Solving Problems

I had an amazing lesson with my year 9 class today!
They’re such a beautiful bunch of kids – we get along well and they’re all so keen.

We’ve been working on solving linear and quadratic equations and we’re about to move onto simultaneous equations. I decided to introduce them to the concept and the mathematical ideas that they’re going to need, without actually telling them that they were doing these scary things called simultaneous equations.
I also wanted to force them to practice communicating mathematically, because they can always do with some practice.

I split the class into 5 groups and gave each group a problem that they needed to solve and would explain to the class later in the lesson. Some problems were harder than others so I strategically gave those to my stronger students.

The decorations on this mobile weigh 480g.  Find the weight of each diamond, star and circle.

The decorations on this mobile weigh 480g.
Find the weight of each diamond, star and circle.

How tall are the adults? How tall are the children?

How tall are the adults?
How tall are the children?

How much would one doughnut cost? How much would one muffin cost?

How much would one doughnut cost?
How much would one muffin cost?

What do each of the animals weigh?

What do each of the animals weigh?

What is the value of each of the coins?

What is the value of each of the coins?

Within a few minutes every group knew what the answers had to be, but they’d figured it out by trial and error. Now the fun part – forcing them to find another way to figure out the answers, and be able to explain their method to the class.

I gave a few hints but largely they worked really well together and had some really great discussions. Then each group got up in front of the class and explained how to solve their problem and answered questions from the rest of the class.

We had about 20 minutes left so I handed each student one of these game cards:

I asked them to choose values for x and y, substitute them in and then write their answers. Then they switched with someone else in their groups and had to try and guess their numbers. They started with “nice” numbers (small and positive) and then started challenging each other by choosing negative numbers and decimals.

Most students were just using trial and error, but a few were starting to experiment with substituting. Before we left I asked students to raise their hand if they liked trial and error as a way to answer a question. More than half the students raised their hands. Then I asked if anyone had been frustrated with using trial and error once the numbers got “trickier”. Almost everyone put their hand up. I told them that next week we’ll start looking at more formal ways to solve simultaneous equations.

As if to prove my point, one of my boys then called out “Miss! Miss! I’ve got one for you to try and solve!”. He handed me the card and it only took me a few seconds to use the elimination method in my head and come up with x=-0.5 and y=0.2.

They were amazed: “wow!” “what? No way!” “miss you’re a magician!”

It was brilliant! I ended the lesson with “that’s what I’m teaching you guys to do next week!”

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