Pattern Games Ranked from AB to Three-Part Units

What the ranking means

The list is organized by the number of positions in the repeating unit: AB has two positions, while AAB, ABB, and ABC each have three. The letters label kinds of elements within a unit. In AAB, the first two elements are the same kind and the third is different; in ABC, all three are different. The letters do not have to stand for alphabet letters, and the elements can be shapes, sounds, movements, or other distinguishable items.

This order is a way to organize choices, not a guarantee about difficulty. A child who recognizes a familiar clap-clap-stomp rhythm may find AAB easier than an unfamiliar circle-square row. The number of choices, how the pieces are presented, and whether the child can see or hear the relevant differences all affect the task. Begin with an example that makes sense to the child rather than treating a particular pattern as a required level.

A repeating unit is a group that can be repeated in the same order to make the sequence. In circle-square, circle-square, the unit is circle-square. In circle-circle-square, circle-circle-square, it is circle-circle-square. Pointing to one complete group and then the next helps distinguish the unit from an individual piece. A unit can start at different positions in a cycle if the sequence is described consistently; for a first game, establish the starting point together.

Choose materials that are safe and comfortable to handle. Large paper shapes, blocks, washable picture cards, or familiar objects can work. Color is one option, but it should not be the only way to tell pieces apart when a child needs another distinction. A raised circle and a raised square, for example, can be explored by touch; a spoken description or movement sequence can provide another route into the same idea.

Keep the purpose of each invitation clear. Copying a model, continuing a stated rule, finding a missing item, and designing a new pattern are different tasks. A child may enjoy inventing before copying or may prefer to watch while an adult builds. None of these responses requires a spoken explanation. The child can point, move a piece, direct a partner, use a communication device, or show an idea another way.

A short row does not always determine a unique rule. Circle-square-circle-square could continue with a circle under an AB rule, but a different longer repeating unit might also begin with those four pieces. Show at least two copies of the intended unit, name it, and ask the child to continue that rule. If they propose another rule, build enough of it to see how their idea works rather than treating imagination as an error.

1. AB: make and copy a two-part unit

Set out a paper circle and a paper square. Say, “Our unit is circle, square.” Place a second circle and square directly after the first pair. Read the row from left to right: circle, square, circle, square. Then gesture across each complete pair. The pairs contain the same shapes in the same order; that order is the feature the game asks the child to notice.

Invite the child to make a matching row beneath yours. Place the first circle together if a starting point helps, then offer a circle and a square for the next position. Check the two rows by comparing the items in the same positions. If the child chooses to place the square first, ask whether they are copying the model or making their own sequence. Square-circle is also a possible repeating unit; it is simply not an exact copy of the model’s starting order.

To extend the stated AB rule, put a circle and a square after the two complete units. The full row is circle-square, circle-square, circle-square. A circle is the next item after the last square because the stated unit begins again. Once the circle is placed, a square completes that next unit. Pointing to the first pair during the decision can help the child check the order instead of relying on a guess.

A child can also provide directions while a partner moves the shapes. Ask, “Which piece goes here to keep our circle-square unit repeating?” The child might point to a choice or indicate it on a device. The partner places that piece and asks whether it matches the intended choice. This arrangement separates the pattern decision from the physical task of picking up a card.

Try a movement version when both partners are comfortable: tap the table once, then raise a hand; repeat tap, raise. Each action occupies one position. The child can choose a different pair, such as pointing up and pointing down, or can watch a partner perform it. Avoid assuming every child can hear a clap, stand, or copy a movement. A sequence can be adapted to available senses and movements without changing its structure.

A game can end after one successful pair or after a short shared experiment. If the child rearranges the pieces into a picture, notice the design and ask whether they want to keep playing with the repeating rule. There is no need to turn every arrangement into a pattern exercise. The adult’s model is an invitation, and the child may prefer another activity.

2. AAB: two alike, then one different

Build circle-circle-square, then circle-circle-square again. Say the three items in order while pointing to them. Place a small strip of paper under each complete group if that makes the boundaries clearer. The strip is a visual aid; it is not another element of the unit. The first two positions have the same kind of shape, and the third position has a different kind.

Offer a circle and a square for the next position. Under the stated circle-circle-square rule, the next item is a circle: it begins the third unit. If the child adds it, ask what would come next. Another circle fills the second position, and a square completes the unit. The resulting row contains three copies of the same three-position group.

