Category Archives: Algebra

206. Seek a number pattern

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So I’m all ready to teach a lesson recapping number patterns from the basics for a lower ability group … then a visitor to the Department arrives and asks if it’s okay if they observe my lesson. They’ve been told that there is usually something ‘off the wall’ happening in my room. Thanks … I think!

Well, I’m not one to disappoint. A little fun with the starter perhaps? The sun is shining and I’ve got whiteboards and chalk …

We’ve all seen fence panel number patterns. Here is a fence:
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What can you see?

We discussed the pattern linking number of posts and spacers. We then represented the fence in colour coded symbols (yes, we have chalk in more than one colour!) and annotated it.

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The class were then sent off to find their own patterns. They found repeating patterns and made notes on their whiteboards. Once they were happy with their work they could chalk it out.

This group looked at number of slats on a bench with number of benches.
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They represented each bench as an ‘L’ and each slat with an ‘o’.
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They worked out:
No of benches x 6 = No of slats

Other groups looked at number of windows & number of classrooms and number of benches & number of picnic tables.

We then went back to our quiet number pattern work in the classroom.

This task is easily adaptable for many aspects of number, including ratio and proportion.

200. Website/Resource of the week 4

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Wow! This is proper blog post number 200. How should I mark this occasion? Why, by recommending another splendid site of course!

To quote the folks themselves: JustMaths is born from the passion and spirit of three full time teachers at the “most improved school in England” (January 2013).

The site has both free and subscription resources. The latest initiative is the ‘Bread & Butter’ worksheets. It consists of straight-forward starter worksheets to practice essential skills for students: Just Maths: Bread & Butter. My class use them every lesson and I’ve noticed a real improvement in their confidence and quality of solutions in just two weeks.

198. You sunk my rectangle!

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How about a game of ‘Battleships’ with a graphical twist? My Year 7 class loved playing this game and we developed understanding without resorting to tediously drawing out lots of graphs.

Objective

To be able to draw and label lines parallel to the x or y axes ie x=1, y=3

Equipment

  • Squared paper
  • Pencil
  • Coloured pens or pencils
  • Ruler or straight edge

Preparation

1. In pairs, agree the size of a set of axes and draw two identical sets each. Negative axes can be used as an extension.

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2. On one set of axes draw a rectangle, making sure the edges are on whole numbers.

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3. Extend the edges of the rectangle to give you two horizontal and two vertical lines. Label the lines accordingly. You are now ready to play!

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Playing the game

1. Players take it in turns to guess a straight line eg x=3. Their partner says ‘Hit’ if it is the edge of their rectangle and ‘Miss’ if it isn’t. This information is recorded on the players second grid so they can keep track of their guesses.

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2. The game continues until a rectangle is revealed:

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3. The player must then label where the lines intersect. The losing player may find it useful to continue guessing.

Extension: What do thy notice about the co-ordinates and the equations of their lines?

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4. What is the area of the rectangle?

Extension: Is there a link between the co-ordinates and the area?

188. Top Teachmeet Trumps Resource

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I’m currently trying out ideas from the #mathsmeetnorthwest TeachMeet. Emma Weston did an excellent presentation on ‘Marking for motivation and progress’. She inspired me to look for a Top Trumps activity for my class – they needed some consolidation of solving equations with an unknown on each side and with brackets. I found this brilliant solving equations Top Trumps by Dusher on TES resources.

The Marvel comic themed algebra cards have three tiers of difficulty and went down a storm. My class would have happily played all lesson, if I had let them.

 

Who would have thought that equations could be so engaging?

186. Fantastical algebra

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Have you ever played the parlour game ‘Fantastical Creatures’? Click for a lovely description and example of it by Little Cotton Rabbits.

I’ve adapted this concept for teaching aspects of number and algebra.

Topics
Basic arithmetic
Inverse operations
Order of operations
Setting up simple equations
Using brackets with numbers/letters
Solving single sided equations

Equipment
Strips of paper – one sheet of A4 makes about 6 strips
Coloured pens (optional)

Basic instructions
1. Write an instruction on the top of the strip (portrait orientation). Label it (a).

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2. Fold over the strip twice to hide the writing. Write (b).

