Gather the materials
- Twelve large paper dots
- A blank sheet or square grid
- Space to move the same objects without adding more
Choose large materials and supervise their use. Adjust quantity, print size, response method and pace to the learner. A partner may move or record while the learner points or explains.
Teach the sequence
3 minutes
Check equal groups
Build three groups with four dots in each. Ask what makes the groups equal. Contrast with groups of four, four and three; the total alone does not show equal group size.
4 minutes
Arrange rows
Move the original twelve dots into three rows of four. Count a row and name how many rows there are. Write 4 + 4 + 4 = 12 and connect each addend with a visible row.
4 minutes
Turn and compare
Rotate the paper. The view now has four rows of three. Ask what changed and what remained twelve. For a ready learner, connect the views to 3 × 4 and 4 × 3.
4 minutes
Make and explain
Ask a pair to arrange ten dots in equal rows or groups and describe their arrangement. Another learner checks whether all groups are equal before finding the total.
Adapt the same idea
Provide more support
Use two rows of three, supply a grid and let a partner place dots on instructions. Keep repeated addition meaningful before expecting multiplication notation.
Extend when ready
Compare arrays for twelve and explain why a proposed unequal grouping does not match the selected multiplication expression. Introduce factor vocabulary in the context of the visible arrangement.
What to observe
- Are the groups equal, and can the learner explain how they checked?
- Does each addend correspond to one visible group?
- Can they distinguish number of rows from objects in each row?
Use these observations to decide what to model next. A brief note about a strategy or a misconception is more useful than simply recording a score.
Home follow-up
Draw an array of a familiar equal-group collection. Label the rows with repeated addition, then turn the page and describe it again.