math.gK.s.lesson_14
CGI Story Problems — Compare Difference Unknown (Lin's Stickers vs Sam's)
- Students can solve a Compare Difference Unknown problem (e.g., 'Lin has 7 stickers, Sam has 4; how many more does Lin have?') using one-to-one matching, drawings, and equations.
- Students can use the one-to-one matching strategy to find the 'difference' between two quantities.
- Students recognize that 'how many more' problems use subtraction even though numbers don't seem to 'go away'.
Lesson plan
Warm-up
5 minNumber Talk: teacher shows two collections — 7 red counters in a row and 4 yellow counters in a row below. 'Which has MORE? HOW MANY more?'
- Wait time 30 seconds
- Take 2-3 strategies
- Affirm: 'Lin has 3 more than Sam — because when we MATCH them up, 3 red counters have no yellow partner.'
M-K-S-AT-14-C
Chart
Physical / non-image
Large 24x18 inch anchor chart. Four columns: JOIN (Lesson 5), SEPARATE (Lesson 8), PART-PART-WHOLE (Lesson 11), COMPARE (today). Each column has the problem-type icon (joining hands / separating hands / two-color combination / two parallel rows with arrows), a sample story, and a sample equation. Today's column highlighted with a star. Style: clean grid, primary colors, lesson numbers visible.
Direct instruction
10 minToday the Math Detectives get the TRICKIEST kind of story problem. Listen: 'Lin has 7 stickers. Sam has 4 stickers. How many more stickers does Lin have than Sam?' Re-tell. (Take 2-3 retells.) This problem is DIFFERENT from yesterday's. Nothing is JOINED; nothing is TAKEN AWAY. Both children just HAVE stickers, and we are comparing. Watch. (Place 7 red counters in a row, then place 4 yellow counters below, aligned one-to-one.) Now look — 4 yellows have a partner. (Pair each yellow with a red.) But 3 reds have NO partner. (Circle the 3 unpartnered reds.) Lin has 3 MORE stickers than Sam. So the answer is 3. Now — and this is the surprise — we still WRITE this as a subtraction equation: 7 − 4 = 3. The DIFFERENCE between 7 and 4 is 3.
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Three more in tree A.model Match: 5 pairs + 3 unpaired in A. 8 − 5 = 3.prompt Story: 8 birds in tree A. 5 birds in tree B. How many more in tree A?
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Three more girls.model Match: 6 pairs + 3 unpaired girls. 9 − 6 = 3.prompt Story: 6 boys and 9 girls in line. How many more girls?
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Same number — no MORE cats than dogs. Difference is 0.model Match: 5 pairs + 0 unpaired. 5 − 5 = 0.prompt Story: 5 cats and 5 dogs at the shelter. How many more cats than dogs?
- If Lin has 7 stickers and Sam has 4, can we say 'Sam has 3 FEWER'? (Yes — same answer, different way of saying it.)
- Show with counters: 8 red and 5 yellow. How many more red? (3.)
M-K-S-AT-14-A
Diagram
Two-row diagram. Top row: 7 red sticker icons in a horizontal line. Bottom row: 4 yellow sticker icons aligned with the first 4 red ones. Vertical lines connecting each pair (4 pairs). The last 3 red stickers have no partner — circled in green with the label 'How many more?' = 3. Below: equation '7 − 4 = 3'. Style: clean, large, color-coded.
Guided practice
8 min-
Pairs work through 3 compare problems: (a) 6 apples vs 3 oranges — how many more apples? (b) 4 cars vs 9 trucks — how many more trucks? (c) 8 squares vs 5 circles — how many more squares?scaffold Compare-mat with two parallel rows for one-to-one alignment.
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Strategy share: 'How did you find the difference? Did you match? Did you count up from the smaller? Did you subtract?'scaffold All three are valid.
M-K-S-AT-14-B
Manipulative
Physical / non-image
Top-down photo of a laminated compare-mat — two parallel horizontal rows of 10 circular spots each, labeled 'GROUP A' (top) and 'GROUP B' (bottom). A child's hand placing red counters in the top row (6 placed so far) and yellow counters in the bottom row (3 placed). Vertical alignment is enforced by the dot positions on the mat. Style: documentary, natural light.
Formative assessment
2 min- Story: 'Maya has 6 marbles. Diego has 2 marbles. How many MORE does Maya have?' Draw the matching picture and write the equation.
- Re-tell the story in your own words.
Closure
- Math Detective close: 'COMPARE problems use subtraction TOO — even though nothing went away. The difference is what subtraction means here. Tomorrow we compare WEIGHT and CAPACITY!'
Homework
5 min- Find a compare opportunity at home. 'I have 5 socks; my sister has 3 socks. I have 2 MORE.' Draw and write.
Exercises in this lesson
Differentiation
- Pre-aligned compare-mat with rows pre-marked
- Color-coded counters (Lin's all red; Sam's all yellow)
- Sentence-frame card
- Compare three quantities: 'Lin 7, Sam 4, Maya 5. Who has the most? How many more does Lin have than Maya?'
- How many FEWER does Sam have than Lin? (Same answer; different framing.)
- Bilingual compare-words card
- Picture-supported problems
- Audio read-aloud
- Concrete-only (match counters, point to unpaired; no equation required)
- Reduced range (within 5)
- Pre-aligned compare-mat
Teacher notes
Fourth CGI lesson — the trickiest one. Compare Difference Unknown is conceptually hardest because nothing is added or taken away; both quantities just SIT there and we compare. The one-to-one matching strategy is the bridge. Many children will say 'Lin has 7 + 4 = 11 more' (adding because they see both numbers) — this is the classic compare error. Address by INSISTING on the matching picture before any equation. The 4-problem-type chart (M-K-S-AT-14-C) brings all four CGI types together for the first time — refer to this chart for the rest of the year. Children who solidify all four problem types here are ready for G1 expansion to 'change unknown' and 'start unknown' problem types.