Curriculum
Beast Academy
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Interactive Number Line With Jumps, Fractions and Negatives
Updated · By Edulist · 5 sources
Keyboard and touch help
- Drag a piece from the tray onto the board, or press a tray button (Enter) to add it in the next spot.
- Tab to a piece. Arrow keys move it (Shift for bigger steps). Space adds it to the selection.
- D duplicates, R rotates, G trades up a group, B breaks a piece apart, Delete removes it.
- Ctrl+Z undoes and Ctrl+Shift+Z redoes (Cmd on a Mac).
- Drag across empty space to select several pieces. Drop pieces on the trash or back on the tray to delete them.
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How to use it
- Pick a line
Choose a range: 0 to 10, 0 to 20, 0 to 100, −10 to 10, −20 to 20, fractions in halves, thirds, fourths, sixths or eighths, or decimals in tenths or hundredths.
- Set a start
Type a number in Start at, or drag a point from the tray onto the line. Points snap to the marks. Tab to a point and use the arrow keys to move it one mark at a time.
- Jump
Pick a jump size (tap a quick size or type one, such as 3/4 or 0.5), then press Jump + or Jump −. Each jump starts where the last one landed.
- Read and check
The readout shows the start, every jump and where you land, written as a number sentence. Nine task cards check themselves.
Printables to go with it
What the number line teaches
A number line turns numbers into places and operations into movement. Adding is a jump to the right. Subtracting is a jump to the left, or the distance between two places. That one picture works from kindergarten counting to 6th grade negative numbers, which is why the Common Core standards name number line diagrams in 2nd grade for sums and differences within 100 (2.MD.B.6), in 3rd grade for fractions (3.NF.A.2), in 4th grade for decimals (4.NF.C.6) and in 6th grade for negative numbers (6.NS.C.6).
The What Works Clearinghouse practice guide on helping elementary students who struggle with math devotes a whole recommendation to it: use the number line to teach concepts and procedures, build understanding of grade-level material, and prepare students for advanced mathematics.
The line on this page is exact. Fractions are stored as whole numbers of parts, so a jump of 1/4 from 3/4 lands exactly on 1, never on 0.9999. Points snap to marks, and every jump starts where the last one landed, so a chain of jumps reads as a number sentence.
How to use the interactive number line
- Choose a line. 0 to 20 is a good default for early addition. Use 0 to 100 for tens, −10 to 10 for negatives, and the fraction and decimal lines for 3rd grade on.
- Start somewhere. Type a number into Start at, or drag a point onto the line.
- Jump. Pick a size and press Jump + or Jump −. Arcs above the line go forward; dashed arcs below go back.
- Read the sentence. The readout writes it: 8 + 2 + 5 = 15. Remove the last jump or undo to try another path.
- Compare two points. Put two points on the line and the readout gives the distance between them.
Number line strategies to teach
| Strategy | Example | On the line |
|---|---|---|
| Count on | 6 + 3 | Start at 6, three jumps of +1. |
| Make ten | 8 + 5 | +2 to 10, then +3 to 13. |
| Jump by tens | 34 + 20 | Start at 34 on the 0–100 line, two jumps of +10. |
| Count back | 15 − 6 | Start at 15, jump −6 (or −5 then −1). |
| Count up to subtract | 72 − 68 | Start at 68, jump +2 to 70, +2 to 72: the difference is 4. |
| Skip count | 4 × 5 | Four jumps of +5 from 0. |
| Fractions | 1/4 + 1/2 | On the fourths line, start at 1/4 and jump +2/4. |
| Negatives | −3 to 4 | Start at −3, jump +3 to 0, +4 to 4: a distance of 7. |
Activities to try
- Two ways to 15. Start at 8 and reach 15 in one jump, then in two, then in three. All the sentences equal 15.
- Skip counting. On 0 to 20, jump by 2s from 0, then by 5s on 0 to 100. Say the landing numbers out loud.
- Equivalent fractions. On the eighths line, put a point at 4/8. Switch to the fourths line and put a point at the same spot. What is it called now?
- Decimal jumps. On the tenths line, start at 0.7 and jump +0.5. Do you cross 1? By how much?
