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Ezra's Homework (Lesson 1)
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Lesson 1: Equality, Factoring, and Simplification

Interactive Socratic Mode

Section A: Equality and Equivalent Expressions

Show your reasoning. A statement can be true even when neither side is a single answer.

1.

True or false? Explain: 14 + 9 = 20 + 3

2.

Fill in the blank: 27 + 8 = 30 + ___

Section B: Factors and Prime Factorization

1.

List every factor pair of 24.

2.

Write the prime factorization of 24.

Section C: Simplify & Word Problems

1.

Simplify 12/18.

2.

Calculate: 6 + 3 * 4

3.

Combine like terms: 3x + 2x

4.

Solve for x: x + 7 = 15

5.

A teacher has 3 boxes of pencils. Each box contains 8 pencils. How many pencils are there altogether?

Parent Answer Key & Rubric

True or false? Explain: 14 + 9 = 20 + 3
true
Watch out for: Check your addition on both sides.
Fill in the blank: 27 + 8 = 30 + ___
5
Watch out for: Remember, the equal sign means both sides have the same value. 27+8 is 35, so 30+___ must be 35.
List every factor pair of 24.
[[1,24],[2,12],[3,8],[4,6]]
Routine calculation.
Write the prime factorization of 24.
"2*2*2*3"
Watch out for: 4 and 6 are composite. Break them down into prime numbers.
Simplify 12/18.
"2/3"
Watch out for: 6 and 9 still share a common factor. Divide again!
Calculate: 6 + 3 * 4
18
Watch out for: You added 6 + 3 first. Remember order of operations: multiplication happens before addition.
Combine like terms: 3x + 2x
"5x"
Routine calculation.
Solve for x: x + 7 = 15
8
Watch out for: You added 7 to 15. To undo +7, you need to subtract 7.
A teacher has 3 boxes of pencils. Each box contains 8 pencils. How many pencils are there altogether?
24
Watch out for: You added 3 + 8. "Altogether" here means 3 groups of 8.