Place Value Thinking Mistake: Calculate

Thinking Mistake: Calculating

When I work with students, I love to celebrate mistakes and promote a growth mindset (Dweck, 2016). I encourage all students to see that through mistakes comes learning. I like to label misconceptions as ‘thinking mistakes’. ‘Thinking mistakes’ are in direct contrast to ‘silly mistakes’- ones which I want my students to consciously avoid- these are made when our brain is not ‘switched on’. In stark contrast, ‘thinking mistakes’ are made when our brain is working hard, struggling to make thoughtful and logical conclusions. It is during these times that real brain growth occurs.

This series of blog posts presents six common ‘thinking mistakes’ which have repeatedly surfaced in my research into Year 3-6 students whole number place value understanding. Along with each thinking mistake I also present a piece of teaching advice to help you address these issues.

In this blog I am looking at the ‘calculate’ aspect of place value. In my research I defined this aspect in the following way: Applying knowledge and understanding of the place value system when completing calculations using the four operations (e.g., 45 multiplied by ten is 45 tens, 45 plus 100 is 145, 120 divided by ten is 12)

Thinking Mistake:

When students are asked to multiply or divide by a multiple of ten, you may see them ‘add’ zeros or ‘move’ the decimal point or jump to the algorithm. We need to scaffold students to see the link between place value and multiplication and division. Our place value system is a base 10 system. This means each column is related to the one adjacent to it by a factor of 10. That is, it is either 10 times larger or ten times smaller than its neighbouring column.  Students need opportunities to realise that if we are multiplying or dividing by a place value unit (10,100,1000) we simply need to move the digits. In the example below we can see that it is overkill to use the algorithm, it is so much easier to increase the value of each digit by ten, thus moving each digit one place to the left. It is important to reiterate that we are NOT ‘adding’ a zero. We are in fact ‘placing’ or ‘putting’ a zero in the ones place to show that there are no ones when we complete the multiplication.

Teaching Tip: A Number Slide is a perfect resource to help students to visualise the idea that it is the digits that are moving.

You can find a template for a number slide here:https://extranet.education.unimelb.edu.au/SME/TNMY/Decimals/Decimals/teaching/models/numslide.htm

and here is a video of me using a number slide:  https://player.vimeo.com/external/399786471.sd.mp4?s=51b5ac801029d4a10bd2b61c752b04bf995676b8&profile_id=165