# Ten daily mathematics lessons · Days 21–30 of the year

Each session uses **notice 3 + model 5 + guided build 8 + independent route 6 + exit 3 minutes**. The [learner cards](student-cards.md) provide three fictional contexts per day. Pick one for guided work and reserve a different one for an unfamiliar response. The printed numeral, chart and concrete amount should agree. Let a learner show their thinking with strips, marks, numeral cards, speech, sign, AAC, a tactile line, or directed movement of pieces. Record access support without treating it as a mathematical hint. Use the [teacher key](teacher-key.md) only in teacher view.

## Day 21 — Nine tens and more

**Goal:** build, name, and locate 91–95 from nine full tens and loose ones. **Prepare:** nine audited ten-strips, five loose pieces, H/T/O mat, 91–120 chart, Day 21 cards.

1. **Notice, 3:** Rebuild 90 from Day 20. Place one loose piece after it. Ask what stays nine and what changes. Check one strip is ten.
2. **Model, 5:** Make 92 as nine tens and two ones. Point to the tens and ones positions in 92, write 90 + 2, then locate 92. Contrast a deliberately reversed 29 with two strips and nine ones.
3. **Guided, 8:** Use card A's 91 marks and card B's 94 marks. Build both, pair their nine full tens, then compare one and four loose marks. Ask a learner to identify 93 between them on the chart and explain why.
4. **Independent, 6:** Use card C's 95. Learner makes it in a chosen mode, gives a numeral, then removes two loose pieces to show 93. Offer the chart *after* a tens/ones account.
5. **Exit, 3:** Show nine tens and three ones. Ask for its numeral and one more. **Key:** 93 and 94. If 903 appears, align numeral cards over the T/O columns and rebuild 93.

## Day 22 — Ninety-nine becomes one hundred

**Goal:** preserve the amount across 99 + 1 = 100 and explain that ten tens make one hundred. **Prepare:** nine strips, ten singles, a tenth strip, one hundred square/bundle, Day 22 cards.

1. **Notice, 3:** Build 98. Ask for the next two numbers; add one single at a time and leave the loose pile visible.
2. **Model, 5:** At 99 + 1, audit ten loose ones, trade for a tenth full ten, then audit **ten full tens** and trade them for one hundred square. Show 9 tens + 10 ones = 10 tens = 1 hundred = 100. In each trade, the amount stays equal. Write 100 with zero loose tens and zero ones *in the bundled form*.
3. **Guided, 8:** Cards A and B show 97 and 99 fictional marks. Learners move 97→98→99→100. Ask at which move the ones trade occurs and why a hundred bundle can replace ten strips.
4. **Independent, 6:** Card C begins with ten full strips. Learner shows the same amount as one hundred square and as numeral 100, then identifies the number immediately before it. Do not require a fine-motor-heavy drawing of 100 dots.
5. **Exit, 3:** Show nine strips and ten loose marks. Ask for the total before and after *both* trades. **Key:** 100 in all three arrangements. If “ninety-ten” remains, audit the ten loose and ten full groups physically.

## Day 23 — One hundred and some ones

**Goal:** make, read, and order 101–105 as 100 plus ones. **Prepare:** hundred square or ten strips, five singles, H/T/O mat, Day 23 cards.

1. **Notice, 3:** Compare 100 with one hundred square plus one loose mark. Ask whether the numeral can be 100 still. **Key:** 101.
2. **Model, 5:** Build 103 as one hundred, no separate tens, three ones. Display 100 + 3 = 103, and show the middle zero's place role. Make 130 with a different model only to show that reversing positions changes the amount; 130 is outside today's target range.
3. **Guided, 8:** Cards A/B show 101 and 104. Learners make both, point to the zero tens column, and explain that 104 exceeds 101 by three loose marks. Locate both on the 91–120 chart.
4. **Independent, 6:** Card C shows 105. Learner models it with a hundred and five singles or ten strips and five singles, then gives a number between 102 and 105 and justifies it.
5. **Exit, 3:** Ask what one hundred and two loose ones names, and what is one less. **Key:** 102 and 101. If 12 appears, explicitly keep the hundred square while removing one loose mark.

