Understanding fractions
Move fluently between real-world situations, diagrams, and symbolic equations involving three-digit numbers and fractions, explaining what each part represents
What a learner can do afterwards
- Write an equation with three-digit numbers to match a measurement or money word problem
- Draw a bar model to represent a fraction problem and use it to solve
- Explain how a number line diagram relates to the quantities in a word problem
The lesson
A story problem with numbers can be shown in more than one way. You can draw a picture, like a bar cut into equal parts. You can jump along a number line. Or you can write an equation with numbers and a fraction. All three show the same amounts, just in different forms.
A school trip costs $240. Parents have already paid 3/4 of that. Split $240 into 4 equal parts: 240 ÷ 4 = 60. Then take 3 of those parts: 3 × 60 = 180. Parents paid $180, and the bar model shows it as 3 shaded parts out of 4.
When you switch between a picture, a number line, and an equation, check that they agree. If your bar shows 3 shaded parts out of 4, your equation should also use fourths, and your number line should also jump in fourths.
A diagram, a number line, and an equation can all show the same fraction problem, and when they match, you know your answer is right.
Watch it
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.