FROM GROUPS TO EQUATIONS
Count rows, name the groups, and explain what the factors mean. Start with six printable array questions, then use the examples below to connect pictures, repeated addition and story problems.
6 questions · Dot arrays · 2–9 times tables
80 available facts. Balanced across the selected first factors; every eligible pair is used before a new cycle. No repeated pairs in this sheet.
Name: ____________________ Date: ______________
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Use counters to make five separate groups of three. Draw a circle around each group. Write 3 + 3 + 3 + 3 + 3 = 15, then 5 × 3 = 15. The first factor names the number of groups; the second names how many are in each group.
Now arrange the same 15 counters in five rows of three:
There are five rows and three dots per row, so 5 × 3 = 15. Turn the array to see three rows of five: 3 × 5 = 15. The factors exchange roles while the total stays the same. Accept a clearly labeled model with either orientation.
A gardener plants 4 trays with 6 seedlings in each tray. Draw the trays and seedlings. Write a multiplication equation and label the total.
4 × 6 = 24 seedlings. A suitable drawing shows four groups with six marks in each. Repeated addition is 6 + 6 + 6 + 6 = 24. The answer needs the unit “seedlings.”
Three tables each need 8 brushes. There are 20 brushes in the cupboard. How many more brushes are needed? Draw the equal groups before comparing totals.
3 × 8 = 24 brushes are needed. Since 24 − 20 = 4, the class needs 4 more brushes. A drawing can show three groups of eight with 20 marks checked off.
Choose “Equal groups” above for grouped pictures. For fresh printable stories or fact families, use the full worksheet generator.
These activities use the US Common Core Grade 3 operations topics: interpreting products as equal groups, multiplication and division situations, and unknown factors. The Grade 3 Operations & Algebraic Thinking standards include fluent multiplication and division within 100 and recall of products of two one-digit numbers. This page offers a short selection of activities. England’s Year 3 is a different year-group system.
The array preset uses selected first factors 2–9; its second factors initially run 1–10. For a sheet containing only one-digit factors, adjust the range in the full worksheet generator. Read the diagram before opening the answer key, and accept another correct drawing that represents the same quantities.