Multiplication Game

 

I love simple mathematics games that can be reused over and over. Also ones that combine strategy and fluency, such as this multiplication game. 

Fairly self explanatory - two players, each take turns to choose a number from the top and the bottom and multiply them together. The answer will be in the grid, and the aim is to get four in a row on the grid.

Link to PDF Here

One observation is watching students reverse their thinking, "Oh I need 3204, that is an even number and it ends in 4, which numbers will help me achieve that result"

Completeness - Fraction Multiplication

 

I recently came across a fun question (I think from White Rose Maths) but I thought it had missed a trick, so I amended it to allow for more explanation:

This first question proved much more difficult than the second one, given you have less numbers to use. I think I would have preferred the other way around first.

It was fascinating to see the different approaches to solving it. Most dived in with brute force, trying as many numbers as they could. One student was adamant it was impossible, so I asked her to prove it was impossible.

"How do I prove that it is impossible"

"Well, start with why you think it is impossible?"

"Because it is hard"

"What exactly is hard?"

"There are no fractions that work, I've tried them all"

"Show me you have tried them all then"

At this point she realised she hadn't considered improper fractions and so was focused in on a more rigid approach.

One student made an excellent discovery (we have only taught up to multiplication of fractions). 

"We can just flip the numbers and it still works"

"Which numbers did you flip? Do you have to flip all of them?"

"Just the fractions, but they both have to be flipped"

"Does that help when finding non-solutions"

"Maybe. Maybe all the answers are in pairs"

Turning a question into one of completeness and asking them to PROVE and EXPLAIN really gets the students thinking about how to strategise and solve complex problems. It also sowed the seeds of reciprocals and division, but I did not need to explain this here, it was of no significance to their process at this time and would cognitively overstretch them and take them away from their own strategies.

 This year I've been working with a small group of students who are aiming for any level of pass in their upcoming IGCSE.

In order to simplify the study, we've concentrated our efforts on about 45% of the paper. Pretty much all of the algebra (apart from completing the square and graphing and lines of equations) and FDP, as well as data.

Some of the students have difficulty with processing complex information or struggle with cognitive load, so most of the topics we cover are the straightforward questions that can be solved with a a simple algorithmic approach.

Anyway each week se spend 45 minutes on only algebra, and 45 minutes on everything else, leaving the extra double lesson to look at past papers or teach/refresh a new topic.

The constant spaced repetition seems to be working - so sharing the sheets I created, questions, taken from a variety of places, including the amazing Dr Austin and Boss Maths to name a couple. When I get to the end, I simply start again from the start! I'm adding more to the Everything Else sheets as we teach it.

Algebra Qs

Answers

Everything Else Qs

Answers

Division Games

Here are some activities for division, particularly useful in a primary setting.

The 'Race To One' sheet is particularly liked by my recent year 3 class.

Slideshow of them (So I can dynamically add to the slides over time) or you can download as PDF version below.

Download Slides as PDF

Circles and Pythagoras

I've not used Geogebra for a while - I forgot how fun it is!

This is similar to a problem from many sources, such as this excellent University of Georgia article

Find Me... Grids

A simple but rich activity.

Find Me Grids

There is a template version available to create your own - although it isn't hard to create the model yourself.




Depending on age and ability, they could create their own - or explain understanding.

The document is visible on google slides, you can print any page you need - there are a couple that are slightly different just because it is hard to create fractions in google slides.


I will keep adding to the slide link below so keep this page bookmarked.

Template Link

A New Chapter

A lot has changed since I last posted on the blog. And I do mean a lot. After spending a year working in Primaries and tutoring students from age 6 to 26 in Maths and English, and most importantly caring for my children, it was time for a fresh start.

So... we moved... to Hong Kong. This is not a blog about moving to Hong Kong. That is here. I am now part of an international school, working at primary level. So as a result, my blog is being resurrected, as this past year I have spent collating and sharing some of the great resources we have in secondary with primary teachers. Now, my big job is to support this idea of mastery - identify resources that allow teachers to dig deeper into certain topics, and offer tips and hints on some of the basics too.

Many of the resources I refer to will be referenced and praised as they should - but there will be a real mix of age related resources so I will at some point try to organise it in the way Don Steward or Resourcaholic does.