## Day 24 — Ten more beyond the hundred

**Goal:** connect 106–110 and explain 109 + 1 = 110 without changing the total during exchange. **Prepare:** hundred square, ten singles, one ten-strip, Day 24 cards.

1. **Notice, 3:** Build 106 and 107 from the hundred plus loose pieces; ask which amount grows and where the numeral changes.
2. **Model, 5:** Build 109, add one, count ten loose ones, trade them for one full ten. Show one hundred + one ten + zero ones = 110. Contrast 110 with 101 using the tens and ones columns.
3. **Guided, 8:** Cards A/B start at 107 and 109. Learners count from 107 to 110 with three one-steps, then show 110 as 11 verified tens and as a hundred plus one ten. Keep the chart visible for order, but require a quantity explanation.
4. **Independent, 6:** Card C is a schematic of 110. Learner represents it in two ways, changes it to 108 by removing two loose ones *from an unexchanged 100 + 10 ones model*, and describes the needed trade-back. Alternatively start at 110 and trade the one ten for ten singles before removing two.
5. **Exit, 3:** Ask for one more than 109 and one less than 110. **Key:** 110 and 109. If 101 is named, align 110 and 101 above the mat and compare their ten and one columns.

## Day 25 — Choose a model; collect Week 5 evidence

**Goal:** transfer representations and ordering across 91–110, then collect a fresh sample. **Prepare:** Day 25 cards, strips/square/singles, chart, [Check 1](student-checks.md) face down.

1. **Notice, 3:** Show 99 and 100 as models. Ask whether the new hundreds digit represents a new piece or the same ten-tens amount bundled.
2. **Model, 5:** Make **102** with a hundred and two singles and with ten strips and two singles. Put it beside 98. Say/show that 102 has a full hundred, while 98 does not. Do not model the check numbers.
3. **Guided, 8:** Cards A/B/C give 93, 100 and 106. Learners build any two, order all three from their structures, and challenge one adjacency with chart location and quantity. **Key:** 93 < 100 < 106.
4. **Independent, 6:** Give Check 1 and preserve the first response. Read the prompt or provide a tactile/large version without supplying place-value hints. Record which representation was independent.
5. **Exit, 3:** Ask for one fact that helped order 93 and 106. **Key:** 106 contains a full hundred while 93 does not. Plan Day 26's entry from the check: if 99→100 is uncertain, reteach exchange before adding the 110s.

## Day 26 — A hundred, a ten, and loose ones

**Goal:** represent and compare 111–115, distinguishing 111 from 101. **Prepare:** hundred square, one strip, five singles, H/T/O mat, Day 26 cards.

1. **Notice, 3:** Put models of 101 and 110 beside each other. Ask what each extra piece is worth.
2. **Model, 5:** Make 112 as 100 + 10 + 2. Point to the 1, 1 and 2 in their H/T/O columns. Put a model of 102 beside it to show that the extra full ten changes the total by ten.
3. **Guided, 8:** Cards A/B show 111 and 114. Build or select both models, match numerals, and compare their equal hundred and ten pieces before comparing singles.
4. **Independent, 6:** Card C shows 115. Learner makes it and changes it to 113 without moving the hundred or ten. Give a large H/T/O mat if digit writing obscures the reasoning.
5. **Exit, 3:** Ask for the numeral one hundred + one ten + three ones and one more. **Key:** 113 and 114. If 103 is named, place the ten-strip in view and ask which column records it.

## Day 27 — Twenty more than one hundred

**Goal:** reach 120 by trading at 119 + 1 and show 120 as a hundred plus two tens or twelve tens. **Prepare:** hundred square, two strips, ten singles, twelve verified strips, Day 27 cards.

1. **Notice, 3:** Build 118 as hundred + ten + eight. Ask for one more and what the *next* added one will require.
2. **Model, 5:** Add one to 119. Trade ten loose ones for another ten-strip. Display 100 + 20 = 120 and 12 tens = 120. Audit twelve strips in ten-and-two groups; do not count a bundle as an extra amount when its strips are still displayed beside it.
3. **Guided, 8:** Cards A/B represent 117 and 119. Move 117→118→119→120 on a chart and model; ask which change creates a new ten and which quantity remains the same during that trade.
4. **Independent, 6:** Card C gives 120. Learner chooses hundred + two tens or twelve strips, explains their equivalence, and names one less than 120. Two modes are offered; writing 120 is not the only acceptable response.
5. **Exit, 3:** Show one hundred, one ten and ten singles. Ask for total and exchanged form. **Key:** 120 and one hundred + two tens + zero singles. If 1110 appears, exchange the ten singles and reread all columns.