If a square is placed immediately after the second complete unit, compare the choice with the model without assuming the child’s reason. Point to the beginning of the first unit and ask, “What starts our group?” The child may want to replace the square, may have been using a different starting point, or may be creating a new sequence. Explore that intention before deciding how to proceed.

For a copying task, give the child three spaces and the pieces needed for one unit. A partner can model circle-circle-square above the spaces; the child places or directs the placement of a matching group below. Afterward, compare each position. This smaller task asks the child to reproduce one group without also tracking where two previous groups ended.

For a gap task, build circle-circle-square, circle-[gap]-square and state that the same unit repeats. The missing piece in that stated rule is a circle. Show the corresponding position in the complete first group, then invite the child to choose or indicate the matching piece. Leaving one clearly marked gap is different from presenting a short ambiguous row with no stated rule.

Two identical actions followed by a contrasting one can express the same AAB structure: tap, tap, wave; tap, tap, wave. Agree on what counts as one action. A long wave is still one position if that is how the partners define it. The adult can perform the actions at the child’s direction, or the child can choose a more comfortable set of actions.

3. ABB and ABC: compare units with three positions

An ABB unit places one kind of item first and two of another kind afterward. Build circle-square-square, circle-square-square. Point to the first unit and say what repeats. After the final square, a circle begins the next unit; the following two positions are squares. This sequence differs from AAB because the repeated shapes occupy different positions.

Place an AAB example and an ABB example in separate rows: circle-circle-square twice in one row, circle-square-square twice in the other. Both units contain three positions, two circles and one square in the first case, one circle and two squares in the second. The child can compare which shape appears twice and where those repeated items sit. Use separate pieces so moving one row does not accidentally change the other.

For ABC, build circle-square-triangle, circle-square-triangle. State that the unit contains those three shapes in that order. After the second triangle, a circle begins the next unit, followed by a square and a triangle. The letters A, B, and C identify three different kinds; replacing shapes with a block, a spoon, and a paper cup preserves the ABC structure if each object consistently represents one position.

Try matching a model to an action sequence. Circle could mean tap the table, square could mean show a hand, and triangle could mean touch a paper card, provided those actions are comfortable and available. Read the shape unit and perform the actions in the same order. The partner may perform the movements at the child’s direction. This is a translation from one set of elements to another, not a requirement to perform a particular gesture.

An ABC row need not use colors to make the items distinct. Choose shapes with different outlines, objects with distinguishable textures, or recorded sounds that the listener can comfortably identify. When texture matters, invite the child to examine the pieces before the sequence begins. A child who cannot use the chosen sensory information can help select another representation; the mathematical rule does not depend on a particular sense.

Do not assume a three-position unit always requires three different items. AAB and ABB also have three positions but use two kinds. Conversely, three different pieces scattered on a table are not yet a repeating pattern. The arrangement becomes an example of the intended repeating rule when the ordered unit is repeated, such as circle-square-triangle appearing twice in the same order.

The same AAB structure can be represented by different physical items. Two spoons followed by a cup, repeated in that order, have the same arrangement of sameness and difference as circle-circle-square. A child can line up one group under the other and compare positions. The objects do not need to look alike across the rows; the relationship is that the first two match each other and the third differs within each group.

Be careful when a piece has several features. A red circle and a blue circle are the same shape but different colors. Before asking whether they count as the same kind, say which feature the current rule uses. If the rule is about shape, both are circles; if it is about color, they differ. A child who notices the other feature has observed something real, even though the stated game focuses elsewhere.

4. Find a missing part and explain the rule

Once a child has seen a complete model, cover one position with a blank card. In circle-square-triangle, circle-[blank]-triangle under the stated ABC rule, the missing shape is a square. Point to the first unit and line up the corresponding positions. The child can choose among shapes, describe the missing one, direct a partner, or simply ask to uncover the answer.

Make the location of the gap unambiguous. A space between two cards might mean a missing item, a larger gap in the layout, or the end of one group. A blank placeholder makes the intended position visible. For a tactile version, use an empty marked space or a distinct placeholder that does not resemble one of the pattern pieces. Explain what the marker means before asking for a choice.

Move the gap to the beginning or end of a unit only when the child wants another challenge. In [blank]-square-triangle, circle-square-triangle, the missing first item is a circle if the same circle-square-triangle unit starts at the first position. That starting point is part of the rule you state. If the child suggests triangle because they are thinking of the end of a previous unit, discuss where each of you placed the boundary.

