Name:
Date:
Version (A / B):
How to use this test. This is the last check-in of the course — you have been building to this. Every equation here comes apart in the same two moves, so slow down and take them one step at a time.
- For fill-in questions, write your answer on the line. For circle one questions, circle the letter of the choice you pick.
- Every part has a Clarify box. Try the part first; read the hint only if you get stuck. It gives you a method, never the answer.
- Show your thinking. A right answer with the steps shown is worth more to you than a lucky guess.
VERSION A
Test A
PART 1
The First Step
Before you solve anything, decide which move comes first. Circle the correct first step.
1.In the equation
2x + 1 = 9, what do you do FIRST?
(circle one)
a) Subtract 1 b) Divide by 2
2.Circle the first step for
3x − 2 = 10:
a) Add 2 b) Divide by 3
3.Circle the first step for
5x + 5 = 20:
a) Subtract 5 b) Divide by 5
4.True or False: You should remove the constant (the number alone) first. Answer:
5.Which part is the variable term in 2x + 1? Answer:
Clarify — Undo the equation in the reverse of the order of operations: peel off the added or subtracted number first, then deal with the number that is multiplying x. The variable term is the piece that has an x attached to it.
PART 2
Solve the Equation (Step by Step)
Follow the two guided steps. Whatever you do to one side, do to the other.
Equation: 2x + 2 = 8
6.Step 1: Subtract 2 from both sides. What is 8 − 2? Answer:
7.Step 2: Now you have 2x = 6. Divide by 2. What is x? x =
Equation: 3x − 1 = 8
8.Step 1: Add 1 to both sides. What is 8 + 1? Answer:
9.Step 2: Now you have 3x = 9. Divide by 3. What is x? x =
Clarify — Two moves, always in the same order: (1) cancel the constant by doing the opposite operation on both sides, then (2) divide both sides by the number in front of x. The steps are laid out for you — just carry out the arithmetic.
PART 3
Solve It — Find X
Now do both steps yourself. Solve for x.
10.2x + 1 = 5 → x =
11.2x + 4 = 10 → x =
12.3x + 1 = 7 → x =
13.4x − 2 = 6 → x =
14.5x + 5 = 30 → x =
15.2x − 4 = 0 → x =
Clarify — Same recipe every time: move the constant across first (opposite operation), then divide by the coefficient of x. When you get an answer, plug it back into the original equation to check that both sides match.
PART 4
Word Problems
Turn the words into an equation, then solve it.
16."Twice a number plus one equals 5." Write the equation. Answer:
17.Solve the equation you wrote in #16. Answer:
18."Three times a number minus one equals 2." Write the equation. Answer:
19.Solve the equation you wrote in #18. Answer:
20.How confident do you feel about algebra now? (1–5) Answer:
Clarify — Translate word by word: "a number" is your x, "twice" means 2×, "three times" means 3×, "plus"/"minus" is the constant, and "equals" is the = sign. Once the equation is written, solve it with the exact same two steps you used above.
VERSION B
Test B
PART 1
The First Step
Before you solve anything, decide which move comes first. Circle the correct first step.
1.In the equation
2x + 3 = 11, what do you do FIRST?
(circle one)
a) Subtract 3 b) Divide by 2
2.Circle the first step for
4x − 1 = 7:
a) Add 1 b) Divide by 4
3.Circle the first step for
3x + 4 = 10:
a) Subtract 4 b) Divide by 3
4.True or False: You should divide first. Answer:
5.Which part is the constant in 2x + 1? Answer:
Clarify — Undo the equation in the reverse of the order of operations: peel off the added or subtracted number first, then deal with the number that is multiplying x. The constant is the number standing on its own, with no x attached.
PART 2
Solve the Equation (Step by Step)
Follow the two guided steps. Whatever you do to one side, do to the other.
