Respond

Provide resources that mokopuna can take apart, combine, or move to explore maths concepts, (e.g., balls for exploring movement and shape; blocks, natural materials, puzzles, shells, and nested bowls for exploring shape, pattern, number, and measurement; and cylinders for exploring number and measurement in water and sand play).

Support mokopuna to enjoy maths in everyday experiences (e.g., pattern, number, and shape in kapa haka and siva dance; pattern in daily routines; and number and measurement when sharing food and organising excursions).

Use simple language and gestures related to maths (including comparison) during every day interactions (e.g., bigger, tiny, wide, more, and pair).

Provide resources that children can use creatively to model or represent their ideas (e.g., paint, sticks, fabrics, clay, blocks and sand).

Tune into and comment on children’s actions and decisions as they explore materials and create models or representations (e.g., “You’ve flattened the dough and laid it under the other piece”; and “You’ve put the curved block on top - it’s wobbling”).

Encourage children to explore the properties of resources by using their senses (e.g., how it feels to twist harekeke, the weight of containers filled with frozen or warm water, and the feel of a feather brushed across their skin).

Provide commentary while jointly moving or manipulating resources (e.g., “It’s very heavy - shall I hold this end steady?”).

Provide resources that mokopuna can explore with all their senses and use to express their maths thinking through play (e.g., musical instruments to create a fast or slow beat; clay to shape and reshape; and water and sand with different-sized containers).

Use spoken and non-spoken language for routine happenings (e.g., a regular song or piece of music to signal kai, or photos mokopuna can attach to a chart to indicate they are present).

Present resources (across a range of modes) in ways that highlight their potential for maths exploration (e.g., display patterned artwork alongside shapes that mokopuna can use to make similar patterns; or display drums alongside playing music).

Use language and gesture to comment on, wonder out loud, and pose questions. Give children time to engage, and tune into their cues.

Foreground maths thinking during stories, play, and routines (e.g. wonder out loud about the ways Maui and his brothers plaited paraharaha (flat), tapawā (square), and tuamaka (round) flax ropes to catch the sun.

Use language and gesture to describe tactile models (e.g. weaving). Encourage mokopuna to touch and explore these, using language to prompt thinking about aspects of the construction (e.g. flat, over, and under).

Learn more about children’s interests related to maths investigations from a range of perspectives, including colleagues, whānau, and other children. Investigations could include measuring for baking, designing indoor huts, and constructing with Duplo or blocks.

Provide opportunities for children to puzzle about shape and quantity - for example, by reshaping clay or exploring water quantity using a range of different shaped containers (e.g., narrow, wide, tall and short cylinders).

Respond to children’s curiosity and notice potential to extend maths thinking in their experiences by observing, asking questions, offering materials, and creating space and time for exploration.

Initiate opportunities for children to be part of larger groups when exploring maths experiences (e.g., together create a long, wide river in the sandpit).

Expand the range of resources that children can join, separate, and reshape (e.g., large beads, tiles, and collections of natural materials, ribbon or string). Encourage children to notice their features, (e.g., large, light, patterned, similar, different, curved, or pointy).

Notice potential maths experiences in children's play. Provide resources to help them explore, problem solve, and test out their working theories about the properties of the materials or objects they are using (e.g., alternatively shaped blocks, or lighter fabric).

Create opportunities for children to be curious and creative in larger groups when using resources in play (e.g., when using dominos as play money).

Document children’s investigations in different ways (e.g., display models or constructions such as weaving or working with clay; photograph or film children testing and choosing resources; note conversations as children wonder and problem solve).

Prompt children to explore potential maths experiences through different modes (e.g., provide different-sized boxes to create a range of constructions, or different objects or musical instruments to create a pattern of beats or sounds).

Expand the range of opportunities children have to experience joining, separating, and reshaping using different modes (e.g., a child interested in connecting and grouping trains may be interested in hanging dolls' clothes on a line (connecting) or grouping clothes after they have dried).

Make visible the way children’s learning expands by documenting their multi-modal interests (e.g., sharing quantities with a playdough pizza could be extended into using blocks in dramatic play).

Use language and gesture to show children how they can share ideas, wonder, and think. Use prompts to help sustain conversations.

During play, comment on mathematical aspects of movement, features of objects, and quantity (e.g. "You’re spinning faster and lower in a circle." (movement);"Those leaves are bigger and more spiky and curvy."(objects); and "There more blocks in this pile." (quantity).

Use language and gesture to draw children's attention to features of visual models and representations (e.g. to look for patterns, notice size and shape, and compare different objects).

