Adding within 100
Add within 100 using strategies based on place value, including adding a two-digit and one-digit number, and a two-digit and a multiple of 10
Lesson
Set out your lesson
“Adding within 100 means combining numbers under 100 by thinking in tens and ones. Two important cases: a two-digit number plus a one-digit number (45 + 7), and a two-digit number plus a multiple of 10 (45 + 30). We will build with tens groups, write the equations, then try mental answers with a quick check.”
Bring to the table
- About 100 large counters grouped in tens, or drawn tens sticks and ones (parent keeps tiny pieces away from mouths)
- Paper and pencil
Extra for the adult
Worked example. 45 + 7 = 52 because five ones and seven ones make twelve ones (one ten and two ones). 45 + 30 = 75 because four tens plus three tens make seven tens, ones unchanged. Place value drives both adds.
Optional challenge. For Adding within 100, solve 67 + 9 and 67 + 30 and explain how the tens and ones changed in each. Optional: invent one short “packs of ten” story that needs a two-digit plus multiple of 10.
What to notice. Keep one parent note: equations tried; answers; whether tens/ones models were used; the child’s place-value words; support used. A photo of tens piles alone cannot record the strategy. This session samples a few sums, not fluency for every case within 100.
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Teaching approaches
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1 approach
Adding within 100 means combining numbers under 100 by thinking in tens and ones. Two important cases: a two-digit number plus a one-digit number (45 + 7), and a two-digit number plus a multiple of 10 (45 + 30). We will build with tens groups, write the equations, then try mental answers with a quick check.
Spend about 12 minutes adding within 100 with tens and ones models—first a two-digit plus ones, then a two-digit plus a multiple of 10—then checking two fresh problems.
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Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
Illustrative Mathematics · Practice link — not the full lesson
Ford and Logan Add 45+36
Before you open · source notes
Two worked strategies for 45 + 36 connect tens and ones. This is a transition from grade 1 toward grade 2, not an independent fluency assessment.
Free, no sign-in. Use the student view with your child.
Before you openAsk which parts are tens and which are ones, and whether each strategy would work on a different pair. One example does not certify fluency within 100.
Opening this link does not save learning or assess mastery.
Source, access and review notes
Public Illustrative Mathematics task page. The .html address responds HTTP 308 to this URL. An anonymous GET of this URL on 2026-11-10 returned HTTP 200 with no login or payment prompt. Where a teacher solution is present, it is on the same page as the student task; this check did not find a separate locked student view. An adult can use the student view section and should not read a solution aloud. Advertising was not observed in the fetched HTML text; that is not a browser, device, or ad-free guarantee. This is a paper or discussion task, not an automatically marked interactive game. Opening the link does not save practice or assess mastery. Diagrams on the page use missing or filename-only alt text, so they are not an accessible image equivalent. Accessibility still depends on an adult describing the picture.
Illustrative Mathematics. “Ford and Logan Add 45+36.” Licensed CC BY-NC-SA 4.0. External task; Gakuva does not copy, host, embed, or redistribute it.
CC BY-NC-SA 4.0 — link only
Check understanding
- Calculate 46 + 7 using place value (46 + 4 + 3 = 53)
- Calculate 38 + 40 = 78 using tens understanding
- Relate the strategy to a written method and explain the reasoning
“Can your child work out sums like '47 + 8' or '35 + 50' by thinking about the tens and ones separately rather than counting up one at a time?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Addition & Subtraction
- Age range
- Ages 6–8
Standards