Change in Quantity to 20
Warm-up
I have 10 cubes on my mat. Watch what I do. Add 4 cubes. What happened? How many now? How do you know? Remove 3. What happened now? How many? Build comfort with describing change before asking students to write equations.
Explore
Build-and-change challenge: students draw a start card (e.g., 12) and an end card (e.g., 17). They build the start with cubes, change it to reach the end, and describe what they did. Record as an equation. Next round: draw an end and change card and find the start.
Formalize
Bring together the three change problem types. Show each with a story mat: unknown result (8+5=?), unknown change (8+?=13), unknown start (?+5=13). For each: what do I know? What am I finding? Give them names. Students will encounter all three types in word problems throughout school.
Change in Quantity to 20
Connect verbal descriptions to formal equations. Your description: I started with 9, added 4, now I have 13 is exactly what 9+4=13 means. The equation is the short form of your story. Show the correspondence between each word in the description and each symbol in the equation.
Practice
Students complete 4 change problems, one of each structure, writing the equation and drawing the change. Exit ticket: teacher poses ?+6=15. Students write the equation and solve.
Exit ticket
Students complete 4 change problems, one of each structure, writing the equation and drawing the change. Exit ticket: teacher poses ?+6=15. Students write the equation and solve.
Step 1: Identify the story type before any arithmetic: something changed, and it's the CHANGE we don't know. Start (7) → change (?) → result (12).
Step 2: Model it: count out 7 counters. Then, hiding your hand behind a cup, add counters until the count reads 12. The cup holds the mystery amount.
Step 3: Solve by counting on from 7 to 12: 8, 9, 10, 11, 12 — that's 5 fingers up. The change was 5 apples.
Step 4: Record it as 7 + ? = 12, and only then connect it to 12 − 7 = 5. Both equations tell the same story.
Watch for: students who hear "got more" and automatically add the two numbers they see (7 + 12 = 19). The story structure — not the keywords — decides the operation.
Step 1: Sort the story: start (?) → change (gave away 4) → result (9). Start-unknown problems are the hardest type in Grade 1 because you can't act them out from the beginning — you don't know where to begin!
Step 2: Act it out BACKWARDS instead: end with 9 counters on the mat. Un-give the 4 (put them back). Count: 13.
Step 3: Check forward: start with 13, give away 4 → 9. ✓ The story works.
Step 4: Record: ? − 4 = 9, solved by 9 + 4 = 13.
The reusable idea: when the beginning is missing, run the story in reverse and undo each change.
What you see: the right answer (7), but when asked "how did you figure it out?", the student shrugs or says "I just knew."
Step 1: Don't accept or reject the answer — get the thinking visible. Hand over cubes or a number line and say: "Show me how someone COULD figure it out."
Step 2: If nothing comes, offer two strategies and let them choose which matches their head: "Did you count back from 15, or did you think 8 + something = 15?" Naming often unlocks explaining.
Step 3: Have them teach the strategy to a partner using different numbers (14 − 9). Teaching forces the implicit steps into words.
Why bother, if the answer was right? Because unexplainable strategies don't transfer. The student who can SAY "I made ten: 8 + 2 is 10, then 5 more is 15, so 7" owns a tool, not a fluke.