Initiate and support investigations that have the potential for maths planning (e.g., for using space, number, and measurement to help design, model, or create a vegetable garden).

Create opportunities for shared conversations about ways of exploring or responding to challenges (e.g., “What have you already tried?”, “What else might work?”; and “Who else in our centre knows about this?”).

Create opportunities for mokopuna to model or represent their maths ideas (e.g., by using clay to compare the concepts of small/iti, medium/wawaenga, and large/nui.

Make visible the ways in which mokopuna generate and refine their working theories over time. Keep aside constructions, notes of conversations, and drawings (models) to illustrate and revisit working theories.

Expand the range of resources that can be used intentionally to construct 3D models (e.g., interlocking jigsaw pieces, interlocking blocks, and fabrics that can be easily joined together).

Provide a range of resources for mokopuna to select, arrange and organise into collections for display or use (e.g., natural materials or different size balls for outdoor use).

Encourage mokopuna to use a variety of resources to predict and test out ideas (e.g.,“How many rocks will sink the boat?”).

Encourage mokopuna to document their models and modelling process in different ways (e.g., by using digital tools, mark-making, and drawings; and by contributing to narrative assessments).

Prompt children to use multi-modal approaches when investigating and problem solving (e.g., to use cardboard, photos, wood, sand, rulers, and/or paint when creating plans (or models) for a vegetable garden).

In conversations with children, explore different modes of exploring, finding out, or responding to challenges (e.g., “Let’s draw what it might look like together"; or “Could we measure the length with our steps instead?”).

Display documentation that illustrates children's investigations as they expand across modes (e.g., display taniwha drawings, taniwha constructed with clay, and photos or videos of children ‘being’ taniwha).

Support mokopuna to invent symbols or other markings to represent their ideas. Encourage them to describe and explain their markings and symbols when appropriate.

Encourage mokopuna to use maths language when communicating - for example, when discussing where a missing piece of equipment might be (outside, under, on top of, or in the middle).

Give mokopuna time and space to communicate their thinking. Use maths terms when responding, to sustain further dialogue and exploration.

Support mokopuna to choose how they want to express their maths thinking (e.g. by using spoken or non-spoken language, drawing, constructions, or through movement).

Intentionally expand the range and challenge of children’s maths investigations. This could involve initiating similar explorations with different materials, in different contexts, or for a different purpose.

Demonstrate strategies that children can use to involve others in maths experiences and investigations (e.g., by seeking a point of view, or asking someone to help fold, twist, or weave harakeke under and over).

Initiate, sustain, and extend conversations that encourage children to share their explorations using maths language.

Notice, comment on, or document when children display dispositions of curiosity and persistence in an increasing range of more complex maths contexts.

Involve mokopuna in creating interesting play opportunities by grouping and displaying resources, equipment and materials.

Help mokopuna to plan their investigations using prompts such as “What do you think you will do first?” and “What could you use?”

Support mokopuna to work together to predict how resources will perform for a specific purpose and to test their predictions (e.g., to predict and then test whether a feather is lighter than pumice and whether both float).

Encourage mokopuna to design, modify, or make new materials and equipment when needed for their investigations (e.g., scrunching paper into a ball to add to their collection of round objects).

Encourage mokopuna to expand their maths thinking across different modes and context (e.g., provide opportunities for mokopuna who confidently use their hands, footsteps, or arms to measure, and to represent these measurements using invented symbols).

Demonstrate strategies that mokopuna can use to include others to help solve maths problems that require a multi-modal approach (e.g., asking a more skilled mokopuna/teina to help figure out different ways of creating a model of a wearable art piece).

Initiate and extend conversations with mokopuna using maths language and symbols in different modes – for example, “It’s twice as long” during carpentry; “Can we make wider and taller movements?” during dance; “It’s three days until our Matariki celebration” when crossing days off a calendar.

Help mokopuna to plan their investigations using prompts such as “How else could you test that idea?” and “You want the pattern of the beat to alternate. What would that sound like?".

Increase complexity of maths language as part of meaningful every day events (e.g. “I see that our shoes are all lined up. You have made a line of twos. Each pair of shoes match").

Plan opportunities for children to use maths language and symbols to help others as they puzzle about maths problems. Recognise the expertise that children can share with others, including kaiako and whānau (tuakana-teina).

When planning larger projects, such as constructions and maths-oriented games, create extended opportunities for children to share, make, justify, and test predictions.

Invite children to communicate about their thinking, and to contribute to their assessment and documentation approaches.