Bar Models for Unknowns (Year 6)

A11Bar Models for Unknowns

Draw the problem as bars.

Bar models turn word problems into pictures where the unknown is visible.

Together Ava and Ben have 10 sweets. Ben has 4 more than Ava. How many has Ava?

two equal bars + 4 = 10 → two bars = 6 → Ava = 3

Draw what you know; the unknown becomes a bar you can measure.

Learn the 3-Step Method

1Draw a bar for each amount.

Ava's bar, Ben's bar (Ava's + an extra 4), and the total 10 across the top.

draw bars

2Remove the known extra.

Take the 4 away from the total: 10 − 4 = 6 fills the two EQUAL bars.

10 − 4 = 6

3Share what's left.

6 ÷ 2 = 3 → Ava has 3, Ben has 3 + 4 = 7.

6 ÷ 2 = 3

💡 Key IdeaThe bar model IS algebra: the drawing solves a + (a + 4) = 10 without a single letter — and prepares children for the lettered version.

Worked Example

A number machine adds 7 and gets 12: solve x + 7 = 12 with a bar.

Draw

→

The gap is x

x = 12 − 7

→

✓ Answer

x = 5

Watch Out! Common Mistakes

Splitting the total in half straight away.

10 ÷ 2 = 5 each ✕

The 4 first! The bars aren’t equal until the extra 4 is removed: (10 − 4) ÷ 2 = 3.

Giving the extra to the wrong person.

Re-read! BEN has 4 more — his bar is longer. Ava 3, Ben 7 (not the other way round).

Forgetting to answer both parts.

Finish! Questions often ask for BOTH amounts. Ava = 3 AND Ben = 7; check 3 + 7 = 10 ✓.

⬇ Cheat Sheet

BAR MODELS FOR UNKNOWNS

Draw a bar per amount; total on top.
Strip the known extras from the total.
Share the remainder between the equal bars.
Check the parts rebuild the total.

Example: total 10, one has 4 more → (10−4)÷2 = 3 and 3+4 = 7.

📖 Continue Your Journey

✓ A1 What Is Algebra?✓ A2 Function Machines ✓ A3 Writing Expressions ✓ A4 Substitution ✓ A5 Simplifying Expressions ✓ A6 One-Step Equations ✓ A7 Two-Step Equations ✓ A8 Sequences ✓ A9 The nth Term ✓ A10 Formulae A11 Bar Models for Unknowns A12 Algebra Problem Solving

→

Next Lesson: A12 Algebra Problem SolvingPuzzles with unknowns, exam style.

📄 Free printable: Download the Bar Models for Unknowns cheat sheet (PDF) — keep it by your child's desk.

Quick summary

Draw a bar for each amount and mark the total.
Remove known extras from the total first: 10 − 4 = 6.
Share the remainder between the equal bars: 6 ÷ 2 = 3.
Answer both quantities and check they rebuild the total.

Frequently asked questions

What is a bar model?

A drawing that shows quantities as bars, making the structure of a word problem visible — especially which parts are equal and where the unknown sits.

How does a bar model solve 'Ben has 4 more' problems?

Draw two equal bars plus an extra 4 making 10 in total; remove the 4 (leaving 6), halve it (3 each), and add the 4 back to Ben (7).

How do bar models connect to algebra?

The bars are unknowns drawn to length: the sweet problem is a + (a + 4) = 10 in picture form, so the method transfers directly to equations.

A12 Algebra Problem Solving