Grade 2 · Data · MAT-02-DATA-003
Answer Comparison Questions from Graphs
Answer how-many-more/how-many-fewer questions from graphs.
Learning objectives
What you should be able to do
- Answer how-many-more/how-many-fewer questions from graphs.
- Use addition/subtraction to combine and compare categories.
- Support answers by identifying exact values read from a graph.
Prerequisite check
Make sure the foundation is ready.
Checks graph decoding before analysis.
Learn
Build the idea from meaning, not memorization.
Read values before calculating
Graph questions require two stages: decode the relevant category values, then apply arithmetic. A calculation using misread bars cannot produce a trustworthy answer.
Comparison asks for a difference
How many more or fewer is found by subtraction. If cats=8 and dogs=5, the difference is8−5=3.
Combined categories ask for a total
If a question asks how many cats and dogs altogether, add the category values.
Evidence should point back to the graph
A complete explanation names the values used and operation: 'Cats8, dogs5, so8−5=3 more cats.'
Interactive math lab
Change it. See what stays true.
Data & Graph Lab
Adjust category values and read the graph numerically.
- read value
- compare bars
- combine bars
- justify answer
Worked examples
Twenty different ways to see the concept work.
Cats8,dogs5. More cats?
38−5.
Red6,blue4 total?
106+4.
A7,B7 compare.
equaldifference0.
Books9,games3. Fewer games?
69−3.
Three categories2,4,6 total.
122+4+6.
Largest among5,8,3.
8 categoryRead endpoints.
Smallest among5,8,3.
3 categoryRead endpoints.
Difference10 and6.
4Subtract.
Combine7 and2.
9Add.
How many more8 vs1?
78−1.
Graph category0 vs5.
5 fewer5−0.
Two categories total15, one6. Other?
915−6.
A4,B9,C2. A+B?
134+9.
B−C?
79−2.
A vsC difference.
24−2.
Why not count bar pixels?
Use scale valueVisual length must be decoded numerically.
Bar key/scale2 per interval?
Multiply interval countRespect scale.
Question 'altogether' operation.
additionCombine values.
Question 'how many fewer' operation.
subtractionFind gap.
Explain answer3 cats more.
Cats8,dogs5;8−5=3Evidence+operation.
Practice
Guided practice with hints
01Bars7 and4; how many more?
Hint: Subtract.
Answer: 3
02Bars5 and6 total?
Hint: Add.
Answer: 11
03Bars9 and9 difference?
Hint: Equal values.
Answer: 0
04Largest of2,8,5?
Hint: Read values.
Answer: 8
05Why identify scale first?
Hint: It determines numerical bar values.
Answer: Accurate decoding
06Complete explanation for6 vs2.
Hint: State values+operation.
Answer: 6−2=4 more/fewer difference.
Practice
Independent practice
018 vs3 difference
Answer: 5
024+7 categories total
Answer: 11
03Equal bars difference
Answer: 0
04Largest2,9,6
Answer: 9
05Smallest2,9,6
Answer: 2
06Question 'altogether'
Answer: add
07Question 'how many fewer'
Answer: subtract
08Evidence statement
Answer: Name graph values and operation.
Common mistakes
Learn to catch the error, not just the answer.
Comparison asks for difference, so subtract.
Decode bar value using scale before arithmetic.
State values read and operation used.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Compare survey categories.
- Analyze simple classroom measurements or preferences.
Challenge problems
A+B=14 andA=8. B?
6
Largest exceeds smallest by7; smallest2. Largest?
9
Why can two visually similar bars differ numerically?
Scale or exact endpoints may differ.
How verify comparison answer?
Add difference to smaller value to reach larger.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 6
Game mode
Graph Detective
Answer data questions and cite the bars used as evidence.
Practice
Mastery check
019 vs5 more
Answer: 4
026+3 total
Answer: 9
037 vs7 difference
Answer: 0
04First thing before arithmetic
Answer: Read scale/category values.
05How-many-fewer operation
Answer: subtraction
06How check difference
Answer: Add difference to smaller.
07Why evidence matters
Answer: Shows answer came from correct graph values.
08Can scale change interpretation
Answer: Yes
Terminology
Words to know
- compare
- Determine how quantities relate in size.
- difference
- The numerical gap between quantities.
- total
- Combined amount.
- evidence
- Specific graph values supporting a conclusion.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — 2.MD.D.10
Solve put-together/take-apart/compare problems using graph information.