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The Reformed Maths GCSE - 3 Lessons

The Reformed Maths GCSE - 3 Lessons

We are coming up to the second set of the reformed 9-1 GCSE examinations this summer. So, what has been the story so far? Well, 3 key themes stick out to me.

 

1. Enhanced Levels of Content

With the government deciding that GCSEs had become ‘too easy’, the recent overhaul has meant that more content has been squeezed into the reformed 9-1 GCSE maths specifications. Combined with little or no increase in teaching time, it has pushed more schools into adopting three-year schemes of work. Even then, the teachers I have spoken to over the last year have said that teaching all of the content in time is a struggle, and the schemes of work leave little time for exploring topics in depth.

 

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Countdown to Exams - Day 32 - Percentages and percentage change

Countdown to Exams - Day 32 - Percentages and percentage change

The focus for today is on Percentages and percentage change. You should be confident with common conversions as seen in the table as well as converting percentages into a fraction or decimal using the conversion flow chart. We then take a look at increasing/decreasing an amount by a percentage manually using two methods (Unitary method and Decimal method)

A calculator method is explored at the end and shows a quick way to increase and decrease an amount quickly using a multiplier factor. This method will help to work out original price problems. Finally we recap the formula used to calculate the percentage change between two values.

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Countdown to Exams - Day 31 - Quantities as fractions/percentages of each other

Countdown to Exams - Day 31 - Quantities as fractions/percentages of each other

For day 31 we take a look at being able express quantities as fractions of each other and how to calculate a fraction of an amount. We then move onto expressing quantities as percentages of each other and how to find a percentage of an amount.

A nice way to think about these sorts of a problem is to treat it like a test score where the first value is your score (numerator) and the second value is how many marks there were.

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Harnessing the power of digital technology

Harnessing the power of digital technology

There are no silver bullets in digital learning. Very few students will be incentivised enough to work under their own initiative. Just like any form of learning, teacher direction and management are essential.

In this context, it is very important to make a good start when implementing a digital approach.

Many schools have found the following approach has helped:

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Our Investment in Scaffolding

Our Investment in Scaffolding

Our Investment in Scaffolding

We are big believers in the power of scaffolding. Scaffolded questions provide students struggling with a topic a ‘way-in’ to an assessment, breaking down what can feel like an unachievable problem into individual steps. This often jogs recollection of previous instruction of the required method. High-achievers also benefit from being forced to consider and interact with each of the required steps. Careful consideration of the solution method helps when tackling more complex problems which may involve implementing steps in different orders or considering the conditions in which an individual step breaks down.

 

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Countdown to Exams - Day 30 - Converting recurring decimals

Countdown to Exams - Day 30 - Converting recurring decimals

For day 30 we are looking at the more complex topic of turning a recurring decimal into a fraction. Here we take a look at converting simple recurring decimals into fractions with denominators of 9/99/999 etc. We then extend onto more complex recurring decimals. The best approach to these questions is to take an algebraic approach and multiply the decimal to get yourself into a position where the recurring element can be eliminated.

Important to remember that a recurring decimal is a decimal number that will have a pattern of number/s repeating infinitely. The whole point of converting the recurring decimal into a fraction is so that it is easier to calculate with.

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Countdown to Exams - Day 29 - Converting Fraction to Decimal

Countdown to Exams - Day 29 - Converting Fraction to Decimal

On day 29 we are taking a closer look at Converting fractions to decimals. Having a look at the table, there are some simple fraction to decimal conversions you should know. For more complex fractions, there are two methods to consider; the first is using a division method and the other is using an equivalent fraction method.

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Countdown to Exams - Day 28 - Converting Decimals to Fractions

Countdown to Exams - Day 28 - Converting Decimals to Fractions

On day 28 we are taking a closer look at Converting decimals to fractions. Having a look at the table, there are some simple decimal to fraction conversions you should know. If in doubt, use place value to place your number over 10/100/1000 etc. and then look to simplify your answer.

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Countdown to Exams - Day 27 - Fractions - Multiplying and Dividing

Countdown to Exams - Day 27 - Fractions - Multiplying and Dividing

On day 27 we continue calculating with fractions focusing on Multiplying and Dividing fractions. Unlike addition and subtraction there is no need to have a common denominator if we are asked to multiply/ divide fractions. All you need to do is multiply numerators, multiply denominators, simplify your answer. When dividing fractions you need to flip the second fraction and multiply. (Keep Change Flip)

 Always look to see if you can cross cancel first. This will mean that you don't have to multiply large complicated numbers. When faced with mixed numbers, look to convert to improper fractions first.

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Proof by Deduction

One of the topics that is most difficult for a digital platform to assess is Proof. As a result, it is often the first place teachers evaluating the EzyMaths A Level course will head to! (Tough crowd!!)

