Standards Unit A2:Creating and solving equations

.Students need to.

1 to 2 hours. Teams of.My.

Suitable for high level 5, or low level 6?

Should not be scared of seeing things like,Even if they have not met quite that difficulty before

Must know how to expand single brackets, and understand division operator

Consumable Resources Needed:

Re-usable Resources Needed:

Minin-whitebaordsCamera?

Each student needs a single A4 worksheet + lots of spares. Students might want to try it quite a few more times. And can also be used a a revision activity in later lessons, once they understand the process of using the sheets.

Lots of copies of second worksheet. Expect many students (pairs) to progress to this, but do not give it to them at the start. Let them progress to this level in their own time.

Lots of copies of third worksheet. Expect some students (pairs) to progress to this, but do not give it to them at the start. Let them progress to this level in their own time.

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=Operations

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Check you’ve made no errors

Build your 1st equation

Name: . . . . . . . . . . . . . . . .Building harder equations!

Substitute your original value into the final equation.

=Operations

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Check you’ve made no errors

Build your 2nd equation

Substitute your original value into the final equation.

Solve 1st equation

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Solve 2nd equation

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=Solution

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=Solution

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Mark your partner’s work. Did they follow your steps and get the correct answer? What difficulties do you think they had?

Copy 1st equation to

here

Copy 2nd equation to

here

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Check.

Build your 1st equation

Name: . . . . . . . . . . . . . . . .Building equations on your own

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Check.

Build your 2nd equation Solve 1st equation

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Solve 2nd equation

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Solution:

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Solution:

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Mark your partner’s work. Did they follow your steps and get the correct answer? What difficulties do you think they had?

Copy 1st equation to

here

Copy 2nd equation to

here

Students can start with mini-whiteboard which they can use from the start to show each step of an equation being built. I should not do too much correcting or assessing on their work at this stage. We want a speedy start. It’s just getting them involved and thinking.Mini-whiteboards needed at end too.

Pre-assign partners too.

Differentiation. More able students can use square and square root operations too. They could also use fractions, or negative numbers. They should also use more ‘steps’. Less able should not use division operator when building equation, and need only use two or three steps initially.

Pre-distribute worksheets, possibly in plastic folders to stop too much playing at start.But useful for them to see the format of worksheet whilst working through even early examples.

Important that when modelling, I do NOT simplify. This would make reversing the process much harder. i.e. Write

Solving Harder Equations

We will be learning to solve hard equations, but first we’ll look at things in reverse, by building complex equations starting from their solution!

What does the solution to an equation normally look like?

Building an Equation

Operations

Numbers123456789

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Lettersxy…

Start with a solution!

Becoming more complicated!

Becoming simpler

Equation is ‘solved’!

Check the equation: substitute x=3 back in

Building an equation together

Operations

Numbers123456789

10

Lettersxy…

We start with the Solution to an equation!

Becoming more complicated!

Becoming simpler

Equation is ‘solved’!

How did we build that equation?

The final equation we built was:

It tells the story of ‘a day in the life of’ the letter

What happened to it FIRST? Can you tell be looking only at the equation?

What happened next?

How would we solve that equation?

Solving our Equation

Our final equation was:

Build Your Own Equations

LHS of worksheet

Build two equations of your own.Then check that they really work!

Do not go on to the RHS yet.

Solving Your Partner’s Equations

RHS of worksheet

Before passing your worksheet to your partner:1. Copy your final equations onto the RHS.2. Fold worksheet so that partner cannot immediately see your earlier work

If you get a bit stuck, ask your partner for help. But try NOT to look back over the other side until you have solved it.

When finished, pass back again.Now complete question 5.Please answer in as much detail as possible. It will help me plan future lessons.

Choose what to do next

Have another go at Worksheet 1

Try the harder, guided Worksheet 2

Free-style (unguided) Worksheet 3

You can also… - use fractions, or negative numbers as well as the digits 1 to 10- use squaring, or square roots, as well as + - x /- even use reciprocal (1/x) and ‘change the sign’ (+/-) operations- trig functions etc.

6 steps rather than 4.

Write one of your favourite equations here

Working with your partner, choose one of the above equations and solve it. Then write your solution beside the corresponding equation above.

Assessment: ‘Think of a number’Use mini-whiteboards individually, but work with a partner if you wish

I am thinking of a number. Call it n

Double it.

Add four.

Divide your answer by seven.

Multiply your answer by two.

The result is 4.

Show me your equation

Q1

Show me your equation

Q2I am thinking of a number. Call it

The result is

Correct solution: