Grade 2 · Deal equal shares and keep leftovers · 603 of 750
Deal equal shares and keep leftovers: objects available: 31; recipients: 4
At a classroom activity, 31 counters must be shared among 4 recipients. Find the equal whole-object share and the remainder, 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
At a classroom activity, 31 counters must be shared among 4 recipients. First find the equal whole-object share and the remainder. Then answer: How many more whole objects would be needed to complete the next full round of 4 recipients?
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
Fair whole-object sharing gives everyone the same integer count. Deal only the objects that fit complete rounds; objects left after those rounds form the remainder.
Work through the reasoning
Step 1
Identify the quantities and the task
At a classroom activity, 31 counters must be shared among 4 recipients. The first task is to find the equal whole-object share and the remainder. Fair whole-object sharing gives everyone the same integer count. Deal only the objects that fit complete rounds; objects left after those rounds form the remainder.
Step 2
Calculate the original result
31 = 4 × 7 + 3. Each recipient receives 7, and 3 stay unshared. Whole objects are not silently cut into fractions.
Step 3
Complete the follow-up calculation
How many more whole objects would be needed to complete the next full round of 4 recipients? 1 more. With no remainder, an entire additional round needs 4; otherwise fill the remaining positions in the next round.
The answer
31 = 4 × 7 + 3. Each recipient receives 7, and 3 stay unshared. Whole objects are not silently cut into fractions. Follow-up: 1 more. With no remainder, an entire additional round needs 4; otherwise fill the remaining positions in the next round.
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
At a classroom activity, 31 counters must be shared among 4 recipients. Fair whole-object sharing gives everyone the same integer count. Deal only the objects that fit complete rounds; objects left after those rounds form the remainder. Each recipient receives 7, and 3 stay unshared. Whole objects are not silently cut into fractions.
31 = 4 × 7 + 3
03 · Reflect and transfer
Explain what changes and why.
Move the timeline to distribute the complete rounds. During a round the temporary counts can differ by one; at the end the full shares agree. 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.