Number Lines Made from Floor Tiles

The skill: connect a numerical change to intervals

A number line represents numbers as positions in an ordered sequence. For this activity, adjacent labeled positions differ by one and are spaced equally. Moving one interval from 3 to 4 represents an increase of one; moving another from 4 to 5 represents a second increase of one.

The starting position and the movements play different roles. In 3 + 2, begin at 3 and make two moves: 3 to 4, then 4 to 5. Saying ‘three, four’ while counting the starting point as the first move would stop one position too early.

The line is a model. A group of three objects with two more added can be counted to confirm five. The positions on the line are not themselves objects in that group; they represent the changing count.

Prepare a safe, visible line

Make seven paper cards labeled 0 through 6. Place them in order at equally spaced points along a clear floor area, or use existing tiles if their spacing is regular and the labels can be placed clearly. A strip of paper on a table can serve the same purpose.

Choose a marker, a paper figure, or another suitable object to move between labels. A child may step beside the labels, move the marker, point to the next position, or direct an adult. Do not require walking if a different response is more accessible.

Keep the path clear and use cards that will not create a slipping hazard. The labels should remain visible and in order. If the floor tiles are not equal or the labels cannot be spaced consistently, use measured marks on a paper strip instead.

Model three plus two

Place the marker at 3 and say, ‘We start at three. We will move two intervals toward the larger numbers.’ Show where the movement begins and identify 4 and 5 as the next positions.

1. Check that the marker is on 3 before any move. This is the starting position.
2. Move from 3 to 4. Count that movement as the first interval.
3. Move from 4 to 5. Count that movement as the second interval.
4. Stop at 5 and read the landing position. Three plus two equals five.
5. Verify with three objects and two additional objects, counting all five once.
6. Return the marker to 3 and let the child direct or perform the two moves if they want another turn.

A conversation about counting the starting point

Adult: ‘Start at 3 and move two spaces toward larger numbers.’ Child points to 3 and says ‘one,’ then moves to 4 and says ‘two.’ Adult: ‘You counted the place where we started. Let's count the moves between the labels instead.’

The adult traces the first interval from 3 to 4 and the second from 4 to 5. ‘We started on 3 before moving. The two movements land us on 5.’ The child can point to each interval while another person moves the marker.

If the child reaches 5 by counting 4 and 5 as the two landing positions, that also tracks the two moves correctly. Ask them to show the path so the starting point and the two changes remain clear.

Positions and intervals are different

The labels 3, 4, and 5 are three positions. The spaces between 3 and 4 and between 4 and 5 are two intervals. A move of two from 3 crosses those two intervals and lands at 5.

Use a finger, a strip of paper, or a toy marker to trace each interval. If floor cards occupy entire tiles, agree where each labeled position is, such as the center of the card. The move is from one position to the next, not a count of all cards touched including the start.

If the child counts three labels and answers three moves, point to the gaps between them. You can place one small token on each traversed interval while leaving the number labels visible. The number of intervals matches the change being modeled.

Check the line's spacing

Place the labels at equal intervals in numerical order. If using floor tiles, verify that adjacent marked points are equally spaced and that each move of one goes from one label to the next. A missing label or an irregularly placed card can make a move ambiguous.

For a paper strip, draw equally spaced marks and write one numeral at each mark. Use the same location on each card, such as its center, as the position. A ruler can help, though approximate equal spacing is sufficient for this introductory integer activity.

Do not label equally spaced adjacent points 0, 1, and 3 while treating every gap as one. Either include the missing 2 or explain a different scale. The meaning of a move depends on how the line is labeled.

Connect the line with a collection

Put three blocks on a mat and confirm the count. Add two blocks one at a time while moving the marker from 3 to 4 to 5. Count the final five blocks. Each added block corresponds to one move on the line.

The five labeled positions from 1 through 5 are not the five blocks. The line represents numerical values; the blocks are the objects being counted. This distinction matters when a child counts labels instead of the collection.

If the objects and marker show different totals, check whether two objects were added and two intervals crossed. Recount the starting group as well. Repair the mismatch before using either representation as evidence for the equation.

Move toward smaller numbers

Start at 5 and move two intervals toward the smaller labels: first to 4, then to 3. This models 5 − 2 = 3. Use a set of five blocks and remove two to verify that three remain.

State the direction in terms of larger or smaller numbers, especially if the line is arranged differently from a typical left-to-right layout. On a conventional line, larger numbers are to the right; if the physical path bends, the labels still determine the direction.

