Learning Specialist News

THE BIG IDEAS OF MATHS

Last week, I discussed the Big Ideas of Writing and how they built upon each other to create successful writers. This week we are diving into the Big Ideas of Maths and the importance of each skill to build strong foundations for further learning, to create highly numerate flexible thinkers who are able to apply their learning to solve problems. 

The first Big Idea of Maths is ‘Trusting the Count.’ Students must understand the numbers 1 to 10 inside out, including being able to subitise them and recognise them as part-part-whole knowledge. For example, recognising 7 as 7 eggs, 6+1, 3 less than 10, 7 people in my family, 5+2, 1 less than 8, etc. When students deeply understand these numbers, they are able to work with them flexibly and understand them in relation to other numbers. 

Students then move onto the Big Idea of ‘Place Value.’ They learn to understand that our number system is made up of ‘10 of these is 1 of those,’ allowing them to view large numbers in terms of place value structure. 457 is bigger than 189 because the 4 is worth 400, and that is more than the 1 which is worth 100. Representing numbers visually, with manipulatives, through expanded form (457 = 400 + 50 + 7), and through ordering numbers, including on number lines, helps students to develop their understanding of place value. 

As students move from Grade 2 to Grade 4, they begin to focus on ‘Multiplicative Thinking.’ Exploring multiple representations of multiplication and division allows students to build conceptual understandings, leading to fact fluency and the ability to apply their learning to solve more complex problems. Students learn about factors and products and gain another way to find patterns and think about numbers flexibly. 

Working towards Grade 6, the focus deepens to ‘Multiplicative Partitioning’ also known as ‘Equi-partitioning.’ Think of partitioning as the process of dividing numbers into equal groups and then be represented as part of its original group. For example, ½ an orange or 0.2 days of the working week. This stage is all about understanding fractions and decimals, including multiple representations, comparing and ordering fractions, number lines and solving simple problems involving fractions. 

In Secondary College, the final stages of the Big Ideas will be focused on ‘Proportional Reasoning’ and ‘Generalising.’ Students need to be able to recognise rates and ratios and understand proportional relationships as well as recognise and represent patterns in multiple ways, including through symbolic expressions. They also need to be able to devise and apply general rules. 

A final thought on the Big Ideas is that students start learning these skills right from the beginning. Students in junior years will generalise, such as skip counting by 10s, always has a 0 in the one's place value. It is important that these Big Ideas become deeply embedded, allowing students to fully grasp the next Big Idea. By building automaticity and fluency, students will develop more efficient skills and ways to think about numbers flexibly, allowing them to be increasingly strategic in solving problems and thinking mathematically.