## Level 4a

# Number and Algebra

## Chapter 7 - Expressions, formulae

and equations

**Overview of the chapter**

**Rich tasks**

- These are problem solving open-ended questions that require students use formulae. The tasks can be given at the start of a topic and done as the students gain enough knowledge to complete them, inserted into a topic at an appropriate place or given as homework or extension.

- Can you work a spread sheet?
- Shoes on feet

> More on "Rich tasks for this Chapter"...

**1. (Printable Master - Can you work a spread sheet?)**

- Students will need to be shown how to enter information and a formula into a spreadsheet.
- Students could find and use other formulae that interest them to use as examples in their lesson on using spreadsheets.

**2. (Printable Master - Shoes on feet)**

- Students should be encouraged to measure accurately in mm. This gives them practice in measuring using small units of measurement.
- The class will need to measure the feet of at least 50 adults and 50 children (students could measure 2 adults and 2 children each) in order to answer question 5. This could be given as a homework exercise.

**Writing and understanding expressions**

- Explores how expressions can be used to model situations

> More on "Writing and understanding expressions"...

**Students should already know points 1 and 2.**

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**Teaching ideas**

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**Writing expressions (Teacher resource sheet 20)**

This link displays cards for you to print and cut out.

Give the cards out to the class/group and ask students to find the matching pairs of cards.

You could give one card to each student and then ask them to pair up or you could give a set to a group of students to make matching pairs.

**Teacher notes**

- It is very important that students understand that the rules of algebra are the same as the rules for numbers.
- Reinforce the idea that letters stand for numbers.

**Modelling real life situations with formulae**

- Explores how formulae can be written from rules written in words and how they are used to model situations.
- Gives practice at using formulae to solve problems.

> More on "Modelling real life situations with formulae"...

**Students should already know points 1 and 2.**

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**Teaching ideas**

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** Creative formulae (Teacher resource sheet 21)**

Displays three formulae for students to make up a meanings.

Example A = 20h + 5 might be

Amount paid = hours worked × $20 + $5 travel allowance.

Students could be divided into groups, share their meanings and vote on the best one.

**Teacher notes**

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- Letters often relate to the initial letter of the word, for example h for hours, but point out that this does not have to be the case and in fact any letter can be used.
- Point out that if a letter has already been used in a formula, another must be chosen if the intention is to relate it to something else.
- Encourage students when writing formulae using letters, to say what each letter stands for.

**Equations**

- Explores writing equations for Cuisenaire rods and how these equations can be written in different ways.
- Introduces solving equations using inverse operations using “I think of a number” problems.

> More on "Equations"...

**Students should already know points 1 and 2.**

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**Teaching ideas**

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**Think of a number ****(Printable Master - Number Tiles 0-50)**

This link dispalys number cards 0 - 50 and cards with n, +, -, =, x for you to print and cut out.- Give the cards out to a group of students. Model the writing of an equation with "I think of a number" problem.

I think of a number n (have the person with the n card come to the front)

I add six n + 6 ( have those with the + and 6 cards hold them)

The answer is 14 n + 6 = 14 (have those with the = and 14 cards hold them)

Make up some more “I think of a number" problems and have students write the equation for them on mini whiteboards or paper and hold them up.

The rest of class could write the inverse of the equations which would be a good way to engage all students and perhaps even enact the solving of the “I think of a number” problem.

**Teacher notes**

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- This section introduces students to the idea of using inverses to solve equations. This is explored in much more depth in Level 4B.
- Encourage students to check answers by substituting the answer back into the original equation formed.