Build and Count Sets

Overview

In this first lesson of Tatau, Tāpiri, Tango, students explore addition as joining two groups. They use familiar kai or natural materials, counters and ten-frames to connect concrete collections with drawings, oral explanations and addition equations.

Learning intentions

• WALT represent addition by joining groups.
• WALT count forwards and backwards in English and te reo Māori.
• WALT show addition using materials, pictures and equations.
• WALT explain how we found how many altogether.

Success criteria

• I can make two groups.
• I can find how many altogether.
• I can draw or write an addition equation.
• I can explain my strategy to a partner.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking and problem solving.
• Mathematics and Statistics — Mathsteasers / Alignment: connecting practical mathematical activity with relevant number learning.
• Mathematics and Statistics — Mathsteasers: Additional resources for advanced learners: providing challenge and deeper understanding through open-ended problems.
• Te Mātaiaho classroom practice: students use mathematical language, representations, reasoning and discussion to communicate their thinking.

Lesson structure (30 minutes)

1. 0–5 min · Warm-up: tatau/count. Teacher displays the counting warm-up slides and leads the class in counting forwards and backwards in English and te reo Māori, using small collections of safe kai or natural materials such as shells, stones or kūmara models. Students touch and move each item once as they count, then notice what changes when one more item is joined or one item is taken away.

2. 5–15 min · Explicit teaching and modelling. Teacher shows two groups, for example 3 and 2, and says: “We join the groups. E hia katoa? How many altogether?” Model moving counters onto a ten-frame, counting all, drawing the two groups and recording 3 + 2 = 5 using the visual language “and altogether”. Use the joining-sets modelling slides to show colour-coded groups, the plus sign and the equals sign. Students copy the model with counters, rehearse the sentence “___ and ___ makes ___ altogether”, and show the answer on their fingers or ten-frame.

3. 15–27 min · Differentiated group investigation. Teacher places students in three flexible groups of approximately 6–7 and works first with the Emerging group, while the other groups follow the group task slides. Rotate briefly between groups, asking “How do you know?” and “Can you show it another way?” Students use the build-and-count practice sheet only when ready to record their practical work.

• Emerging: Make and count two sets to 5 with one-to-one correspondence. Students build each group with counters, push the groups together, count the total and say the joining sentence. Provide a ten-frame and adult or peer support.
• Developing: Combine two sets to 10. Students build, draw and record matching equations, such as 4 + 3 = 7. Encourage them to check the equation by rebuilding the sets.
• Consolidating: Solve addition problems to 20 using efficient counting-on. Students start with the larger number, count on the smaller number and explain why this is quicker. Include problems such as 8 + 5 and 12 + 4, using materials if needed.

4. 27–30 min · Share strategies and exit check. Teacher displays the strategy-share and plenary slides and invites two students to show different ways of solving the same joining problem. Students share orally, then complete a quick individual check: build or draw 2 and 4, find the total and write or dictate the equation. Collect responses to plan the next lesson.

Independent Rotation Activities (No Independent Reading Required)

Use these quiet activities for groups working without the teacher. Model every activity before rotations begin. Display the steps as picture/visual cards, using photos, drawings, colour coding and simple words or te reo Māori labels where helpful. Students can show their thinking by building, pointing, saying, drawing or demonstrating with a partner.

1. Build-a-set with counters and numeral cards

• Teacher preparation: Put numeral cards and a matching picture cue at each tray. Model choosing a card, building the set and checking by touching each counter once.
• Materials: Counters, numeral cards, trays, picture cue cards.
• Students do: Choose a numeral card, build that many counters, then show the set to a partner. The partner counts to check.
• Visual success criterion: I built the number on the card. Show a numeral beside an equal-sized set of dots or counters.

2. Ten-frame fill and check

• Teacher preparation: Prepare ten-frames with numeral and picture cards. Model filling spaces from left to right and checking by counting or noticing the full spaces.
• Materials: Ten-frames, counters, numeral cards, dot cards.
• Students do: Select a card, fill the ten-frame to match and compare it with the picture or numeral card.
• Visual success criterion: My ten-frame matches my card. Display a matching card and filled ten-frame.

3. Sort collections by quantity

• Teacher preparation: Make small collections using classroom objects, natural materials or classroom taonga, and label sorting hoops with 1–5, 6–10 or picture quantities. Model sorting one collection and explaining the match.
• Materials: Shells, stones, bottle tops, linking cubes or other safe objects; hoops or trays; numeral and quantity cards.
• Students do: Count each collection, place it with the matching numeral or quantity card and check with a partner.
• Visual success criterion: Collections with the same amount are together. Show two equal collections in one hoop.

