Name:
Date:
Score:
How to use this worksheet. Work each part in order. Write your answer on the blank line, and where it says
circle one, circle the single best choice.
- You can show your work in the margin — nobody is grading how you got there, only that the answer is right.
- Every part has a Clarify hint. Try the part first; read the hint only if you get stuck. It gives you a method, never the answer.
- Take your time. The numbers change from problem to problem, so read each one fresh.
PART 1
Matching Families
Are these "like terms"? (Can you add them together?) Circle one for each.
1.2x and 3x (circle one): Yes | No
2.4x and 2y (circle one): Yes | No
3.5 and 2x (circle one): Yes | No
4.7 and 3 (circle one): Yes | No
5.2x and x (circle one): Yes | No
Clarify — Like terms share the exact same letter part. Compare only the letters: if they match, the terms belong to the same family. A plain number is like another plain number, but never like a letter-term.
PART 2
Simplify (Combine the Xs)
Add or subtract the terms together.
6.2x + 3x
7.5x − 2x
8.x + 4x (Hint: x is the same as 1x)
9.10x − 9x
10.3a + 2a
Clarify — Keep the letter exactly as it is; only add or subtract the numbers in front of it. Remember a lone letter (like x) counts as 1 of that letter.
PART 3
Simplify Expressions
Combine the numbers with numbers, and letters with letters.
11.2x + 1 + 3x
12.4x + 2 + 5
13.3x + 2y + x
14.5 + 2x + 1 + 2x
15.6m − 2m + 4
Clarify — Sort before you solve: gather the letter-terms into one group and the plain numbers into another, then combine each group on its own. The letter part never changes when you combine.
PART 4
Advanced Sorting & Powers
Sort the terms, finish the simplifying, then try some powers.
16.Circle the terms that have an x: 3x + 2 + 5x
17.Circle the constants (just numbers): 4x + 1 + 9
18.Simplify: 2x + 3x + 4x
19.Simplify: x + x + x
20.Simplify: 5x + 3 − 2x
21.32 (three squared)
22.42 (four squared)
23.13 (one to the power of 3)
24.23 (two to the power of 3)
25.True or False: 42 means 4 × 4. (circle one): True | False
Clarify — For sorting, underline the pieces that match before you write anything. For a power, the small raised number tells you how many times to multiply the base by itself — write it out as repeated multiplication first, then work it out left to right.
Name:
Date:
Score:
PART 1
Matching Families
Are these "like terms"? (Can you add them together?) Circle one for each.
1.5y and 2y (circle one): Yes | No
2.3x and 4 (circle one): Yes | No
3.6x and 2x (circle one): Yes | No
4.9 and 1 (circle one): Yes | No
5.3a and 3b (circle one): Yes | No
Clarify — Like terms share the exact same letter part. Two different letters (like a and b) are never a family, even when the number in front is the same. Compare the letters, not the numbers.
PART 2
Simplify (Combine the Xs)
Add or subtract the terms together.
6.4x + 2x
7.7x − 3x
8.2x + x
9.8x − 7x
10.5b + 3b
Clarify — Keep the letter exactly as it is; only add or subtract the numbers in front of it. A lone letter counts as 1 of that letter.
PART 3
Simplify Expressions
Combine the numbers with numbers, and letters with letters.
11.3x + 2 + 4x
12.5x + 3 + 4
13.2x + 3y + 2x
14.4 + 3x + 2 + 3x
15.8m − 3m + 5
Clarify — Sort before you solve: gather the letter-terms into one group and the plain numbers into another, then combine each group on its own. The letter part never changes when you combine.
PART 4
Advanced Sorting
Sort the terms, then finish the simplifying.
16.Circle the terms that have an x: 2x + 5 + 4x
17.Circle the constants (just numbers): 3x + 2 + 8
18.Simplify: x + 2x + 3x
19.Simplify: 2x + 2x + 2x
20.Simplify: 6x + 4 − 3x
Clarify — For sorting, underline the pieces that match before you write anything. For simplifying, combine only the terms that share the same letter, and keep any plain numbers in their own group.
FOR MENTOR USE — WORK THIS THROUGH TOGETHER
Mentor Guide
How to coach a student through Week 5 — combining like terms and a first look at powers
1. What this worksheet builds
It moves in four small steps: spotting like terms → combining a single letter → simplifying a mixed expression → sorting terms and reading a power. Each part depends on the one before it, so if a student struggles in Part 3, the fix usually lives back in Part 1. Two parallel tests (A and B) let you re-test the same skills with fresh numbers. The goal is confident, correct simplifying — not speed.
2. Run it with gradual release: I do → we do → you do
- I do: Work one Part 2 problem out loud, saying "same letter, so I just add the numbers in front."
- We do: Do a Part 3 problem together — you point to each term, they decide which group it joins.
- You do: Let them run Part 4 alone, stepping in only when they reach for a Clarify hint.
3. Using the Clarify hints
Let the student attempt each part first; read the Clarify box only if they stall. The hints coach method ("sort first," "a lone x is 1x"), never the answer. Once a skill is landing, ask the student to say the hint back to you before reading it — that is the strategy becoming their own.
4. Common slip-ups to watch for
- Adding unlike terms — e.g. writing "5xy" for 2x + 3y. Unlike terms stay separate.
- Forgetting the invisible 1 — a lone x is 1x, so x + 4x = 5x, not 4x.
- Powers read as multiplication — 4² is 4 × 4 = 16, not 4 × 2 = 8. Have them write the repeated multiplication out first.
- Dropping the letter — 2x + 3x is 5x, not just 5. The letter carries through.
5. Reviewing it together — without an answer key
You do not need a key to check this work; the math checks itself.
- Count the terms. A correct answer should have fewer terms than the question, and no two remaining terms should share a letter — if they do, it can still be combined.
- Substitute a number. Pick x = 2, plug it into both the question and the student's answer; if the expressions are equal, they should give the same total.
- Re-add out loud. Read the numbers in front of the matching letters and add them together with the student — hearing it catches slips the eye misses.
- Compare A to B. The two tests drill identical skills, so a student who gets Part 2 right on Test A should reason it the same way on Test B — inconsistency points to a step worth re-teaching, not a number to look up.