# Arranging for learning

An effective mathematics and statistics programme includes sustained daily engagement and opportunities to work both independently and collaboratively to make sense of ideas.

#### Guidance for effective practice:

1. Ensure that you prioritise sufficient teaching time for sustained mathematics learning.
Kim’s class attend an inter-school sports day. On the following school day Kim develops her language and mathematics lessons around the sports day. She compensates for the missed day by increasing the length of her language and mathematics lessons during the week that follows.

2. Manage the grouping of ākonga (individual, small group, and whole class) to suit the purpose of lessons. Use mixed ability grouping to encourage all ākonga to engage with a range of ideas and strategies along with needs-based grouping for targeted support.
Marcus and his Year 8 class are learning about measuring angles. He begins the unit with a short pre-test and sorts his students into groups by the results. Although the small groups work well for teaching skills like using protractors, Marcus is concerned that he is over-using achievement-based grouping. His competent students seem complacent and some less competent students are losing confidence. Using the tuakana-teina model, he puts the students into mixed pairs to encourage a better exchange of ideas and support the self-belief of those losing confidence.

Knowing that pizza was the preferred option for a shared class lunch, Marcus sets the whole class a challenge based on this scenario:
“Antonella is an expert pizza cutter. Tell her the number of pieces you want a pizza cut into, and she’ll do it exactly.
Can you?”

Each pair of students is given paper plates (pizzas), protractors, rulers, calculators, and scissors. They are invited to create pizzas equally divided into different numbers of parts.

Marcus notices the students are discussing how to divide a full turn of 360⁰ into equal angles, to find the exact centre of a circle, and to name the parts as fractions. The range of ideas ‘in play’ is far greater than students experienced with achievement-based groups.

3. Deliver interactive lessons about concepts and procedures to the whole class, or to a selected group, when you notice significant gaps in knowledge.
Jo starts the unit on fractions with her Year 5 class with an investigation. Using a set of circular fraction pieces, students find as many ways to make one (whole) as they can. The students work in small collaborative groups and share their findings with the whole class. That process takes two whole lessons.

Jo notices that many students do not know the meaning of the numerator and denominator in fraction symbols, particularly for non-unit fractions like 3/4 and 2/5. Using an online digital tool that displays fraction circle pieces, Jo teaches the whole class. She invites students to draw fractions, like “four fifths”. Individual students display each fraction on the interactive whiteboard for all to see. Jo asks students to record the fractions using symbols, and to talk to their partner about the meaning of the numbers.

Most students have an “out of” view of fractions. Jo explicitly explains that the numerator (top number) is a count, and the denominator (bottom number) tells the size of parts being counted. She illustrates the meaning of both numbers using carefully chosen examples.

To see if her students understand fraction symbols, she asks them to draw “seven quarters” and write the fraction symbol. Some students think that the challenge is impossible…