Grade 4 Math · Equivalent fractions

Equivalent Fractions with Minecraft Crafting Recipes

Use a 3×3 crafting bench as a fraction model, then split each square to prove that two fractions name the very same amount.

Section 1 · Crafting bench fractions

See equivalence by splitting the grid

By the end of this section I can show two fractions are equivalent using crafting-grid models — so I can prove equal amounts even when the pieces look different.

Success criteria 0 / 3 ticked

Tick each one when you can do it without help.

1A A crafting bench is a fraction model

A Minecraft crafting bench is a 3 × 3 grid — that is 9 squares. Any recipe that fills some of those squares is really showing a fraction: filled squares over total squares.

The pickaxe recipe as a fraction

numeratordenominatorequivalent

The pickaxe pattern fills 5 of the 9 squares. So the recipe fills 5/9 of the bench. The numerator (5) is how many squares are filled; the denominator (9) is how many squares the whole bench has.

Splitting every square in half — twice

Start: 5 filled out of 9 → 5/9 the pickaxe recipe
Cut each of the 9 squares into 2×2 = 4 smaller squares same shape, more pieces
Filled squares now: 5 × 4 = 20 each filled square became 4
Total squares now: 9 × 4 = 36 each of the 9 became 4
New fraction: 20/36 same area, smaller pieces
5/9 = 20/36 ✓ equivalent — same amount of bench

Interactive · split the crafting bench

1

Check yourself

A crafting bench has 9 squares. A "door" recipe fills 4 of them. What fraction of the bench is filled?

Write it as filled-over-total.
Filled squares = 4, total squares = 9, so the fraction is 4/9.

Take that same 4/9 recipe and split every square into 2×2 smaller squares. What is the new equivalent fraction?

Multiply the top and the bottom by the same number — how many smaller squares fit inside one big one?
Each of the 9 squares becomes 4 smaller ones. Filled: 4 × 4 = 16. Total: 9 × 4 = 36. New fraction: 16/36. Same amount, so 4/9 = 16/36.

1B Same point on the number line

If two fractions are equivalent, they land on the exact same spot on a number line. Splitting the bench just gives the same amount a different name.

The rule that grows equivalent fractions

Multiply the numerator and the denominator by the same whole number n:

a/b = (a × n) / (b × n)

The pieces get smaller, but there are more of them — the total amount does not change.

Interactive · build an equivalent fraction on the line

1
3
2

Check yourself

A recipe fills 3/5 of a bench. Write an equivalent fraction with denominator 20: 3/5 = ?/20

What number times 5 gives 20? Multiply the top by the same number.
5 × 4 = 20, so multiply the numerator by 4 too: 3 × 4 = 12. Therefore 3/5 = 12/20.

Section 2 · Generate & simplify

Make equivalent fractions — both directions

By the end of this section I can generate equivalent fractions by multiplying and simplify them by dividing — so I can pick the simplest name for a recipe amount.

Success criteria 0 / 2 ticked

Tick each one when you can do it without help.

2A Simplify a recipe fraction

Simplifying is the same idea run in reverse: divide the numerator and the denominator by the same number. You are gluing smaller squares back into bigger ones.

Simplifying a stew recipe

A stew fills 6 of 9 squares → 6/9 given fraction
Both 6 and 9 divide by 3 find the common factor
6 ÷ 3 = 2, 9 ÷ 3 = 3 divide top and bottom
Simplified: 2/3 same amount, simplest name
6/9 = 2/3 ✓ equivalent

Check yourself

A recipe fills 6/8 of a bench. Simplify it to a fraction with denominator 4: 6/8 = ?/4

What number divides 8 to give 4? Divide the top by that same number.
8 ÷ 2 = 4, so divide the numerator by 2 as well: 6 ÷ 2 = 3. Therefore 6/8 = 3/4.

A pattern fills 8/12 of a crafting bench. Write this fraction in simplest form.

Find the biggest number that divides both 8 and 12 evenly.
Both 8 and 12 divide by 4: 8 ÷ 4 = 2, 12 ÷ 4 = 3. So 8/12 = 2/3 in simplest form.

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