# Developing key topics

The following information will give you ideas for teaching various topics, regardless of the level your learners are working at. These topics are fundamental “building blocks”, and the tips here aren’t comprehensive, but they should give you some ideas. The tips cover:

- aspects you need to ensure that learners know and understand
- ideas for learning activities you can give to students

#### Place value

‘Place value’ refers to the value we give a number depending on where it sits in relation to other numbers (and the decimal point). In the number 217, the 7 is worth 7 units, the 1 is worth 1 ten, and the 2 is worth 2 hundreds.

**What learners need to know and understand about place value:**

- our number system is decimal – as you move to the left, each place is ten times bigger than the place on its right (and vice versa)
- that we use a “place holder” (zero) if a place has no value attached to it
- when writing large numbers we use a comma to separate whole numbers into groups of three (hundreds, tens and units) (eg. 1,234,567)
- we use a “decimal point” to separate whole units and tenths of units, and so on.
- if you multiply a number by 10, all the numbers move one place to the left, and you will use zero as a place holder if need be (eg. if you multiply 217 by 10 you get 2170)
- if you multiply a decimal number by 10, the numbers move one place to the left – and the decimal point stays where it is

**Ideas for learning activities:**

- give learners cards with single digits written on them. Ask them to work in pairs or small groups to arrange the cards to show the largest number they can make, the smallest number they can, and a number in between.
- give learners a card with a decimal point on it. Ask them to make a decimal number. Ask them to multiply that number by ten. Make sure they understand that the numbers move and that the point stays where it is.
- use formulas in an Excel spreadsheet to multiply numbers by 10, 100, 1000 etc (or to divide by the same). Ask learners to enter numbers to see what happens to them in each case.
- use online interactive activities such as these available on BBC Skillswise.

#### Reading and writing large numbers

Many people struggle to read – and write – large numbers, especially ones that involve zeros. Don’t assume that people feel comfortable reading or writing them.

**What learners need to know and understand about large numbers:**

- students need to understand place value, in particular that the pattern of hundreds, tens and units (HTU) repeats itself as you describe thousands, millions, and so on, separated by commas.

**Ideas for learning activities:**

- find a context that is of interest to the students. For example, if they follow Twitter, or like celebrities, ask them to find the celebrities with the most Twitter followers. Ask them to write out the numbers in words. Ask them to work out, for example, how may followers Lady Gaga has than Barack Obama.
- other contexts that use large numbers are:
- Facts about space
- Populations of cities, countries and continents
- Profits of the banks and other multinational corporations
- Health statistics

- make sure learners can not only read out a number from digits, but can hear a number read out and note it down correctly
- it’s hard to try to visualiselarge numbers, so try to make the numbers as real as possible
- ask learners to explore the website Information is Beautiful. It sets out statistics (often involving very large numbers) in visual ways that are easier to comprehend and compare; for example, the Billion Dollar-o-Gram

#### The four rules

If learners are secure in the decimal number system and place value, it’s time to move on to the building blocks of mathematics: the four rules of number:

- addition
- subtraction
- multiplication and
- division

**What learners need to know and understand about the four rules:**

- that the operations for the four rules are connected:
- addition is the opposite of subtraction
- multiplication is the opposite of division
- multiplication is multiple addition
- division is multiple subtraction

- we often use different terms without realising It is important that learners know the language we use for the four rules:
- addition: plus, total, sum of, “and” (3 and 4 is 7)
- subtraction: take away, minus, “from” (2 from 5 is 3)
- multiplication: times, by, product, “of” (3 lots of 4 is 12)
- division: shared among, “into” (3 goes into 15 5 times)

- learners need to be secure in using the symbols for each of the rules.
- Symbols appear differently on computers. The multiplication symbol on a computer is *(a star); division is /
- In continental Europe the symbol for multiplication is often a single dot 3 . 4 = 12
- Sometimes learners might confuse +and x, or even +and

- The order in which we carry out operations is crucial. We cannot work in a linear fashion. We need to apply the BODMASrule:
- anything in Brackets first
- Orders next (such as powers and roots)
- Division and/or Multiplication next
- Adding and/or Subtraction last

This webpage explains BODMAS well: http://www.mathsisfun.com/operation-order-bodmas.html

**Ideas for learning activities:**

- Learning and practisingthe four rules can be dry, so encourage learners to use numbers in a context they are interested in, or in problem solving.
- Link the four rules to worded problems and ask learners to hunt for the operations hidden in the words.