My school was lucky enough to recently have Mignon Weckert talk during a maths job a like. She is passionate about how important posing challenging maths problems are.
So off I went...
The process I went through is based on readings and advice from people who are leaders in inquiry maths and with more knowledge than myself, most notably Mignon.
First, I started with a Central Idea:
Multiplication and division are effective and efficient ways to solve problems.
- Some students are skip counting
- Some students are using repeated addition
- Some students are using multiplication facts
- Some students are using materials
- Some students are answering it ease!
- Some students have no idea (they told me so!)
- Some students counted all.
NOTE: I don't group students any more. The benefits of students working in mixed groups are just too great. I am just aware of where each student is at in their learning.
- It was challenging for most, due to the 21
- To extend those who needed it. I said each group should have even boys and girls (knowing we have more boys than girls).
- I had rich conversations with my strugglers. We used materials, talked about skip counting or using basic facts. One student even said that multiplication makes it easier BINGO!
- Some kids drew pictures others used materials.
- I challenged the higher, some even said that it was tricky.
- Some said 4 groups of 5, that didn't work. So we then talked about 5 groups of 4, with 1 more remaining. Commutative properties!
- Posing harder problems opened up a range of strategies.
- Students worked in groups and learnt from listening to other strategies.
- Students had the flexibility to solve problems in different ways using different operations.
- Students made connections between all 4 operations.
- It didn't really challenge those higher working students. This is something that I still need to work on.
Problem Number 3.
I went to hang out my washing I had 19 pieces of clothing to hang up and 35 pegs. If each piece of clothing needs two pegs do I have enough?
- We discovered the link between addition, subtraction, multiplication and division. i.e. split 19 into 10 and 9 or round up to 20 to help us solve 19 x 2.
- Kids who tried 35 divided by 19 were stumped. Then one said lets use multiplication 19 x 2 as it is easier to solve.
- When working with larger numbers such as 19, it allows you to challenge those who need it and to also support the others. I could work with students on 9 x 2 by creating arrays, but still allowing them to solve the problem.
I have between 15 and 23 apples. How many different ways could I divide them into equal bags?
50 / 5 + 10 = 20 write a story to explain what happens here?
3 X 5 = 30/2 - true or false why?
Use 23 linking cubes to show your understanding the 2, 3, 5 times tables.
Create your own stories using the 2,3,5 times tables.
9 x 0 = 0 Why?