Begin with a start, a move and a landing
For 4 + 3, place a counter on 4. Move one space to the right three times, landing on 5, then 6, then 7. The answer is 7. The 4 tells you where to start; the 3 tells you how many moves to make; the landing number tells you the sum. Keeping these three jobs separate helps explain why the starting number is not the first hop. Use a number line labeled from 0 to 10 for this example, with equally spaced tick marks.
Check the learner can use the line first
Ask the learner to find 4, show the next number to its right, and move a counter exactly one space. Then ask for two spaces from a different starting point. If finding the labels or matching one move to one count is difficult, model those actions before introducing an equation. A larger hand-drawn line can make pointing easier. Keep a small set of objects available so the learner can check a sum by combining two groups. These are teaching observations, not a test or diagnosis.
A short routine for 4 + 3
Model the routine aloud once, work through it together, then invite the learner to explain a new example. Count the moves while also naming where the counter lands.
- Read the equation: four plus three. Put the counter on 4 and say, “This is my start. I have made zero hops.”
- Move to 5: “One hop; I landed on 5.”
- Move to 6: “Two hops; I landed on 6.”
- Move to 7: “Three hops; I landed on 7.” Stop because the equation asked for three more.
- Read the whole equation, 4 + 3 = 7. Ask which number told you to stop hopping and which number was the answer.
Two examples that reveal different ideas
For 6 + 0, start on 6 and make no moves: the answer stays 6. For 2 + 7, you can start on 2 and make seven one-space moves, landing on 9. Once that meaning is clear, compare it with 7 + 2: start on 7, move to 8, then 9. Both totals are 9, but starting with the larger addend takes fewer hops. Show both equations rather than silently swapping the numbers. Counting on is useful for small additions; it need not become the only method a learner uses.
If the learner gets 4 + 3 = 6
Watch the counter before giving another problem. A learner who says “4, 5, 6” while pointing at the start may be counting three labels rather than making three moves. Keep the counter on 4 and ask, “Have we moved yet?” Name that position as the start, then count only when the counter crosses a space. If the counter lands correctly on 7 but the learner answers 3, separate the hop count from the landing label. If the counter moves left, revisit which direction shows larger values on this left-to-right number line.
Connect the equation to a short story
Say, “There are five books on a shelf. We put two more books there. How many books are on the shelf now?” Let the learner identify the starting amount before writing 5 + 2. Start at 5, land on 6 after one hop, and land on 7 after two hops. The answer is seven books. Ask the learner to point to the part of the story represented by each number. A correct landing alone does not tell you whether the child understood the story.
Choose a printable after the demonstration
The linked Hop-to-It Addition worksheet is an existing Easter-themed resource with number-line addition. Preview it before choosing problems: its catalog description includes both single- and double-digit additions, so not every item is a within-10 starting task. Select an item that fits the learner or keep modeling with your own 0–10 line. The printable has seasonal artwork; the counting-on idea can be discussed at any time of year. Email and newsletter signup are required for its free download. Reading this guide does not require signup.
Decide what to do next
Try 3 + 2 together, then ask the learner to explain 5 + 1. The landings are 5 and 6. Look for a correct start, one space per hop, a stop after the requested moves and an answer taken from the landing label. If one part is uncertain, repeat that action with smaller numbers. If the routine is comfortable, compare adding zero or reversing two addends before extending the range. Choose a short, focused session rather than using speed as the only sign of understanding.
Further reading for adults
The What Works Clearinghouse elementary mathematics intervention guide discusses number lines as a teaching representation, including attention to equal intervals and the distance between tick marks. Its recommendations concern mathematics intervention; they do not certify this page or the linked printable. The worked examples above are original demonstrations for this guide.