\) & Calculate:
Is the equation True or False?
True (Solution) False (Not)
Unit 2: Expressions, Equations & Functions Turn to Page 2 for Guided Practice →
P2
Part 2: Guided Practice
Work through each multi-step problem with teacher guidance and structured steps.
Guided Notes
Page 2 of 3
1. Real-World Context: Writing an Equation Writing
Sophia buys \(3\) notebooks that cost \(n\) dollars each and a backpack for \(\$24\). Her total bill is \(\$45\).
Identify the variable & parts:
Write the complete algebraic equation:
2. Scaffolded Simplification: Distribute & Combine Simplifying
Simplify completely: \(5(2k - 3) + 4k + 8\)
Step 1: Distribute \(5\)
Step 2: Group like terms
Step 3: Final simplified form
3. Geometry Application: Write and Simplify Write & Simplify
A rectangle has length \((3x + 2)\) units and width \((x - 1)\) units. Write an expression for the perimeter, then simplify it. (\(\text{Perimeter} = 2L + 2W\))
Write perimeter expression:
Simplified perimeter expression:
4. Verification: Testing a Solution by Substitution Substitution
Determine whether \(m = 6\) is a solution to the equation \(4(m - 2) = 16\).
Substitute \(m = 6\):
Evaluate left side:
Conclusion:
Left = Right?
Yes No
5. Solution Search: Testing Candidate Values Substitution
Which value from the set \(\{2, 4, 7\}\) makes the equation \(3x + 5 = 17\) true? Test each value:
Test \(x = 2\):
True or False: _____
Test \(x = 4\):
True or False: _____
Test \(x = 7\):
True or False: _____
Algebra Workshop: Practice Section Complete Turn to Page 3 for Exit Ticket →
Independent Mastery
Part 3: Exit Ticket
Assessment
Page 3 of 3
Name:
Date:
Period:
Final Score:
___ / 5
Complete all 5 questions independently to demonstrate your understanding of expressions, equations, and substitution.
1. Translate to an Algebraic Expression: Writing (1 pt)
"Twelve decreased by the product of \(5\) and a number \(k\)"
Your Expression:
2. Write an Equation from Real-World Context: Writing (1 pt)
An electrician charges a flat diagnostic fee of \(\$45\) plus \(\$35\) for every hour \(h\) worked. The customer's total bill is \(\$185\).
Your Equation:
3. Simplify the Expression Completely: Simplifying (1 pt)
\(6(2x - 1) - 8x + 10\)
Show Step-by-Step Work:
Final Simplified Answer:
4. Check Solution via Substitution: Substitution (1 pt)
Is \(y = 4\) a solution to the equation \(5y - 7 = 13\)?
Show Substitution & Evaluation:
Is it a solution? (Circle one):
YES, it is a solution NO, not a solution
5. Determine Which Value Makes the Equation True: Substitution (1 pt)
Which value of \(w\), either \(w = 3\) or \(w = 5\), makes \(2(w + 4) = 18\) true? Test both.
Test \(w = 3\):
Test \(w = 5\):
Correct value of \(w\):
How confident do you feel about today's objectives?
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Unit 2 Assessment: Expressions, Equations & Substitution Submit completed packet to teacher