- Below zero. On −10 to 10, start at 3 and jump −5. Where do you land? Then start at −4 and jump +6.
- Guess the jump. One person sets a start and a landing; the other finds the jump size.
- Story problems. "The temperature was −2 degrees and rose 7 degrees." Build it and read the answer.
Tips for teachers and parents
- Name the jump, not the hops. A child who jumps +10 once instead of ten +1 hops is using place value. Encourage it.
- Use the scale. Big jumps should look big. On this line, a +10 arc is ten times as wide as a +1 arc, so children can estimate before they jump.
- Turn off the value. Press Hide value, make the jumps, and ask for the answer before showing it.
- Draw on it. Circle the landing numbers with the Pen, or label a jump with Text ("make ten").
- Go to paper. Print number lines to 20, fraction number lines or negative number lines, or make your own with the number line generator.
Why one line works for every kind of number
Whole numbers, fractions, decimals and negative numbers can feel like separate topics. On a number line they're the same thing: a distance from zero. Two fourths and one half land on the same point. 0.5 lands there too. −3 is three steps the other way. Ask learners to explain why the numerator and denominator describe a single number rather than two unrelated quantities.
That's also why the number line is useful for checking. A sum that lands to the left of where you started is wrong. A fraction sum bigger than both parts but past 1 should make you look again. Estimating where the answer will land before you jump is a habit worth building.
Common mistakes and fixes
| What you see | Try |
|---|---|
| Counts the starting number as a jump | Jumps are spaces between marks, not the marks. Start the count after the first number. |
| Puts 1/3 at the third mark of any line | Pick a line split into thirds. The denominator decides the marks. |
| Thinks −5 is bigger than −2 | Put both on the −10 to 10 line: −2 is to the right, so it's bigger. |
Number lines by grade
| Grade | Typical work |
|---|---|
| K–1 | Count forward and back; add and subtract within 20; make ten. |
| 2nd | Sums and differences within 100 as lengths (2.MD.B.6); jumps of 10 and 100. |
| 3rd | Fractions as points: 1/b is the length from 0 to the first mark of b equal parts (3.NF.A.2); rounding. |
| 4th–5th | Equivalent fractions and mixed numbers; decimals in tenths and hundredths; comparing. |
| 6th | Negative numbers, opposites and absolute value as distance from 0. |
When children are ready to do the jumps in their heads, move to the open number line, which drops the marks and keeps only the numbers that matter.
Choosing an activity
Grade bands describe possible curriculum connections, not an assessment of an individual learner. Start with an example the learner can explain, then change one feature at a time. The activity suggestions here are editorial teaching ideas, not results from a classroom trial of this software. Use the model alongside written work and physical materials when useful. The linked standards describe learning objectives; they do not endorse Edulist or require this particular tool.
Sources
- What Works Clearinghouse: Assisting Students Struggling with Mathematics, Recommendation 4: number lines (2021)
- Common Core State Standards: Grade 2, Measurement and Data (number line diagrams)
- Common Core State Standards: Grade 3, Number and Operations—Fractions
- Common Core State Standards: Grade 4, Number and Operations—Fractions (decimals on a number line)
- Common Core State Standards: Grade 6, The Number System (negative numbers)
Questions
How do you add on a number line?
Start at the first number and jump to the right as many times as the second number, or in one big jump of that size. Where you land is the sum. For 8 + 5, start at 8 and jump +5 to land on 13, or jump +2 to 10 and +3 to 13.
How do you subtract on a number line?
Two ways. Count back: start at the bigger number and jump left. Or count up: start at the smaller number and jump right until you reach the bigger one, then add up the jumps. Both give the same difference.
How do you show fractions on a number line?
Split each whole into equal parts named by the denominator, then count parts from 0. On a line marked in fourths, 3/4 is the third mark after 0. Pick a fraction line from the Line menu to try it.
Why do number lines matter so much?
They show numbers as distances, which works for whole numbers, fractions, decimals and negatives alike. The What Works Clearinghouse practice guide on helping students who struggle with math gives number lines their own recommendation.
What is the difference between this and an open number line?
This line has evenly spaced, labeled marks, so jumps are to scale. An open number line has no marks; children write only the numbers they need. Try both: the open number line is built for mental math.
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