Grade 3 · Multiply complete equal groups · 237 of 750
Multiply complete equal groups: rows: 7; objects in each row: 1
A rectangular arrangement for a classroom activity has 7 rows with 1 counter in each row. Find the number of objects in the original array, explain the calculation, and check a related question.
Try the question, use a hint when you need one, and compare your reasoning with the worked solution. The animation starts with this chapter’s values; changing its controls explores a new case.
01 · Make a prediction
Your practice question
A rectangular arrangement for a classroom activity has 7 rows with 1 counter in each row. First find the number of objects in the original array. Then answer: What total would one additional full row produce?
Use this scratch space or work on paper. Your notes stay on this page and clear when you leave. Answers are for self-checking; they are not automatically graded.
A starting point
An array organizes multiplication as equal rows. Changing the order of the factors rotates the organization but preserves the number of individual objects.
Work through the reasoning
Step 1
Identify the quantities and the task
A rectangular arrangement for a classroom activity has 7 rows with 1 counter in each row. The first task is to find the number of objects in the original array. An array organizes multiplication as equal rows. Changing the order of the factors rotates the organization but preserves the number of individual objects.
Step 2
Calculate the original result
7 × 1 = 7 objects. The complete rectangle contains 7 objects; a missing row would remove exactly 1.
Step 3
Complete the follow-up calculation
What total would one additional full row produce? 8 objects, because 7 + 1 = 8.
The answer
7 × 1 = 7 objects. The complete rectangle contains 7 objects; a missing row would remove exactly 1. Follow-up: 8 objects, because 7 + 1 = 8.
Compare the method as well as the result. A different valid method may reach the same answer. Keep exact values until the last step when the question asks for rounding.
02 · Explore the model
See the mathematical relationship move.
Use Play, Pause, and the timeline to inspect the construction. Reset restores the question’s original settings. The displayed assumptions describe where this model applies.
Watch the relationship
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The mathematical idea
A rectangular arrangement for a classroom activity has 7 rows with 1 counter in each row. An array organizes multiplication as equal rows. Changing the order of the factors rotates the organization but preserves the number of individual objects. The complete rectangle contains 7 objects; a missing row would remove exactly 1.
7 × 1 = 7 objects
03 · Reflect and transfer
Explain what changes and why.
Advance the timeline one full row at a time. Compare the running count with the equal size of each completed row. Explain which quantity changes and which relationship stays valid. Use the starting values again before checking your written answer.
This is a distinct guided scenario using a reusable mathematical model. Similar-looking diagrams can represent different given values and conclusions; they are not different mathematical theories.