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3. Pass on the strip, do not unfold it.
4. By the ‘(letter label)’, write the next instruction. The letters help you keep track of how many times it has been passed on.
5. Fold over the strip twice and put a label for the next letter of the alphabet.
6. Repeat steps 3 – 5 as required.

The beauty of this activity is that each problem is constructed by a group of pupils and they are in control of the level of difficulty.

Activity 1: Setting up simple equations

Follow the basic activities with the following instructions:
(a) I think of a number and write an instruction
(b) & (c) Now I write an instruction
(d) The answer is write a number
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Pupils fold the puzzle up tight and either pass it on one last time or hand them in (to be randomly distributed).

Pupils unfold their mystery puzzle and construct the equation, step by step. My pupils quickly realised the importance of simplifying, but many forgot the importance of using brackets. This was a useful misconception to identify.

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Pupils then use inverse operations to calculate the unknown.

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The algebraic operations and numerical operations can then be compared.

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Activity 2: Problem solving

This follows the same structure as the equation activity, but pupils are describing a geometric problem. In the examples the blue sections are up to the pupils to choose.

Example 1
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Example 2

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In the second example pupils can visualise the problem as well as using algebraic terms.

Activity 3: Number Skills

This activity can also be used for setting up BIDMAS problems by omitting the algebra.

164. Plant a Learning Tree

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Do you know that feeling when you are starting a topic which is building on existing knowledge and you are not sure how much to recap? Too much recap and they start the topic bored, too little recap and the new work is too difficult. What to do?

To quote an old UK TV ad: “I want to be a tree!” (Prudential, 1989).

I have a bright class of 13/14 year olds and needed to start some algebra work. We ended up making a tree.

Equipment

  • Coloured paper
  • Felt pens or markers
  • Glue
  • Scissors
  • Roll of backing paper or wallpaper (I cut mine to fit on the back of a door)
  • Optional: mini-whiteboards for mindmaps

Activity 1
In small groups, pupils draw mindmaps for the word ‘Algebra’. Encourage them to group or link topics.
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Activity 2
Collect the answers on the main board. Any concepts which are not specifically algebra can be categorised as foundation skills eg understand calculating with negative numbers.
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Activity 3
Split the diagram into parts:
Stones: foundation skills which are essential for algebraic success

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Branches: subdivisions of algebra
Leaves: specific topics or objectives
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Fruit: examples
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Activity 4
Assign the different stones, branches, leaves and fruit to pupils to complete.

Activity 5
Assemble your tree. I added an owl and a disembodied voice asking ‘which careers need algebra?’. My branch labels were quickly covered by leaves, so I substituted extra leaves with these labels instead.

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Variation
This could work for any topic in any subject. Imagine how good a tree lined corridor would look – a new tree for every area of study.

Review
I moved around the room chatting to pupils as they worked and got a good idea for where I need to start the next lesson. The pupils now have a visual representation of how algebraic concepts link and overlap. In hindsight, I’d probably make the leaves and fruit smaller so that links are clearer.

Show me your learning trees on twitter and I’ll share them on here. @Ms_KMP

141. Book(s) of the week 3

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If you remember ‘The Wonder Years’ you are probably old enough to remember grunge the first time around and television programmes that didn’t involve so called ‘Reality TV’.

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So what happens to female child stars?

Some have a rocky youth, work really hard and become hugely successful (Drew Barrymore). Some have a rocky youth and become hugely notorious (Lindsay Lohan). Some work really hard, do research, writing and acting, have a theorem named after them and become advocates for women and maths education!

Step forward Danica McKellar!

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Apart from playing ‘Winnie Cooper’ in ‘The Wonder Years’, Danica is also a successful mathematician. She has written four books aimed at promoting maths to high school students, in particular girls. I strongly suggest you have a look at them or get your school library to purchase them as they are full of inspirational ideas and new ways to think about ‘dusty’ topics.

Her books to date are:

Girls Get Curves: Geometry Takes Shape (2013)

Hot X: Algebra Exposed! (2011)

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Maths Doesn’t Suck: How to survive year 6 through year 9 maths without losing your mind or breaking a nail (2010)

Kiss my Math: Showing Pre-Algebra who’s boss (2009)