Grade 3 · Read totals and differences from bars · 245 of 750
Read totals and differences from bars: category a: 22; category b: 50; category c: 10
A survey display at a classroom activity records three category counts: 22 counters, 50 counters, and 10 counters. Find the total count and the largest and smallest category counts, 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 survey display at a classroom activity records three category counts: 22 counters, 50 counters, and 10 counters. First find the total count and the largest and smallest category counts. Then answer: How many observations separate the largest and smallest final categories?
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
A bar graph compares category counts using a common baseline and a common vertical scale. The height represents a count; the width of a bar is decoration and does not represent another variable.
Work through the reasoning
Step 1
Identify the quantities and the task
A survey display at a classroom activity records three category counts: 22 counters, 50 counters, and 10 counters. The first task is to find the total count and the largest and smallest category counts. A bar graph compares category counts using a common baseline and a common vertical scale. The height represents a count; the width of a bar is decoration and does not represent another variable.
Step 2
Calculate the original result
Total = 22 + 50 + 10 = 82. The largest final category has 50, the smallest has 10, and all categories together contain 82.
Step 3
Complete the follow-up calculation
How many observations separate the largest and smallest final categories? 40 observations, found by subtracting 10 from 50. The sum answers a different question.
The answer
Total = 22 + 50 + 10 = 82. The largest final category has 50, the smallest has 10, and all categories together contain 82. Follow-up: 40 observations, found by subtracting 10 from 50. The sum answers a different question.
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
PausedHD animation studio
From experiment to screen.
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The mathematical idea
A survey display at a classroom activity records three category counts: 22 counters, 50 counters, and 10 counters. A bar graph compares category counts using a common baseline and a common vertical scale. The height represents a count; the width of a bar is decoration and does not represent another variable. The largest final category has 50, the smallest has 10, and all categories together contain 82.
Total = 22 + 50 + 10 = 82
03 · Reflect and transfer
Explain what changes and why.
Advance the timeline to add the observations to their three categories. Compare the live counts, then inspect the final bar heights on the shared scale. 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.