Grade 2 · Add through a new ten · 525 of 750
Add through a new ten: first amount: 43; second amount: 27
At a classroom activity, a first group contains 43 counters and another group brings 27 counters. Find the total after both groups join, 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, a first group contains 43 counters and another group brings 27 counters. First find the total after both groups join. Then answer: If one extra object joins the second group, what is the final total?
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
Addition joins two disjoint groups. Keep the starting group in the count while the second group arrives; the result includes every object from both groups.
Work through the reasoning
Step 1
Identify the quantities and the task
At a classroom activity, a first group contains 43 counters and another group brings 27 counters. The first task is to find the total after both groups join. Addition joins two disjoint groups. Keep the starting group in the count while the second group arrives; the result includes every object from both groups.
Step 2
Calculate the original result
43 + 27 = 70. The final 70 can be checked by removing the 27 arrivals and recovering 43. For larger totals the bars summarize quantities rather than drawing every object.
Step 3
Complete the follow-up calculation
If one extra object joins the second group, what is the final total? 43 + (27 + 1) = 71. One additional arrival increases the total by one.
The answer
43 + 27 = 70. The final 70 can be checked by removing the 27 arrivals and recovering 43. For larger totals the bars summarize quantities rather than drawing every object. Follow-up: 43 + (27 + 1) = 71. One additional arrival increases the total by one.
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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From experiment to screen.
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The mathematical idea
At a classroom activity, a first group contains 43 counters and another group brings 27 counters. Addition joins two disjoint groups. Keep the starting group in the count while the second group arrives; the result includes every object from both groups. The final 70 can be checked by removing the 27 arrivals and recovering 43. For larger totals the bars summarize quantities rather than drawing every object.
43 + 27 = 70
03 · Reflect and transfer
Explain what changes and why.
Scrub from no arrivals to all arrivals. The current total grows by the number of objects that have joined so far. 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.