DMIC PD - Understanding and Planning for Big Ideas
NZ Maths Home Page - Curriculum Elaborations, under this 'Key Ideas of Mathematics'. These are no finite, they are infinite. Big idea is CENTRAL to the learning of mathematics, big ideas make connections. Big ideas develop a deep understanding of mathematics.
You need to know the curriculum. Do you research google: 'Key mathematical ideas', you must understand these ideas. Books such as Van de Walle are great.
Step 2: Think about your students
Think about what they bring to the classroom culturally and mathematically.
Put current knowledge and interests at the centre of your instructional decision making
How can you best present mathematical concepts can match your students prior knowledge base?
Step 3: Decide on a task/ problem
Be clear about the big idea you want to connect and the maths you want to explore.
It must be group worthy with an appropriate level of challenge.
Low floor, high ceiling - all kids can come in at the start of the problem ... problems gets harder or deeper as we go.
Culturally responsive and relevant to your students.
If you feel like your lesson is a failure and your kids don't 'get' the big idea you are trying to get across, ask them what they did learn, e.g. "I really liked the way you asked lots of questions today to try and understand".
Big Idea: Repeated addition, skip counting and multiplication are all multiplicative thinking
The distributive law (focus) Some basic addition and multiplication facts can be found by breaking apart the unknown fact into known facts. Then the answers to the known facts are combined to give the final value. Numbers can be decomposed into parts in an infinite number of ways.
Step 4: Predict what will happen
Anticipate all the approaches your students might take - inducing misconceptions.
This is important so you can recognise what your students are thinking, and how to take them forward.
During the lesson you'll be able to identify what you're looking for, why you're going to get to share and why.