---
title: "Moving between bar models, number lines and equations"
description: "Move fluently between real-world situations, diagrams, number lines, bar models, and symbolic equations involving multi-digit multiplication, fractions, decimals, and percentages, explaining connectio"
canonical: https://lightmysky.com/learn/mathematics/moving-between-bar-models-number-lines-and-equations-mt_CUmjcE7W6c
source: https://lightmysky.com/learn/mathematics/moving-between-bar-models-number-lines-and-equations-mt_CUmjcE7W6c.md
retrieved: 2026-09-02
---

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# Moving between bar models, number lines and equations

Move fluently between real-world situations, diagrams, number lines, bar models, and symbolic equations involving multi-digit multiplication, fractions, decimals, and percentages, explaining connections between representations

Subject: Mathematics · Area: Mathematical Thinking · Ages 9 to 10
Page: https://lightmysky.com/learn/mathematics/moving-between-bar-models-number-lines-and-equations-mt_CUmjcE7W6c

## Ready when they can

- Represent a scaling problem as both a bar model and a multiplication equation
- Show how 0.35, 35/100, and 35% all represent the same quantity on a hundredths grid
- Translate a line-graph reading into a subtraction equation to find the difference

## Lesson: Same Number, Different Pictures

You already know fractions, decimals, percents, and multiplication on their own. Now it's time to connect them. The same number can show up as a bar model, a number line, or an equation, and they all tell the same story.

*(drawing: Three strips with 4 blocks in each.)*

**Example.** A bar model shows multiplication as equal groups. Two strips with 5 blocks in each are 2 lots of 5, so the equation is 2 x 5 = 10. Scaling works the same way: if one strip is 6 tiles long and you want it 3 times as long, that is 3 strips of 6, or 6 x 3 = 18. The picture and the equation carry the same numbers.

**Example.** 0.35, 35/100, and 35% are the same amount. Picture a grid of 100 squares. If 35 are shaded, you can write that as the decimal 0.35, the fraction 35/100, or the percent 35%.

**Example.** A line graph shows a puppy weighed 3 kg in June and 8 kg in September. To find how much it gained, read both points and subtract: 8 - 3 = 5. The puppy gained 5 kg.

Some amounts come in tenths instead of hundredths. A strip split into 10 big parts and a grid split into 100 small squares are the same size, so each big part covers 10 small squares. That makes 7/10 the same as 70/100, 0.7, and 70%. When two amounts are written in different ways, change them to the same way first, then compare them.

**Tip.** If you're not sure your equation is right, try drawing it as a bar model or a number line. If the picture and the equation tell the same story, you've got it.

**Recap.** Bar models, number lines, and equations are different pictures of the same math. Learn to move between them.

## Practice

24 questions on this page, each with its working shown.

## Needs first

- [Moving between diagrams and equations with fractions](https://lightmysky.com/learn/mathematics/moving-between-diagrams-and-equations-with-fractions-mt_3VmBdlAeOZ)
- [Long multiplication](https://lightmysky.com/learn/mathematics/long-multiplication-mt_q9EaJc2FP8)
- [Understanding Percentages](https://lightmysky.com/learn/mathematics/understanding-percentages-mt_ZM9mhHsyYZ)
- [Reading and Comparing Bar Graphs](https://lightmysky.com/learn/mathematics/reading-and-comparing-bar-graphs-mt_H6LlpWgEYS)

## Opens up

- [Moving between representations of a relationship](https://lightmysky.com/learn/mathematics/moving-between-representations-of-a-relationship-mt_9KmVWCuh5_)