Name:
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How to use this worksheet. This week is all about letters that stand for numbers. Take it one small step at a time — you already know the arithmetic, we are just adding a letter or a box.
- For fill-in questions, write your answer on the line. For circle one questions, circle the single letter of your choice.
- Every part has a Clarify hint. Try the part first; read the hint only if you get stuck. It gives you a method to start with, never the answer.
- There are two versions below (A and B). Do the one your mentor assigns — the second is for extra practice.
Version A — complete Parts 1–4
PART 1
Identify the Parts
Look at the math problem below and pick out its pieces.
4x + 2 = 10
1.Circle the
variable in the problem above.
(circle one)
a) 4b) xc) 10
2.Circle the number that is a
constant (the number that stands alone).
(circle one)
a) 4b) xc) 2
3.In the term
4x, what is the hidden math sign between 4 and x?
(circle one)
a) Plus (+)b) Minus (−)c) Multiply (×)
4.Is y + 5 an Expression or an Equation?
5.Is y + 5 = 9 an Expression or an Equation?
Clarify — Method: the variable is the letter that stands for a mystery number; a constant is a plain number sitting by itself. When a number is written right against a letter with no sign, that missing operation is always the same one. To sort expression from equation, check one thing only — is there an equals sign?
PART 2
Substitution (Plug it in)
Solve each problem using the given values.
If x = 3 and y = 5
6.x + 4
7.y − 2
8.2x (remember: this means 2 times x)
9.x + y
10.10 − x
Clarify — Method: substitute means swap the letter for its number first, then do the arithmetic. Rewrite the problem with the value in place of the letter before you calculate. Remember a number touching a letter means multiply.
PART 3
The Mystery Number
Find the missing number for the empty box [ ].
11.[ ] + 2 = 7 (what is in the box?)
12.5 − [ ] = 1
13.2 × [ ] = 10
14.[ ] + [ ] = 8 (the boxes are the same number)
15.If n represents the number of apples, and you have 3 apples, what is n?
Clarify — Method: ask "what number makes this true?" Work backwards using the opposite operation to undo what is done to the box, or simply test small numbers until both sides match.
PART 4
Math Translation
Turn the English words into math symbols.
16."A number plus five"
(circle one)
a) n − 5b) n + 5
17."Three times a number"
(circle one)
a) 3 + nb) 3n
18."Ten minus a number"
(circle one)
a) 10 − nb) n − 10
19."A number divided by two" — write the math:
20.A student has x dollars. They spend 2. Write the math expression.
Clarify — Method: read the operation word — "plus/more" adds, "times" multiplies, "minus/less" subtracts, "divided" splits. Translate the words left to right in the same order they are spoken, one piece at a time.
Version B — extra practice, same skills
PART 1
Identify the Parts
Look at the math problem below and pick out its pieces.
3y + 5 = 11
1.Circle the
variable in the problem above.
(circle one)
a) 3b) yc) 11
2.Circle the number that is a
constant (the number that stands alone).
(circle one)
a) 3b) yc) 5
3.In the term
3y, what is the hidden math sign between 3 and y?
(circle one)
a) Plus (+)b) Minus (−)c) Multiply (×)
4.Is x − 2 an Expression or an Equation?
5.Is x − 2 = 8 an Expression or an Equation?
Clarify — Method: the variable is the letter that stands for a mystery number; a constant is a plain number sitting by itself. When a number is written right against a letter with no sign, that missing operation is always the same one. To sort expression from equation, check one thing only — is there an equals sign?
PART 2
Substitution (Plug it in)
Solve each problem using the given values.
If x = 4 and y = 2
6.x + 6
7.x − 1
8.3y (remember: this means 3 times y)
9.x + y
10.10 − y
Clarify — Method: substitute means swap the letter for its number first, then do the arithmetic. Rewrite the problem with the value in place of the letter before you calculate. Remember a number touching a letter means multiply.
PART 3
The Mystery Number
Find the missing number for the empty box [ ].
11.[ ] + 3 = 8 (what is in the box?)
12.9 − [ ] = 5
13.4 × [ ] = 8
14.[ ] + [ ] = 12 (the boxes are the same number)
15.If n represents the number of cats, and you have 2 cats, what is n?
Clarify — Method: ask "what number makes this true?" Work backwards using the opposite operation to undo what is done to the box, or simply test small numbers until both sides match.
PART 4
Math Translation
Turn the English words into math symbols.
16."A number plus seven"
(circle one)
a) n − 7b) n + 7
17."Five times a number"
(circle one)
a) 5 + nb) 5n
18."Eight minus a number"
(circle one)
a) 8 − nb) n − 8
19."A number divided by four" — write the math:
20.A student has x cookies. They eat 3. Write the math expression.
Clarify — Method: read the operation word — "plus/more" adds, "times" multiplies, "minus/less" subtracts, "divided" splits. Translate the words left to right in the same order they are spoken, one piece at a time.
💡 Tips for You: Working with Letters and Boxes
- A letter is just a placeholder. Wherever you see the letter, you can pencil in the value you were given, then solve the plain number problem.
- No sign means multiply. 2x, 3y, and 5n all mean "multiply." If you forget, write the × back in to remind yourself.
- Check by plugging back in. Found the mystery number? Drop it back into the problem and make sure the two sides really are equal.
Reflection
Which part felt the easiest? Which part made you slow down and think? Name one thing you now understand about letters standing in for numbers.
FOR MENTOR USE — WORK THROUGH THIS TOGETHER
Mentor Guide
How to coach a beginner through variables, substitution, and translation
1. What this worksheet builds
Week 2 introduces the single biggest idea in beginning algebra: a letter can stand for a number. The four parts move from naming the pieces (variable vs. constant) → plugging in a value → finding a missing value → translating words into symbols. The goal is comfort with the idea, not speed. If the student leaves saying "a letter is just a number I don't know yet," the week worked.
2. Run it with gradual release: I do → we do → you do
- I do: Work the first problem of Part 1 aloud, thinking out loud as you point to the variable and the constant.
- We do: Do Part 2 together — you name the value, they make the swap, you both do the arithmetic.
- You do: Let them attempt Parts 3 and 4 alone, stepping in only when they reach for a Clarify hint.
3. Using the Clarify hints
Let the student try each part first; read the Clarify box only if they stall. The hints coach method ("swap the letter first," "use the opposite operation," "is there an equals sign?") and never hand over the answer. Once a hint has helped, ask the student to say it back in their own words before the next part — that is the strategy becoming theirs.
4. Common snags and quick fixes
- "2x confuses me." Have them rewrite it as 2 × x every time until the shortcut feels natural.
- Mixing up variable and constant. Point out that the variable is always the letter; the constant is the number standing alone with no letter attached.
- Word problems freeze them. Read the phrase aloud and circle the operation word together before writing anything.
5. Reviewing it together — without an answer key
- This sheet has no answer key by design. Check answers by having the student prove each one: substitute the number back in and confirm both sides match, or re-read the phrase to see the symbols say the same thing.
- When something is off, don't mark it wrong — ask "walk me through how you got that." The mistake usually reveals itself, and self-correction sticks better than a corrected key.
- For circle-one items, ask the student to explain why the other choice is wrong. If they can rule out the distractor, they truly understand it — no key required.