Equation: 2x + 4 = 10
6.Step 1: Subtract 4 from both sides. What is 10 − 4? Answer:
7.Step 2: Now you have 2x = 6. Divide by 2. What is x? x =
Equation: 3x − 2 = 7
8.Step 1: Add 2 to both sides. What is 7 + 2? Answer:
9.Step 2: Now you have 3x = 9. Divide by 3. What is x? x =
Clarify — Two moves, always in the same order: (1) cancel the constant by doing the opposite operation on both sides, then (2) divide both sides by the number in front of x. The steps are laid out for you — just carry out the arithmetic.
PART 3
Solve It — Find X
Now do both steps yourself. Solve for x.
10.2x + 3 = 7 → x =
11.2x + 2 = 12 → x =
12.3x + 2 = 11 → x =
13.4x − 1 = 7 → x =
14.5x + 2 = 12 → x =
15.2x − 6 = 0 → x =
Clarify — Same recipe every time: move the constant across first (opposite operation), then divide by the coefficient of x. When you get an answer, plug it back into the original equation to check that both sides match.
PART 4
Word Problems
Turn the words into an equation, then solve it.
16."Twice a number plus three equals 9." Write the equation. Answer:
17.Solve the equation you wrote in #16. Answer:
18."Three times a number minus two equals 4." Write the equation. Answer:
19.Solve the equation you wrote in #18. Answer:
20.How confident do you feel about algebra now? (1–5) Answer:
Clarify — Translate word by word: "a number" is your x, "twice" means 2×, "three times" means 3×, "plus"/"minus" is the constant, and "equals" is the = sign. Once the equation is written, solve it with the exact same two steps you used above.
Reflection — Looking Back on 7 Weeks
Which type of problem felt easiest this week? Which one made you slow down and think? Name one thing about math you can do now that you could not do in Week 1.
FOR MENTOR USE — WORK THROUGH THIS TOGETHER
Mentor Guide
How to run the Week 7 equations check-in — and how to review it without an answer key
1. What this test measures
This is the final week. Every question rests on one idea: a two-step equation comes apart in the reverse of the order of operations — undo the +/− first, then undo the ×. Part 1 checks that the student can name the first move, Parts 2–3 check that they can carry it out, and Part 4 checks that they can build an equation from words. Watch which of those three stages breaks down; that tells you where to spend time. There are two parallel versions (A and B) with identical structure and different numbers — use one as the test and the other as a re-take or warm-up.
2. Run it with gradual release: I do → we do → you do
- I do: Solve one Part 2 equation aloud, narrating each move ("the +2 is bothering me, so I subtract 2 from both sides…").
- We do: Work a Part 3 problem together — you ask "what's the first step?", they answer and do the arithmetic.
- You do: Let them finish Part 3 and Part 4 alone, stepping in only when they reach for a Clarify box.
3. Using the Clarify hints
Each Clarify box coaches method only — "undo the constant first," "translate word by word" — never the numeric answer. Let the student attempt the part before reading it. A strong habit: ask them to tell you the strategy before they look, so the method becomes theirs rather than the paper's.
4. Common slips to watch for
- Wrong first step: dividing before removing the constant. Point back to Part 1 and ask which piece is "attached" to x.
- Sign errors: subtracting when they should add (or the reverse). Have them say the opposite operation out loud before writing it.
- Only doing one side: reinforce "whatever you do to one side, do to the other" — the equation stays balanced.
- Word-problem freeze: let them translate one phrase at a time instead of the whole sentence at once.
5. Reviewing it together — without an answer key
This sheet has no key on purpose. You do not need one:
- Check by substitution. Take the student's x and plug it back into the original equation. If both sides come out equal, the answer is right — this proves it without you having pre-solved anything.
- Have the student prove it to you. Ask "how do you know?" and let them run the substitution. Explaining the check is worth more than the answer itself.
- Re-derive together when a check fails. Rather than marking it wrong, redo the two steps side by side and let them spot where the paths differ.
- Praise the process, then pick one thing to fix. Compare this test to their own Week 1 work — growth over the seven weeks is the real measure.