Math Number Line Worksheets - Counting by halves - Free Printable

I need to solve this worksheet about placing numbers on number lines that go up by halves. Let me work through each problem carefully.

The key instruction is: "These number lines are going up by halves." This means each tick mark represents 0.5 (or ½).

Let me solve each problem:

Problem 1: Numbers to place: ½, 1½, 4
- Number line goes from 0 to 5
- Each tick = ½
- ½ = first tick after 0
- 1½ = third tick after 0 (0.5, 1.0, 1.5)
- 4 = eighth tick after 0 (counting by halves: 0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4)

Problem 2: Numbers to place: 3½, 5, 6½
- Number line goes from 2 to 7
- Starting at 2, counting by halves: 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7
- 3½ = third tick after 2 (2 → 2.5 → 3 → 3.5)
- 5 = sixth tick after 2 (2 → 2.5 → 3 → 3.5 → 4 → 4.5 → 5)
- 6½ = ninth tick after 2 (2 → 2.5 → 3 → 3.5 → 4 → 4.5 → 5 → 5.5 → 6 → 6.5)

Problem 3: Numbers to place: 5½, 7, 8½
- Number line goes from 4 to 9
- Starting at 4, counting by halves: 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5, 8, 8.5, 9
- 5½ = third tick after 4 (4 → 4.5 → 5 → 5.5)
- 7 = sixth tick after 4 (4 → 4.5 → 5 → 5.5 → 6 → 6.5 → 7)
- 8½ = ninth tick after 4 (4 → 4.5 → 5 → 5.5 → 6 → 6.5 → 7 → 7.5 → 8 → 8.5)

Problem 4: Numbers to place: 1, 2½, 4½
- Number line shows 3 in the middle
- Need to figure out the range. If there are 10 ticks and 3 is shown at position 6 (counting from left), then:
- Position 6 = 3
- Each tick = 0.5
- So position 1 = 0.5, position 2 = 1, position 3 = 1.5, etc.
- Actually, let me count: if 3 is at the 6th tick from the left, then going backwards: 2.5, 2, 1.5, 1, 0.5, 0
- Going forward from 3: 3.5, 4, 4.5, 5, 5.5
- So the line goes from 0 to 5.5
- 1 = second tick from left
- 2½ = fifth tick from left
- 4½ = ninth tick from left

Problem 5: Numbers to place: 3½, 5, 8½
- Number line shows 6 somewhere
- If 6 is at a certain position and we count by halves...
- Let me think: if there are 10 ticks total and 6 is shown, I need to figure out where it is
- Looking at the pattern, 6 appears to be around the middle-right
- If 6 is at position 8 (from left), then: position 1 = 2, position 2 = 2.5, ..., position 8 = 6
- So the line goes from 2 to 6.5
- Wait, but we need to place 8½ which would be beyond 6.5...
- Let me reconsider. Maybe 6 is at position 9? Then position 1 = 1.5, position 9 = 6, position 10 = 6.5
- But we need 8½...
- Actually, looking more carefully at the spacing, if 6 is shown and we have 10 ticks, and we need to fit 8½, the line must extend further
- Let me assume the line goes from some starting point to accommodate all three numbers
- If 3½, 5, and 8½ need to fit, and counting by halves, the range would be roughly 3 to 9
- So maybe it goes from 3 to 8 or 3 to 9
- If it goes from 3 to 8: 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5, 8
- That's 11 values for 10 ticks... hmm
- Let me try: if it goes from 2.5 to 7.5: 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5
- Still doesn't work for 8½
- Maybe it goes from 3 to 9 with different spacing? No, it says "going up by halves"
- Let me try: from 3 to 8 with 10 intervals means each interval is 0.5, so: 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5, 8
- That's 11 marks for 10 spaces
- For 8½ to fit, we'd need to go to at least 8.5
- So maybe: 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5, 8, 8.5, 9
- With 6 shown somewhere in the middle... if 6 is at position 7, then we have room for 8½ at position 12
- But there are only 10 ticks shown...
- Let me look at this differently. The 6 might not be at an endpoint. If the line has 10 tick marks and 6 is one of them, and we're counting by 0.5s:
- Possible ranges that include 3½, 5, 6, and 8½ while counting by 0.5s:
- From 3 to 8.5: gives us 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5, 8, 8.5 (12 values, too many)
- From 3.5 to 8: gives us 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5, 8 (10 values!) ✓

So for Problem 5, the line likely goes from 3.5 to 8:
- 3½ = first tick (leftmost)
- 5 = fourth tick from left (3.5 → 4 → 4.5 → 5)
- 8½... wait, that's beyond 8!

Let me reconsider. Maybe the range is different. What if it goes from 2.5 to 7.5?
- 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5
- That's 11 values again

What about 3 to 7.5?
- 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5
- That's 10 values! And 6 is the 7th value.
- But we still can't fit 8½...

Actually, I think I need to look at this more carefully. Let me check if maybe the last problem has a different scale or if I'm miscounting the ticks.

Looking at problem 5 again with fresh eyes: if we MUST place 3½, 5, and 8½ on a number line going by halves, the minimum range needed is from 3.5 to 8.5, which requires these marks: 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5, 8, 8.5 - that's 11 marks.

But the image shows what appears to be 10 tick marks. Unless... maybe one of the endpoints isn't labeled, or maybe I should just focus on relative positions?

Let me try a different approach for #5: Perhaps the line extends beyond what's visible, or perhaps there's flexibility. Given that 6 is marked and we need to place 3½, 5, and 8½:

If 6 is roughly in the middle-right area, and we count by 0.5s:
- Working backward from 6: 5.5, 5, 4.5, 4, 3.5, 3, 2.5...
- Working forward from 6: 6.5, 7, 7.5, 8, 8.5, 9...

For all three numbers to fit with reasonable spacing, let's say the line goes from about 2.5 to 8.5 or 3 to 9.

Given the constraints and typical worksheet design, I'll assume for #5 the line accommodates these values with 6 positioned appropriately. The relative positions would be:
- 3½ comes before 5
- 5 comes before 6 (which is already marked)
- 8½ comes well after 6

Final Answer:

1) On the number line from 0 to 5:
- Place ½ at the 1st tick mark
- Place 1½ at the 3rd tick mark
- Place 4 at the 8th tick mark

2) On the number line from 2 to 7:
- Place 3½ at the 3rd tick mark (after 2)
- Place 5 at the 6th tick mark (after 2)
- Place 6½ at the 9th tick mark (after 2)

3) On the number line from 4 to 9:
- Place 5½ at the 3rd tick mark (after 4)
- Place 7 at the 6th tick mark (after 4)
- Place 8½ at the 9th tick mark (after 4)

4) On the number line (appears to go from 0 to 5):
- Place 1 at the 2nd tick mark
- Place 2½ at the 5th tick mark
- Place 4½ at the 9th tick mark

5) On the number line with 6 marked:
- Place 3½ at the appropriate tick before 5
- Place 5 at the tick before 6
- Place 8½ at a tick well after 6 (likely near the right end)