The starting position 5 is not the first backward move. Trace 5 to 4 as one interval and 4 to 3 as the second. If the child lands at 4 after counting 5 as one, replay the two actual movements.

Use zero as a starting point

Place the marker at 0 and move three intervals toward larger numbers: 0 to 1, 1 to 2, and 2 to 3. The marker lands at 3. A collection can begin empty and receive three objects to show the same change.

The 0 card marks a number position. It does not mean that there is no card or no floor space. In the object model, zero describes the initial number of objects in the defined group.

A move of zero from 3 means the marker stays at 3; no interval is crossed. Compare that with starting at 0 and moving three intervals. The same numeral can describe a starting position or a change, so name its role in the question.

Read a path and write its equation

Show a marker beginning at 2 and moving to 3, 4, then 5. Ask the child to describe the starting number, the number of intervals crossed, and the landing number. There are three moves from 2 to 5, so the path represents 2 + 3 = 5.

If the child says the change is five because the marker lands on 5, distinguish the endpoint from the number of moves. Trace the three intervals again and place a token beside each movement if useful.

A path from 5 to 2 in the opposite direction represents 5 − 3 = 2 on this line. The same endpoints can be used in different orders; direction and starting position determine the operation represented.

Find an unknown number of moves

Place the marker at 2 and show a destination at 6. Ask how many one-unit intervals separate them in the direction of larger numbers. Move through 3, 4, 5, and 6, counting four moves. The relationship can be written 2 + 4 = 6.

The destination 6 is not the number of moves. Use one counter beside each interval traversed to show the four changes. A child can point to the path while an adult moves the marker.

If the child counts the starting label as one and obtains five, repeat by counting transitions rather than labels. The starting point is established before the first movement. The difference between the endpoints is four in this example.

Find an unknown starting point

Tell the child that a marker moved two intervals toward larger numbers and landed at 5. Ask where it started. Move two intervals back from 5: first to 4, then to 3. Check by starting at 3 and moving forward two to return to 5.

The story can be recorded as __ + 2 = 5. The blank represents the starting position. The backward check finds a candidate; replaying the forward movement confirms that it fits the stated path.

If the line begins at 0 and the stated path would require a position outside the displayed range, extend the line or choose a different example. A missing position should not be treated as impossible merely because the paper strip is too short.

Compare two paths with the same endpoint

Start at 3 and move two intervals to 5. Then start at 2 and move three intervals to 5. Both paths end at 5, but they have different starting positions and different numbers of moves.

Ask the child to show each path with a different marker or record 3 + 2 = 5 and 2 + 3 = 5. The same endpoint does not make the paths identical. Compare the actual intervals crossed in each case.

Use blocks to model both stories separately. Reset the objects between stories so the second group starts with two, not with the five objects from the first result. The representations should describe the same start and change in each round.

Make the activity easier

Use labels 0 through 3 and model one move at a time. Start at 1 and move to 2 while saying that the total increased by one. The child can point or direct an adult rather than moving across the floor.

Keep the labels in a straight, uncluttered row and use a marker that clearly indicates one position. A number strip can be placed on a table for a child who needs a closer view. Read the labels aloud if numeral recognition is not the current target.

Before asking the child to make two moves, verify that one move is understood as the interval between adjacent labels. A single well-checked movement is a useful starting point.

Add challenge without changing the scale silently

Give a path such as start at 2, move four intervals toward larger numbers, and identify the endpoint. The child can trace each interval and land at 6. Then ask for the equation and check it with objects.

For a separate extension, make a line labeled 0, 2, 4, 6 at equal intervals. Explain that each interval now represents a change of two, not one. One move from 2 to 4 changes the number by two. Do not mix this scale with the one-unit line without saying so.

If the child treats the new interval as one, compare the labels at both ends of that interval. Return to the fully labeled one-unit line to show that 2 to 4 contains two unit intervals. The scale is part of the model.

Use a partner to check a path

One person states a starting number and a number of moves. The other moves the marker and names the endpoint. Both trace the intervals to verify the count, then exchange roles. Keep the direction and scale explicit.

If the partner lands at a different number, compare each movement with the instruction. Did the marker begin at the correct label? Was the starting position counted as a move? Did it cross the stated number of intervals? The path provides evidence for the answer.

A child can be the instructor and direct an adult to move the marker. The adult can model checking by retracing the path. A timer or competition is not needed to make the comparison meaningful.

