MMati Learning Hub

TOPIC 5 · GRADE 3

Equations, Unknowns, and Two-Step Problems

Interpret equality, locate unknowns in any position, and model one- and two-step situations.

Grade 3 focus: Meaning of equality, true/false equations, unknown values, inverse operations, and two-step problem solving.

BIG IDEA

An equation states that two expressions have the same value. An unknown can appear anywhere, and a solution must make the entire equation true.

INTERACTIVE MATH LAB

Build it. Change it. Explain it.

MODEL 1 OF 3

MATH LANGUAGE

equation
a statement that two expressions are equal
expression
numbers and operations without an equal sign
unknown
a value not yet known
inverse operations
operations that undo each other

REPRESENT IT

  • balance model
  • bar model
  • fact family
  • input-output table

STRATEGY STEPS

  1. 1Read the equal sign as “has the same value as.”
  2. 2Name what the unknown represents before choosing an operation.
  3. 3Use inverse operations or a related fact to find the unknown.
  4. 4For two-step problems, solve one relationship at a time and check the final value in the original context.

WATCH OUT

The equal sign is not a signal to calculate only what comes before it. It compares the complete value on the left with the complete value on the right.

TRY IT

Change the unknown and operation, then use the balance and bar model to decide which inverse step comes first.

WORKED EXAMPLE

4 × x + 3 = 27

  1. The 3 was added after the multiplication, so undo it first.
  2. Subtract 3 from both sides: 4 × x = 24.
  3. Divide both sides by 4: x = 6.
  4. State what 6 represents in the problem context.