## Day 28 — Locate numbers between landmarks

**Goal:** use a line and chart to locate and order selected numbers from 90 to 120. **Prepare:** [number line](number-chart.svg), text/tactile equivalent, number cards 94, 100, 107, 113, 119, Day 28 cards.

1. **Notice, 3:** Point to 90, 100, 110, 120. Ask what one interval of ten covers, and whether 95 lies halfway between 90 and 100.
2. **Model, 5:** Place 107 seven equal one-steps after 100 on the line. Confirm with 100 + 7 loose marks. Warn that visual distance only works when marks use equal spacing.
3. **Guided, 8:** Cards A/B name 96 and 112. Learners locate each from the nearest full ten, check on chart, then order 96, 107, 112. Ask how they know 112 is beyond 110 rather than between 100 and 110.
4. **Independent, 6:** Card C names 119. Learner locates it one before 120 and gives one other number between 112 and 119. Accept a tactile line or numbered sequence read by the learner. Ask for the two bounding tens.
5. **Exit, 3:** Hide 109 on the chart and ask what sits immediately before 110 and why. **Key:** 109; one more completes ten loose ones. If a child places 109 after 110, rebuild both amounts.

## Day 29 — Same amount, different representations

**Goal:** connect a numeral, a chart/line position and two equal concrete representations for a number at most 120. **Prepare:** square, strips, singles, H/T/O mat, chart, Day 29 cards.

1. **Notice, 3:** Display 108 as one hundred + eight ones and ten strips + eight ones. Ask what is different and what amount is unchanged.
2. **Model, 5:** Choose 116. Show 100 + 10 + 6, then 11 tens + 6 ones. Place 116 six equal steps after 110. Ask what each digit records in the standard bundled model.
3. **Guided, 8:** Cards A/B show 104 and 118. Pairs build each in a hundred-based and all-ten-strips model, select its numeral and chart location, then order the two. Use the audit rule: the square *replaces* ten strips.
4. **Independent, 6:** Card C names 120. Learner chooses a hundred and two strips or twelve strips, sketches/points to its chart cell, then explains why there are zero loose ones. Capture a second route only if independent time remains.
5. **Exit, 3:** Show one hundred + one ten + six ones and ask for another equal form. **Key:** 116 and eleven tens + six ones. If a learner adds the square *and* ten replacement strips, remove the duplicate and recount.

## Day 30 — Transfer check and responsive next step

**Goal:** collect an unfamiliar sample of representation and ordering through 120, then choose reteaching. **Prepare:** Day 30 cards, chart/line and manipulatives, [Check 2](student-checks.md) kept separate.

1. **Notice, 3:** Present the three fictional contexts without their totals. Ask which could be greater than 110 and how a model might show it. Withhold answers until learners justify them.
2. **Model, 5:** Use unrelated **92**: nine strips + two singles, numeral 92, between 90 and 100 on the line. Model a full sentence or AAC sequence: “I know it is less than 100 because…”. Do not model Check 2's numbers.
3. **Guided, 8:** Cards A/B/C show 97, 109, 115. Learners choose two to represent and locate, then order all three. Ask them to explain which has a hundred and which has a separate ten. **Key:** 97 < 109 < 115.
4. **Independent, 6:** Give fresh Check 2. Note independent mathematical explanation separately from adult reading, tactile access, chart use and conceptual prompts. Save the first response.
5. **Exit, 3:** Ask for a number one less than 120 and one reason it is less. **Key:** 119; it lacks one loose one before the trade to another ten. Use individual evidence to choose the next lesson; reaching 120 today does not establish the whole Year 1 achievement standard.

**Reuse:** Original lesson scripts © NeuroForgeIO Pty Ltd 2026, [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/). [Scope and checks](source-and-review.md).