4. Roll-and-build

• Teacher preparation: Prepare a large dot die or numeral die and a build mat. Model rolling, saying the number, building the set and checking with a ten-frame or partner.
• Materials: Dot or numeral dice, counters or linking cubes, build mats, ten-frames.
• Students do: Roll, build the number shown and repeat for several turns. Partners take turns rolling and checking.
• Visual success criterion: My build shows the number I rolled. Display a die face beside a matching set.

5. Count-and-match picture cards to numeral cards

• Teacher preparation: Make picture cards showing familiar objects, kai, natural materials or classroom taonga in sets to 20. Model touching each picture once before finding the numeral.
• Materials: Picture cards, numeral cards, matching mats or hoops.
• Students do: Count a picture set, find the matching numeral and place the cards together. Say the number in English or te reo Māori if able.
• Visual success criterion: I counted each picture once and found its numeral. Show a picture card joined to its numeral.

6. Subitising dot plates

• Teacher preparation: Prepare dot plates for quantities to 10, including familiar Māori-inspired patterns where appropriate. Model looking, saying how many and then checking by counting if needed.
• Materials: Dot plates, numeral cards, counters or mini ten-frames.
• Students do: Turn over a dot plate, say or show the number without counting every dot when possible, then check with counters or a partner.
• Visual success criterion: I can see and show how many. Display a dot plate, numeral and matching set.

7. Make-and-check collections

• Teacher preparation: Place target cards with a numeral and picture prompt, such as “Make 7 shells.” Model making the collection, counting it and using a check card.
• Materials: Target cards, baskets, counters, shells, stones, cubes or other safe natural materials; check cards.
• Students do: Choose a target, make the collection, count it and ask a partner to check. Rebuild if the amount is not correct.
• Visual success criterion: My collection has the target amount. Show a target card beside a checked collection with a tick.

8. Practical classroom collection hunt

• Teacher preparation: Place picture prompts around the room, such as “Find 5 pencils” or “Find 8 blocks.” Model collecting safely, counting in a tray and returning everything to its place. Use classroom taonga or natural materials only with care and permission.
• Materials: Picture prompt cards, baskets or trays, numeral cards, clipboards or ten-frames if useful.
• Students do: Work with a partner to find the pictured quantity, place items in a tray, count and match the numeral card, then return the items.
• Visual success criterion: We found, counted and returned the right amount. Display three pictures: find, count, return.

Differentiation

• Learners needing support: Use quantities to 5, larger objects, clear ten-frames, dot or photo cues, colour-matched numeral cards, repeated modelling and a supportive partner. Allow students to point, gesture, use fingers or say the number in either language.
• Extension: Use quantities to 20, mixed representations and hidden or scattered collections. Ask students to make two sets that total a target, explain how they know, record an equation or create a new picture prompt for a partner.

Resources

• the complete counting, modelling, group-task and plenary slide deck
• the build-and-count practice sheet
• Counters, linking cubes or bottle tops
• Ten-frames
• Small collections of safe kai or natural materials
• Large-print numeral and operation cards
• Whiteboards and pens
• Three clearly labelled group areas
• Visual word cards: join, altogether, tatau, tāpiri, and +

Assessment

• Observe whether students touch each object once, keep track of both groups and state the total.
• Listen for accurate use of addition language and check whether students connect a practical model with a drawing or equation.
• Use the final 2 + 4 check to identify students needing further work with one-to-one counting, joining or recording.

Differentiation

• Support: Read every instruction aloud, model one step at a time, use uncluttered cards, large-print numerals, colour-coded groups and symbols, and provide counters and ten-frames. Accept pointing, moving objects, drawing or oral responses instead of written recording.
• EAL and bilingual learners: Pair English with te reo Māori naturally, use gestures and repeated sentence frames such as “___ me ___, e hia katoa?” and allow students to explain in either language before sharing.
• Dyslexia-friendly options: Use a clear sans-serif font, generous spacing, minimal text, high contrast and large symbols. Keep the worksheet visually uncluttered and read it aloud.
• Additional needs: Offer a quiet working space, larger manipulatives, a peer model and extra processing time. Keep groups flexible and praise careful counting and explanation rather than speed.

Extension

• Create a joining story using a familiar classroom or local context, such as collecting harakeke leaves, sharing fruit or gathering shells.
• Represent the story with materials, a drawing and an equation, then challenge a partner to solve it.
• Ask advanced learners to find two different addition equations with the same total and explain how they know.