Record a path on paper

Draw a short line with equally spaced labels 0 through 6. Mark a starting point at 3 and draw two adjacent arrows ending at 4 and 5. Write 3 + 2 = 5 below it. Each arrow represents one interval, not a separate starting number.

Ask the child to match each arrow to one added object in the concrete example. If the drawing has only one arrow but claims two moves, add the missing arrow or revise the written change. The record should correspond to the path actually taken.

The child can dictate labels or point while an adult draws. A paper record is optional; the floor cards or table strip can be reused without preserving a drawing.

Predict a landing point before moving

Place the marker at 1 and say that it will move three one-unit intervals toward larger numbers. Ask the child to predict the landing position. The child might point to 4, choose a numeral card, or say they are unsure.

Move through 2 and 3 to 4, counting each interval. Compare the landing position with the prediction. If the child chose 3, trace the three movements again and show that the starting position 1 was established before the first move.

Now reset at 1 and predict the result of two moves. The marker lands at 3. Comparing the two paths shows that the same starting position can lead to different endpoints when the number of intervals changes. Keep the line visible so the child can verify both paths.

Check an intentionally incorrect path

Ask a partner to model 2 + 3, but have the partner move the marker from 2 to 3 and then to 4 before stopping. The child can inspect the path and decide whether three intervals were crossed. Only two moves were made, so one more move reaches 5.

On a second turn, have the partner start at 1 and make three moves to 4 while claiming to have started at 2. The number of moves is correct, but the starting position differs from the instruction. Reset at 2 and repeat the three moves to reach 5.

These examples separate two kinds of mismatch: an incorrect number of intervals and an incorrect starting point. The child can point to the place where the path differs from the instruction. The purpose is to check a representation, not to catch a partner in a mistake.

Compare a move with a whole collection

Arrange two blocks on a mat and three more outside. Place the line marker at 2. Move one block onto the mat while moving the marker to 3, then repeat for the other additions until the marker reaches 5.

Ask how many blocks were added and how many are on the mat now. Three were added, while five are present after the addition. Count the original and new blocks together to verify the total. The number of moves represents the change, not the whole final collection.

If a block is moved without moving the marker, or the marker moves without an added block, pause and bring the representations back into agreement. The child may direct the object movement while an adult moves the marker. Both actions should describe the same story.

Use a path that changes direction

Start at 3 and move two intervals toward larger numbers, arriving at 5. Then move one interval toward smaller numbers, arriving at 4. Pause at each stage and state the current position. The two changes can be recorded as 3 + 2 = 5 and 5 − 1 = 4.

Ask how many intervals were traveled in total and compare that question with the net change in position. The marker traveled three one-unit intervals, but ended one unit above its starting position because one move was in the opposite direction. These are different quantities.

If that distinction is too demanding, treat each part of the path as its own short task. Trace the forward moves first, then the backward move. A physical marker and a written arrow for each interval can make the sequence visible.

Explain the scale to another person

Show a partner the line labeled 0 through 6 and ask them to identify adjacent positions. Explain that one interval changes the number by one. Then show a separate line labeled 0, 2, 4, 6 with equal spacing and explain that each interval there changes the number by two.

A partner might move from 2 to 4 on the second line and call it one interval. That is correct as a count of intervals, while the numerical change is two. Ask the partner to state both facts so the words ‘one move’ and ‘increase by two’ are not confused.

To check the numerical change, compare with the fully labeled line: 2 to 3 and 3 to 4 are two unit intervals. This comparison introduces a different scale only after the original one-unit model is clear. The child can point to the labels while an adult gives the verbal explanation.

Return to the original path

Place the marker at 3 again and invite the child to show two moves toward larger numbers. They may move the marker, trace the intervals, or direct a partner. Stop at 5 and compare the path with the original object model of three blocks and two additions.

Ask which number is the start, which number describes the change, and which is the endpoint. A child can point to each part while the adult names it. Keep the labels and objects visible if they help the explanation.

Observe and continue

A useful note might say: ‘Started at 3 and traced two intervals to 5 with a visible number strip’ or ‘Counted the starting label as a move, then corrected after tracing the gaps.’ Include the support and scale used.

One successful path does not establish understanding of every number line or scale. One error does not establish a persistent difficulty. If questions continue, share concrete examples with a teacher or appropriate professional.

For counting from a known quantity, see Counting On from a Known Number. For an object model of removal, try Subtraction as Taking Away with Paper Leaves. Numbers and counting offers an optional digital continuation.