Monthly Archives: June 2013

99. Factor Races

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I rather like teaching prime factor decomposition as you can assess lots of numerical skills within the topic. I can easily cover:
*Division
*Tests of divisibility
*Multiplication
*Quick recall of multiplication facts
*Prime numbers
*Factor/Multiple misconceptions
*Powers & Index notation
*Venn diagrams*
*Products
*HCF & LCM¤
*Vocabulary related to all the above

Many people already use prime factor trees to teach this topic, but if you are unfamilar with them here is a quick summary:

Find two numbers that multiply to give the top number.

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Repeat for each branch, circling the prime numbers. These are like the fruit on the end of the branch.

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Repeat until every branch has ‘fruit’ at the end.

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Write out the factors, in numerical order, as a multiplication.

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Collect like factors into index notation.

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And that’s how to make a prime factor decomposition tree.

The Race
You will need as many pupils as you can standing at your board, all equipped with a whiteboard pen. Depending on which room I am in, I get about 10 pupils out.

Their team mates sit near them – it is up to you as to whether calculators are allowed. Only the person at the board can write.

You call out a number and every team must work out the prime factor decomposition on the board. The winning team is the first to write the number as a product of prime factors.

Teaching Point
Once everyone has completed the task, leave the calculations on the board. You can now ask for comments and corrections. The class should notice that even though the number was split up differently, they all got the same answer. If they didn’t, the class can check for errors.

I like to use this as a plenary or a recap starter. It effectively demonstrates that even though your brain chose to breakdown the calculation differently, you are still correct. This can be a confidence boost to those pupils who think there is only one possible method and don’t ‘get’ that method. Maths is about the strategies and skills to solve problems, not just one approved technique.

¤ To be covered in the next blog post

98. All sewn up

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It’s not often you have to get a sewing machine out to mount display work:

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These are the dragon curves stitched by Year 5 pupils as part of a Community Gifted and Talented programme I run. I thought that by making them out of fabric and thread they would last longer – hopefully long enough that the Year 5 can see them up in the Maths Department when they join in Year 7. It’s also different to a ‘normal’ display and a bit of a talking point.

The cross stitch fabric makes rather good squared paper. Imagine what you could do with fabric, thread, a bit of creativity and a friendly sewing machine owner.

97. The Dancing Cipher (part two)

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If you look back to one of my early blog posts called ‘The Dancing Cipher’ on code breaking, I explained how to use the ‘Dancing Men’ code as an extended homework project.

You can now download the instructions/task, self assessment sheet and solution below:

Self-assessment sheet

Letter frequency analysis project

Letter frequency analysis project answer

96. Free (editable) Flashcards

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I was looking for some Maths paper when I was on Printablepaper.net, when I came across a ‘sister’ site: Printableflashcards.net. This website has free flashcards covering many different subjects/topics and is worth a browse.
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The biggest selling point to me was you can create flashcards without requiring a double sided printer or cursing the photocopier for misaligning your originals. You don’t have to glue them (unless you want to) as they will stand nicely on the desk once they are folded, with the answer face down on the table. You can use the Flash Card Generator to create your own set of 4/6 (or multiples of 4/6) flashcards.

95. Quadratic puzzles

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To an experienced mathematician, factorising a quadratic (with real roots) is a little number puzzle, into which the algebraic terms fall gently into place.

To a secondary (high) school student of middling ability they can be algebraic torments conjured from the darkest recesses of a fevered genius’ imagination. Impossible!

This year I have introduced factorising with no mention of algebra, equations, solving or factorising. My class are at least C grade students who have convinced themselves they are no good at algebra. We started by considering this puzzle:

What values of a, b, c &d make this multiplication grid true?

bc = 1
ad = 30
ac + bd = 13

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The solution is fairly straightforward:

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Once they got the hang of this kind of puzzle, I compared it to the grid method for expanding double brackets. I asked them to think about what the brackets could be if I gave them the values for bc, bd, ac & ad.

Finally the stabilisers were taken off. I asked them what the brackets were if I gave an algebraic form of the number puzzle. First we considered:

bc = X squared co-efficient
ac + bd = X co-efficient
ad = constant

Once it clicked that this was just a fancy number puzzle they were flying. I was really impressed by their positive attitude and willingness to try.

You can download a set of questions (and answers) here.

94. Help with no hands up

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I recently discovered two rather handy classroom assessment tools on Pinterest:

Rectangular cards

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Circular cards
These double-sided cards are from Ateacherswonderland blog

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I liked the design and wording of both. On one side pupils rate themselves on a scale of 1 to 4 (from Novice to Expert). On the other side they can tell you where they are, without causing a fuss. I incorporated the circular wording with the rectangular shape, reinforcing the punched edge with tape.

Example:
“I’m okay but may need help in a minute”.
I particularly like the fact that you don’t have to interupt or draw attention to a child to find out how they are.

These are my cards. I’m going to use them with my new classes this half term.
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Thank you to Ronnie for sharing her idea.
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