Understand a fraction as a number on the number line; represent fractions on a number line diagram.
Official wording from the Common Core State Standards for Mathematics (Β© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
A number line turns a fraction into a location and a distance. To show 1/4, students treat the stretch from 0 to 1 as the whole and cut it into 4 equal lengths. The point at the end of the first length, measured from 0, is 1/4. To show 3/4, they mark off three of those lengths from 0, and the endpoint lands on 3/4. Each fraction is a point, and it also names how far that point is from 0.
This shift matters because it shows fractions are numbers in their own right, sitting between whole numbers just as 7 sits between 6 and 8. Students learn that fractions can extend past 1 (5/4 is beyond 1 on a line marked in fourths), that 0/4 sits at 0, and that 4/4 lands exactly on 1. Common slips come from counting tick marks instead of spaces, or from parts that are not equal. Careful partitioning, labeling every tick and counting jumps from 0 build a model that students will use for comparing, adding and measuring with fractions.
A line from 0 to 1 with 3 tick marks inside has 4 equal spaces, so the marks are fourths, not thirds. Have students count the jumps, not the lines.
Some students begin counting at the first tick mark. Each fraction is a distance from 0, so the first jump ends at 1/b.
Hand-drawn lines often have uneven gaps, which makes points misleading. Use folding or a ruler to keep intervals equal.
Students may not believe 5/4 can go on a number line. Extend the line beyond 1 with the same size jumps.
Draw a number line from 0 to 2 and mark 2/3 and 4/3.
Answer: 2/3 is two thirds of the way from 0 to 1; 4/3 is one third past 1.
Start with paper strips folded into equal parts and laid along a line, then move to drawn number lines. Ask students to label every tick, including 0/b and b/b, so they see that b/b sits at 1. Number line clotheslines where students peg fraction cards are a lively whole-class routine.
Test items typically show a number line with a point and ask for its fraction, or ask students to drag a fraction to the correct place. Watch for lines that start at a number other than 0, which test whether students really understand intervals.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: C) 1/4
There are 4 equal spaces, so each space is 1/4. The first mark is one space from 0, at 1/4.
Answer: 6 (also accepted: 6 parts)
5 marks inside the interval make 6 spaces, so each part is 1/6.
Answer: 3/8
Each jump is 1/8, and 3 jumps from 0 is 3/8.
Answer: D) At 1
Four jumps of 1/4 cover the whole interval from 0 to 1, so 4/4 is at 1.
Answer: C) Halfway between 1 and 2
3 jumps of 1/2 from 0 land at 1 and a half, which is halfway between 1 and 2.
Answer: B) The line shows thirds, because there are 3 equal spaces
Two marks inside the interval create 3 equal spaces, so each space is 1/3.
Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.
A full lesson with slides, activities and an exit ticket on fractions on a number line, pitched to grade 3 and editable in PowerPoint or Google Slides.
Make a lesson βA printable, differentiated worksheet on 3.NF.A.2 with an answer key, ready in about a minute.
Make a worksheet βTurn fractions on a number line into a quiz students answer online that marks itself, with a class summary for you.
Build a test βPart a is placing a unit fraction 1/b by splitting 0 to 1 into b equal parts. Part b is placing a/b by marking off a lengths of 1/b from 0.
Number lines show that fractions are numbers with a position and size, which prepares students to compare fractions, find equivalents and later add and subtract them.