Maths teacher, mentor teacher, ed consultant fascinated with discovery learning and inquiry, problem solving, assessment, visualization & making a difference.
Richmond, BC
Joined July 2009
- Tweets11.7K
- Following957
- Followers1.5K
- Likes7.8K
When I had extended the squares question on a checkerboard, I asked, "How many rectangles of any size is on an m x n grid?" The students started with simple cases, organized counting and then one had a breakthrough by organizing the data on a grid. A 6x4 has 210 rectangles Pt.1
And once a class makes this discovery, how many verifications will they need to do to believe their hypothesis?
Attached is my first thought for younger students (middle schoolers who know what a power of 2 is)...
2025^2 and in 2026, we'd need to add 2x2025+1 to this last number to create the next consecutive square
For those with 99, If you are going to solve it by sequential patterns, you need to monitor the first number (odd, odd, odd, odd, even). This then hints at some missing sequential patterns like below. Better to generalize on a row: e.g. shown in 2 ways in the table below:
Visuals are great. I use the same image for division too. Is it 6 ÷ into 2 groups of 3 or 6 ÷ into 2 groups of 3. Visuals can teach a deeper conceptual understanding. Is doubling and halving understood? If I double the number of groups, the groups will be half the size etc.
Discovered (uncovered) by a Gr. 11 student. Find a power of 10 that your divisor goes into with a small remainder. Ex: 10000 ÷ 17 =588 r 4 so break of 4-digit bundles
