# Maths: pedagogy and lesson structure

## Challenge students’ thinking about maths…

In teaching there is never enough time but I think it helps to see how other teachers are structuring their lessons. Here are my weekly maths lessons:

• 1 Lesson with a focus on Reasoning and Problem Solving (rather than curriculum knowledge, although they are connected) where students solve unfamiliar questions.
• 2 Lessons on Content Knowledge (with a focus on the Big Ideas each term: addition/subtraction, place value, multiplicative thinking, fractions/partitioning. Other areas of the curriculum are also covered).
• 30 minutes fluency, mostly game based.

## Is there really an ideal maths lesson?

Here are some thoughts by Tinerney Kennedy:

• work out what you want to achieve in your maths lesson
• set the scene for students and explain what we will be doing today.
• set success criteria in line with your purpose, eg. I struggled with a challenging problem and persisted multiple times

For more detail and examples, click here.

## 6 practices that should be in your mathematical repertoire

See link for the 6 practices explained, with examples: https://primarylearning.com.au/2018/12/03/1828/

1. Noticing: similarities, differences, patterns, connections, errors, change.
2. Wondering: “…wondering helps them pose questions about what they have noticed. Rather than racing to find a solution, wondering allows them to slow down, to think, and do mathematics.”
3. Connecting
4. Talking
5. Justifying, reasoning and working mathematically
6. Prompting: enabling and extending prompts

## Problem Solving

This video shows what happens if we don’t use problem solving skills:

## Content Knowledge

• Starts with exploration and students’ identifying and explaining patterns.
• Sharing strategies and explicit teaching.
• Experience using skills and knowledge to solve non-routine problems.
• Opportunities for students to demonstrate A or B level of understanding through complex, unfamiliar problems.
• Generalise (Ask: Will that always work?) and make connections

Click here for a problem solving strategy called ‘6S Problem Solving’ which I have modified.

## Differentiation

Super Starter

• Students all start with the main task. If they are ‘stuck’ they can get a ‘super starter’ which is an enabling task. I provide a Super Starter for most lessons which is a simplified version of the main task. Often it involves smaller numbers and/or providing question and answers which students need to match.  The aim if for students to problem solve, make connections and take responsibility for monitoring their level of understanding.

Extension

• I also provide an extension for most lessons which students can get when they finish the main task. It is generally a complex, unfamiliar question that requires multiple steps. It might also be open-ended. The content knowledge connects with the main task.
• I base my extension tasks on questions from the book: Open Ended Maths Activities by Peter Sullivan, Pat Lilburn; and Macmillan Maths: Problem Solving Box 1 to 6 pack (expensive but comes with a CD).

## How do you question students in maths???

I use Tierney Kennedy’s approach to questioning. This is my understanding of her approach.

If students are correct, ask:

• Are you sure?
• If no, students need to check their work. Students need to have the confidence that their answer is accurate and have the understanding/reasoning to ‘prove it’.
• If yes, ask: Can you prove it?
• Some students find it difficult to reason and explain their answer, often saying “I just know”. One possible solution is to ask students if the answer could be … (incorrect answer). Often students find it easier to explain why an incorrect answer will never work and this provides students the chance to demonstrate reasoning skills.

If students are incorrect, ask:

• Are you sure? (This gives students a chance to check their work and independently identify the error).
• Ask a closed, narrow question that draws students’ attention to the fact that their answer can never work. We need to address students’ misunderstandings, so they change their own mind.
• Students should not ‘prove’ a wrong answer as it only reinforces the misconception.

## Fluency- Based on Big Ideas in Number

Trust the Count: partitioning, subitising, mental strategies. Practised through games.

• Rainbow Facts/Number Bonds to 10 (also apply knowledge for Bonds to 20 and 100)
• Friendly Numbers
• Nearly Friendly Numbers
• Doubles
• Near Doubles

(I can’t provide copies of games due to copyright)

Activities which develop mental strategies

Sort number sentences based on the mental computation strategy used. Note: some number sentences, can be put into more than one category.

Patterns and Mental Computation: Students independently complete each column. Students then share with their peers what they noticed.

Number Bonds to 10 (Rainbow Facts) Partitioning with counters: students work in pairs and have 10 counters. Student 1 covers some counters, student 2 uses their number facts knowledge to say how many counters are under the bowl/cup. Students take it in turns to cover counters. For example, if a student knows there are 10 counters altogether, and they can see 4 counters , they know that there must be 6 counters under the cup.

Number facts sort with dice: Students work in pairs. Roll two dice and write the addition number sentence the numbers make in the appropriate number section (example recording sheet). Could be recorded on paper or on a whiteboard.

Game: Addition SNAP: Practise selecting the most efficient strategy

• 2 Players
• Take a deck of cards and divide it in half (with face cards removed).
• Give one half to each player
• Without looking, each player takes one card off the top of their pile and places it between the two players, face up. The first person to add up the two cards and say the answer, gets to keep the cards. The winner is the person with the most cards at the end.

Weekly Maths Test: 1min & 15seconds

Students have a test on the mental maths facts they are learning every Friday. They are expected to practise their mental maths fact during the week- this can be done verbally, written in their homework book or practised through games.

Once a student gets 100% correct, within the time limit, they progress to the next set of mental computation facts. There is approximately 20 questions in one test.

The order I use is: Rainbow Facts (number bonds to 10), friendly numbers, nearly friendly numbers, doubles (x2), near doubles, x4, x8, x3, x6, x5, x10, x7, x9, x11, x12. Once students have passed all number facts, they have all the strategies and try to improve their time each week.

Class list mental strategies record

Mental strategies: explanations and examples

Place Value

Biggest Number Place Value Game

Here are some place value questions I ask. Students write the answer on a whiteboard and I encourage them to show the answer in as many different ways as they can. We then share, the MAB images are on ‘infinite clone’ and students drag them from the tool box to make their answer.

## Maths Games Library

• If students completed their homework in the previous week, they can borrow a maths game.
• They record the game number on a class list.
• When students return a game, they need to get a peer to check the contents of the packet and sign for that week.
• Each game is contained within a clear pencil case, with a description of the game and contents on the front.

Maths Games Library- Game labels

Maths Library Borrowing Sheet

## Dr Chris Matthews connects maths and nature

Dr Chris Matthews, from the Aboriginal and Torres Strait Islanders Maths Alliance, explains how maths is everywhere and how we can change mindsets about maths to better respond to children’s natural curiosity.

## Free Teacher Websites- Maths

• Set maths tasks and monitor progress:
• Maths: pictures to practise estimating
• STEM Unit ideas and Engineering Design information
• Maths Inquiry Tasks
• NRich: Rich mathematical tasks
• Interactive Clock
• Pictures as a stimulus for maths discussions

## Free Maths Games

• Place value with MAB:
• Identify a number:
• + 10 and -10, +1 and -1
• Mental computation strategies, including doubles and number bonds
• Number lines:
• Telling time (three levels of difficulty)

## Good Resources (not free)

• Macmillan Maths: Problem Solving Box 1 to 6 pack (expensive)
• Book: Open Ended Maths Activities, Peter Sullivan, Pat Lilburn (reasonably priced)
• Tierney Kennedy resourceshttps://www.backtofrontmaths.com.au/  (expensive)