Standardised Approaches to Numeracy The following slides contain the standard methods for key topics that your child will learn in Mathematics at Denbigh School. This does not mean that they will not learn any other methods but these are the basic methods that all students are taught. The aim is that students will be able to transfer these skills and apply them in different subjects where necessary. By providing these methods to parents, you should be more able to help your child at home with homework or revision when these skills are needed to solve any type of problem across the curriculum.

How to use these slides. By clicking on the icon in the bottom right of the screen, it will open the power-point in full screen mode. This will enable you to click through the steps for a particular method along with an audio explanation. To exit full screen mode at any time, press the ‘Escape’ key on your keyboard. You can choose to look at any method your child requires, you do not have to go through them in order.

Solving Linear Equations Rearranging Formula Conversions Method 1: Loops Solving Linear Equations Rearranging Formula Conversions

Standardised Layout To Solve Linear Equations Example: 4𝑥+1=19 4𝑥=18 𝑥= 9 2 𝑥=4.5 -1 -1 ÷ 4 ÷ 4

Standardised Layout To Rearrange Formula Example: Make 𝑥 the subject of the formula: y= 3(𝑥−2) 2 𝑦 3 = (𝑥−2) 2 𝑦 3 =(𝑥−2) 𝑦 3 +2=𝑥 Or 𝑥= 𝑦 3 +2 What has happened to the 𝒙-value to make it look like this? ÷3 ÷3 What happened first? √ √ +2 +2

Standardised Layout for Conversions Example: A race track is 10km long. What would this length be in miles? 8km = 5 miles 1km = 0.625 miles 10km = 6.25 miles ÷8 ÷8 ×10 ×10

Adding and Subtracting Fractions Multiplying Fractions Method 2: Fractions Adding and Subtracting Fractions Multiplying Fractions

Standardised Layout To Add & Subtract Fractions Example: 8 12 + 3 4 = 8 12 + 9 12 = 17 12 =1 5 12 Key Point: Keep fractions underneath each other. This will help to avoid confusion when converting them to equivalent fractions. × 3

Standardised Approach to Multiplying Fractions 𝑎 𝑏 × 𝑐 𝑑 Multiply straight across in Year 7 & 8. Cancel common factors first in Year 9 and from then onwards.

Method 3: Bubbles & Multipliers Finding Percentages of an Amount Percentage Increase and Decrease

Standardised Approach for Percentage of an amount The method will depend on the paper: Non Calculator Paper – Bubble Method Calculator Paper – Single Multiplier Method

‘Bubble’ Method (Non Calculator Paper) e.g. 30% of 800 25% + 5% 200 + 40 = 240 Stage 1 Fill in the bubbles ÷𝟏𝟎 ÷𝟐 100% 50% 25% 10% 1% 5% 800 80 8 Stage 2 Add up using the bubbles you need: 400 40 e.g. 46% of 800 25% + 10% + 10% + 1% 200 + 80 + 80 + 8 = 368 200

Single Multiplier Method (Calculator Paper) Divide the percentage by 100 50% ÷ 100 = 25% ÷ 100 = 13% ÷ 100 = 6% ÷ 100 = 0.5 0.25 0.13 0.06 This is the….. MULTIPLIER

Single Multiplier Method (Calculator Method) To find the percentage of an amount: Multiplier x Amount Worked examples What is 32% of 600 32% ÷ 100 = 0.32 0.32 x 600 = 192 What is 7% of 600 7% ÷ 100 = 0.07 0.07 x 600 = 42 What is 17.5% of 600 17.5% ÷ 100 = 0.175 0.175 x 600 = 105

Standardised Approach to Percentage Increase / Decrease Single Multiplier Method PERCENTAGE CHANGE CALCULATION MULTIPLIER An increase of 12% An increase of 9% A decrease of 9% A decrease of 88% A shop offering 20% off all prices A city where the population has gone up by 3% A year where there was 4% less rainfall 100% + 12% = 112% 100% + 9% = 109% 100% - 9% = 91% 100% - 88% = 12% 100% - 20% = 80% 100% + 3% = 103% 100% - 4% = 96% × 1.12 × 1.09 × 0.91 × 0.12 × 0.8 × 1.03 × 0.96

Standardised Approach to Percentage Increase Example A box of cereal has 33% extra free. Usually the box has 500grams. How many grams does the new box of cereal have? Work out without using a calculator. (Bubble method) Check answer with a calculator. (Single Multiplier) See next slide for answer

Standardised Approach to Percentage Increase 100% + 33% = 133% 133% of 500g 500 50 5 25 250 125 100% + 25% + 10% - 1% - 1% 500 + 125 + 50 – 5 – 5 = 665 grams Check your answer: 1.33 x 500 = 665 grams

Standardised Approach to Percentage Decrease Example A TV costs £340. A sale gives a 15% discount. What is the price paid for the TV in the sale? Work out without using a calculator. (Bubble method) Check answer with a calculator. (Single Multiplier Method) See next slide for answer

Standardised Approach to Percentage Decrease 100% - 15% = 85% of the original price to pay 85% of £340 340 34 3.4 17 170 85 50% + 25% + 10% 170 + 85 + 34 = £289 (new price) Check your answer: 0.85 x 340 = £289