3A · Chapter 1 · Lesson 05
The Number Line
Read labels and intervals on an equally spaced number line., Locate a four-digit number between benchmark values., Find the step size from endpoints and a known number of intervals.
Your starting challenge
A number line has marks labeled 3,000 and 4,000 with four equal spaces between them. What is each space worth?
By the end, you can…
- Read labels and intervals on an equally spaced number line.
- Locate a four-digit number between benchmark values.
- Find the step size from endpoints and a known number of intervals.
Before starting, you should know…
- Compare and order four-digit numbers.
- Count forward and backward in tens and hundreds.
Entry · 2 questions
Quick prerequisite check
Try these two before the lesson. If either is confusing, review the listed prerequisites first.
- E1 Insert <, >, or =: 4,100 ___ 4,010.
Show answer and reasoning
Answer: >
Compare digits from the highest place that differs. 4,100 > 4,010.
- E2 How much is 1,000 more than 3,250?
Show answer and reasoning
Answer: 4,250
Add one thousand to the thousands place: 3,250 + 1,000 = 4,250.
Vocabulary to know
| number line | A line on which position represents numerical value. |
|---|---|
| interval | The distance in value between two marks. |
| scale | How much each equal interval represents. |
| midpoint | A point equally far from two endpoints. |
Learn the concept
Spacing matters
Equal distances on a number line must represent equal numerical differences. Count *intervals* (spaces), not just marked ticks.
Find the interval value
If 3,000 and 4,000 are four equal intervals apart, the numerical distance is 1,000, so each interval is worth 250.
Place numbers using distance
A number halfway between 2,400 and 2,600 is 2,500. A number closer to 2,400 should be drawn nearer that endpoint; precise placement matters for estimation.
Work through examples
Study the explanation; then try each check before opening its answer.
Worked example 1
Calculate step size
Five equal intervals connect 2,000 and 3,000. How large is each?
- Distance = 3,000 − 2,000 = 1,000.
- Divide by five spaces: 1,000 ÷ 5 = 200.
Result: 200
Now you try · Understanding check 1
A number line runs from 3,200 to 3,800 in 3 equal intervals. What is the step per interval?Reveal answer and explanation
200 — The total distance is 600. Divide by 3 equal intervals: 200.
Worked example 2
Locate a marked tick
A line starts at 4,200 and steps by 100. What is the fourth tick after the start?
- Move four intervals, not three.
- 4 × 100 = 400; 4,200 + 400 = 4,600.
Result: 4,600
Now you try · Understanding check 2
A number line begins at 5,300 and each tick increases by 50. What is the value at tick 3 after the start?Reveal answer and explanation
5,450 — Add 3 intervals of 50: 5,300 + 3 × 50 = 5,450.
Worked example 3
Find a midpoint
What lies halfway between 6,200 and 6,800?
- Difference is 600.
- Half of 600 is 300.
- 6,200 + 300 = 6,500.
Result: 6,500
Now you try · Understanding check 3
What is halfway between 7,400 and 8,000?Reveal answer and explanation
7,700 — The gap is 600, and halfway is 300 above 7,400.
Guided · 4 questions
Guided practice
Try each problem; return to a visual model if you need one.
- G1 A number line begins at 2,600 and each tick increases by 200. What is the value at tick 3 after the start?
Show answer and reasoning
Answer: 3,200
Add 3 intervals of 200: 2,600 + 3 × 200 = 3,200.
- G2 A number line runs from 4,100 to 4,700 in 3 equal intervals. What is the step per interval?
Show answer and reasoning
Answer: 200
The total distance is 600. Divide by 3 equal intervals: 200.
- G3 A number line begins at 7,100 and each tick increases by 50. What is the value at tick 4 after the start?
Show answer and reasoning
Answer: 7,300
Add 4 intervals of 50: 7,100 + 4 × 50 = 7,300.
- G4 A number line runs from 5,000 to 7,000 in 4 equal intervals. What is the step per interval?
Show answer and reasoning
Answer: 500
The total distance is 2,000. Divide by 4 equal intervals: 500.
Independent · 8 questions
Independent practice
Work without looking at examples first. Show your thinking on paper.
- I1 A number line begins at 2,000 and each tick increases by 100. What is the value at tick 5 after the start?
Show answer and reasoning
Answer: 2,500
Add 5 intervals of 100: 2,000 + 5 × 100 = 2,500.
- I2 A number line begins at 3,600 and each tick increases by 250. What is the value at tick 2 after the start?
Show answer and reasoning
Answer: 4,100
Add 2 intervals of 250: 3,600 + 2 × 250 = 4,100.
- I3 A number line runs from 1,200 to 1,800 in 3 equal intervals. What is the step per interval?
Show answer and reasoning
Answer: 200
The total distance is 600. Divide by 3 equal intervals: 200.
- I4 A number line begins at 7,450 and each tick increases by 50. What is the value at tick 5 after the start?
Show answer and reasoning
Answer: 7,700
Add 5 intervals of 50: 7,450 + 5 × 50 = 7,700.
- I5 A number line runs from 8,000 to 9,000 in 5 equal intervals. What is the step per interval?
Show answer and reasoning
Answer: 200
The total distance is 1,000. Divide by 5 equal intervals: 200.
- I6 A number line begins at 4,150 and each tick increases by 75. What is the value at tick 4 after the start?
Show answer and reasoning
Answer: 4,450
Add 4 intervals of 75: 4,150 + 4 × 75 = 4,450.
- I7 A number line runs from 2,200 to 2,800 in 4 equal intervals. What is the step per interval?
Show answer and reasoning
Answer: 150
The total distance is 600. Divide by 4 equal intervals: 150.
- I8 A number line begins at 6,600 and each tick increases by 125. What is the value at tick 4 after the start?
Show answer and reasoning
Answer: 7,100
Add 4 intervals of 125: 6,600 + 4 × 125 = 7,100.
Challenge · 2 questions
Challenge and transfer
These nonroutine problems require you to explain or adapt what you learned.
- C1 Six equally spaced tick marks include 3,250 first and 4,000 last. What is the interval value?
Show answer and reasoning
Answer: 150
Six marks create five equal intervals. The distance is 750, so each interval is 750 ÷ 5 = 150.
- C2 A 100-unit interval is 4 cm long on paper. How far apart should positions 3,250 and 3,425 be?
Show answer and reasoning
Answer: 7 cm
The difference is 175 units. At 4 cm per 100, distance is 175/100 × 4 = 7 cm.
Exit · 3 questions
Exit check
Use these fresh problems to decide whether to proceed. Answers should be independent.
- E1 A number line runs from 6,200 to 6,800 in 3 equal intervals. What is the step per interval?
Show answer and reasoning
Answer: 200
The total distance is 600. Divide by 3 equal intervals: 200.
- E2 A number line begins at 4,700 and each tick increases by 150. What is the value at tick 2 after the start?
Show answer and reasoning
Answer: 5,000
Add 2 intervals of 150: 4,700 + 2 × 150 = 5,000.
- E3 How many spaces lie between 7 marked ticks?
Show answer and reasoning
Answer: 6
Each neighboring pair creates one interval; 7 ticks produce 6 intervals.