math.gK.s.lesson_11
CGI Story Problems — Part-Part-Whole Whole Unknown (Red and Blue Blocks)
- Students can solve a Part-Part-Whole Whole Unknown problem (e.g., '4 red blocks + 3 blue blocks; how many altogether?') using counters, drawings, and equations.
- Students can use the number-bond representation to show the part-part-whole relationship.
- Students share their own counting strategies (CGI Direct Modeling → Counting On) before the teacher names them.
Lesson plan
Warm-up
5 minRead-aloud: a short excerpt from Pat Mora's '¡Vamos a comer!' showing a Mexican family meal scene with food on the table. 'On the table are 4 tortillas and 3 tamales. How many foods on the table altogether?'
- Show the book illustration
- Pose the question; do NOT solve yet
- Bilingual moment: 'In Spanish, 'cuatro y tres' is four and three — same idea as in English.'
M-K-S-AT-11-C
Audio
Physical / non-image
25-second audio clip. Bilingual reader (Spanish-English) reads: 'En la mesa hay cuatro tortillas y tres tamales. On the table are four tortillas and three tamales. Cuántos hay en total? How many are there altogether?' Pause at end for children to respond. Voice warm and warm-toned. Background silent.
Direct instruction
8 minToday the Math Detectives get a NEW kind of problem. Listen: 'There are 4 red blocks and 3 blue blocks. How many blocks ALTOGETHER?' Re-tell. (Take 2-3 retells.) Now — this is different from the JOIN problems (where MORE came) and the SEPARATE problems (where SOME LEFT). Here we just have TWO PARTS — red blocks and blue blocks — and we want the WHOLE. (Place 4 red counters; place 3 yellow counters separately; gather.) 4 + 3 = 7. Number bond: 7 / 4, 3. Now I want to ask: HOW DID YOU FIND 7? Some of you counted all 7. Some of you knew 4 and KEPT COUNTING (5, 6, 7). Some of you might know 4 + 3 from a Number Talk. All three ways are GOOD — they get the same answer.
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Five PLUS two EQUALS seven. The WHOLE is seven.model 5 + 2 = 7. Number bond 7 / 5, 2.prompt Story: 5 birds and 2 squirrels in a tree. How many animals altogether?
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Six PLUS four EQUALS ten — and we know that's a partner of ten!model 6 + 4 = 10. Number bond 10 / 6, 4.prompt Story: 6 apples and 4 oranges in a fruit bowl. How many fruits in all?
- Did anyone count from 4? (Surface count-on strategy.)
- Did anyone count from 1? (Surface count-all strategy.)
- Did anyone JUST KNOW? (Surface known-fact strategy.)
M-K-S-AT-11-A
Illustration
Children's book illustration: a wooden tabletop with 4 red blocks (cube shapes) clustered on the left, 3 blue blocks clustered on the right. Both groups labeled with their counts (4 / 3) and a curved arrow above pointing to a big '?' indicating the whole. Below: number bond template with ? in the whole circle, 4 in left part, 3 in right part. Style: warm watercolor, picture-book aesthetic.
Guided practice
10 min-
Pairs work through 4 Part-Part-Whole problems and SHARE their strategy each time: (a) 3 red + 5 blue blocks, (b) 6 forks + 2 spoons, (c) 4 cats + 4 dogs, (d) 2 red + 7 yellow flowers.scaffold Number-bond mat + part-part-whole bar mat for visual support.
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Strategy share: teacher creates a public chart with three columns — 'COUNT ALL', 'COUNT ON', 'I JUST KNOW' — and tallies which strategy each child used. Names the strategies aloud after children share.scaffold Show MG-2 and MG-3 side by side; same story, two representations.
M-K-S-AT-11-B
Chart
Physical / non-image
Large 18x12 inch chart paper with three columns: (left) header 'COUNT ALL' with a foot icon and example '1, 2, 3, 4, 5, 6, 7'; (middle) header 'COUNT ON' with a leap icon and example 'I knew 4. I counted 5, 6, 7'; (right) header 'I JUST KNOW' with a brain icon and example '4 + 3 = 7'. Tally space below each header. Style: thick black borders, three distinct colors (red / blue / green) for the column headers.
Formative assessment
2 min- Story: 'There are 5 yellow flowers and 3 red flowers in a vase. How many flowers altogether?' Draw the number bond and write the equation.
- Tell your partner: how did you find the answer?
Closure
- Math Detective close: 'Some of you counted all. Some counted on. Some just knew. ALL good ways. Tomorrow we sort and count categories.'
Homework
5 min- Find a Part-Part-Whole story at home. Tell a grown-up: 'We have 4 forks and 3 spoons; we have 7 silverware altogether.' Draw the number bond.
Exercises in this lesson
Differentiation
- Pre-arranged counter sets
- Number-bond mat with the WHOLE space marked '?' for prompt
- Strategy-icon cards (foot for count-all, leap for count-on, brain for I-just-know) for self-tracking
- Three-part Part-Part-Whole: 2 red + 3 blue + 4 yellow = ?
- Make-up your own Part-Part-Whole story for a partner.
- Bilingual story cards (Spanish: cuatro tortillas y tres tamales)
- Picture-rich versions
- Strategy-icon cards
- Concrete-only solution (count out two parts, gather, count whole)
- Reduce range (within 5)
- Number-bond mat with whole and parts pre-marked
Teacher notes
Third CGI lesson. Part-Part-Whole Whole Unknown is the EASIEST CGI problem type because both parts are given — children just combine. The pedagogical move today is STRATEGY ELICITATION: ask 'how did you find it?' BEFORE naming the strategies. CGI research (Carpenter et al.) shows that children develop strategies in a predictable trajectory: Direct Modeling (count-all) → Counting On → Derived Facts → Known Facts. Today is the first time we name these aloud — but only AFTER children share their own strategies. Pat Mora's bilingual book honors the Spanish-speaking children in the room; the cuatro-y-tres parallel English four-and-three reinforces decomposition across languages.