An explanation can be short and concrete: “The middle of the first group is a square.” A gesture pairing the two middle positions can express the same reasoning. A child does not need to use terms such as ‘unit’ or ‘corresponding position’ to demonstrate an idea. Offer language as a description of what they showed, then check that your interpretation matches their intention.

Sometimes a child spots a pattern the adult did not intend. Circle-square-circle-square can be grouped as repeated circle-square, but it can also be described using a longer repeated unit circle-square-circle-square. These descriptions generate the same continuation when repeated consistently. Other longer rules may match the displayed beginning and then diverge. Naming the intended unit prevents a guessing game about the adult’s private rule.

If a choice does not fit the rule both partners agreed to use, point back to the model rather than merely saying ‘wrong.’ Ask, “Our unit starts circle-circle-square. What happens at this position in the first copy?” The child may revise the piece, ask for help, or decide to invent a different rule. A correction becomes useful when the comparison is visible and the child can act on it.

A partially completed third unit can make the next position more interesting. For circle-circle-square repeated twice and then one circle, the next item under the AAB rule is another circle, followed by a square. The final circle already belongs to the new unit; it should not be treated as the end of the previous one. Grouping the completed units first makes that position easier to see.

A sound sequence also needs a clear boundary. If the unit is one soft tap followed by two louder taps, demonstrate it twice and allow the listener to request another demonstration. Volume alone may be hard to distinguish or uncomfortable for some children, so two different visual actions can represent the same order. The goal is access to the relationship, not a test of hearing or tolerance for noise.

5. Create and share a pattern

Invite the child to choose two or three kinds of items and decide on an order. They might select spoon-block-block as a unit and place it twice. Ask them to show where one unit starts and ends, or invite a partner to point to it. If the creator prefers not to explain, simply enjoy the arrangement; creating a design and making a repeat for someone else to follow are both valid uses of the materials.

A partner can try to continue the creator’s rule. Before adding pieces, the partner describes the unit they think they see: “I think you are repeating spoon-block-block.” The creator can confirm or correct that description. This makes the game collaborative and avoids declaring an adult’s interpretation to be the only possible one. The partner then adds a unit and checks whether it matches what the creator intended.

Try changing one feature at a time. Keep circle-square but make the pieces large instead of small, or keep the same pieces while changing the rule to circle-circle-square. Ask what stayed the same and what changed. If a piece changes both shape and texture, decide which feature defines the pattern. A consistent rule about shape can still be present even when textures vary, but the variation may make the intended feature harder to identify.

A child may make a pattern with unequal spacing: circle and square close together, followed by another pair farther apart. If the rule concerns shape order, the gaps do not change circle-square repetition. If the game also specifies a spacing rule, describe that second rule separately. The physical arrangement may matter to the design, but it should not be silently added as a requirement after the child has begun.

For a shared mural, one person starts a unit and the other completes it, provided both agree on the rule. Alternatively, each partner can create a separate row and invite the other to copy it. A child who prefers parallel play can build their own row alongside a partner without exchanging materials. There is no need to require a performance or photograph the work before it is taken apart.

To preserve an idea for another day, the creator may draw the pieces, dictate their order, or ask an adult to take a private photo. Label the beginning of the unit if the record might be confusing later. Ask before sharing the record with anyone else. A temporary pattern that exists only during play has already served its purpose.

Choose a useful next step

If the child is uncertain, reduce the number of choices and keep a complete unit visible. Rather than asking them to remember circle-square-triangle, leave that group in front of them while they copy it. If matching objects is difficult, use two clearly distinct shapes. If handling cards is tiring, let the child direct a partner. Adjust the part that is getting in the way while keeping the chosen pattern idea intact.

If a child enjoys a familiar sequence, repeat it in another setting without insisting on novelty. A circle-square unit made with paper shapes can become cup-spoon using safe everyday objects. Tell the child which object corresponds to each shape and check the order. Familiar structure with different materials can invite comparison; it is not proof that a skill will transfer automatically to every new context.

You can remember a specific observation such as, “With the model visible, she pointed to the square for the gap,” or “He made a repeating rhythm and asked me to copy it.” Note the support that was available. One response does not establish a child’s overall math ability or predict school performance. It can help you choose a comfortable invitation next time.

Stop when the child wants to stop, even if a row is incomplete. You can set the pieces aside, use them for a picture, or return to the pattern another day. The goal is to make repetition and order available for exploration, with a rule that both partners can see or otherwise access and a child who can help decide what happens next.