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Countdown to Exams - Day 26 - Fractions - Addition and Subtraction

Countdown to Exams - Day 26 - Fractions - Addition and Subtraction

Today we extend our fraction knowledge and look at calculating with fractions. The focus here will be Addition and Subtraction of fractions. In order to carry out these calculations, the denominators of your fractions need to be the same. This means that you will have to multiply one or both of the fractions to make equivalent fractions that have the same denominator. 

Remember to simplify your answers where possible to secure full marks and remember how to convert between mixed and improper fractions.

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Countdown to Exams - Day 25 - Fractions - Simplifying, Improper and mixed

Countdown to Exams - Day 25 - Fractions - Simplifying, Improper and mixed

On day 25, we turn our attention to Fractions. It is important to remember that fractions are 'part' of the 'whole'. The numerator is the top number (number of parts you are focusing on) and the denominator is the bottom number (total number of parts). To secure full marks you will have to make sure that your answers are in their simplest form and this is achieved by dividing the fraction to create an equivalent fraction with smaller numbers. 

When you start calculating with fractions you will end up with combinations of improper fractions and mixed numbers. Being able to convert between these two formats will make calculations a lot easier.

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Countdown to Exams - Day 24 - Scatter graphs

Countdown to Exams - Day 24 - Scatter graphs

The focus for today is Scatter graphs. A scatter graph is used to show if two sets of data are related (correlated). There are three types of correlation to watch out for; Positive, Negative and No correlation. Sometimes you will be asked to plot points on a graph, be sure to plot these points like coordinates and try to do it as accurately as possible.

When asked to extract and estimate information from the scatter graph you will normally be marked on constructing a line of best fit so don't forget to do this.

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3 Ways EzyMaths’ Reports Supports Interventions

3 Ways EzyMaths’ Reports Supports Interventions

One of the most important features of the EzyMaths GCSE and A Level courses are the reporting options available to teachers. It is clear that the schools and individual teachers which get the most out of the platform are those who utilise the student activity data to inform in-class interventions. Here we look at three of the most common ways to use the EzyMaths reports:

 

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Countdown to Exams - Day 23 - Histograms

Countdown to Exams - Day 23 - Histograms

On day 23, our focus is on Histograms which is a special 'Bar' chart for grouped data and will often have different widths. Beware the trap that the y axis is NOT frequency but should be labelled frequency density.  The formula for calculating frequency density is covered in this snapshot and you may need to create extra columns in order to calculate this. 

By rearranging the formula, you can calculate the frequency of each bar by multiplying frequency density by the bar width. This will help to fill in an incomplete data table.

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Countdown to Exams - Day 22 - Quartiles and box plots

Countdown to Exams - Day 22 - Quartiles and box plots

For day 22 we extend beyond plotting cumulative frequency graphs and look at Quartiles and box plots. Once the graph has been created, we tend to examine it in more detail by looking at the quartiles which are situated at 25%, 50% (the Median) and 75%. An important area we analyse is the Inter Quartile Range (IQR), this tells about the spread of data of the middle 50% of the data.

A box plot is extracted from a cumulative frequency diagram and is made up of five key elements; Highest and lowest value, Upper and lower quartile (75% and 25%) and the median. These become useful when we want to compare tow or more sets of data.

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Countdown to Exams - Day 21 - Cumulative frequency tables and graphs

Countdown to Exams - Day 21 - Cumulative frequency tables and graphs

On day 21 we move on and have a look at Cumulative frequency tables and graphs. This is essentially a running total where we add up the frequencies as we go along. It is important to check to see if your final value of the cumulative frequency matches the total frequency (normally given in the question).

When constructing a cumulative frequency graph, it is important to plot each point at the end of each group and join the points up with a nice smooth curve ('s' shaped). The graph is used to estimate numbers above and below certain values.

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Countdown to Exams - Day 20 - Representing Data

Countdown to Exams - Day 20 - Representing Data

The focus for today's snapshot is Representing data. Once data has been collected, diagrams are used to represent the data so that it is easier to extract the key points from the data without having to look at all the numbers etc. The most common diagrams that are used are Pie charts, Bar charts, Line graphs and Pictograms. It is important that you follow the rules regarding the construction of the diagrams.

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Countdown to Exams - Day 19 - Averages from a Grouped frequency table

Countdown to Exams - Day 19 - Averages from a Grouped frequency table

On day 19 we extend our understanding of averages by looking at Grouped frequency tables. Here you will find that your data has been grouped into categories. It is important to note a change in the vocabulary for the questions. Because the data is grouped, you will be unable to use specific values as you don't know what they are hence you will be asked to find an estimate for the mean or an estimate for the median.

You will often have to create two extra columns, one for the midpoints of each group and one for your fx column.

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Countdown to Exams - Day 18 - Averages from a frequency table

Countdown to Exams - Day 18 - Averages from a frequency table

On day 18, we focus on calculating averages from a simple frequency table. There will be times where you will need to create the fx column so that the total amount can be worked out. Remember the formula for the median shows you where the median is located.

It will be important to look and check your answers to see if they are reasonable answers and fit within the data set.

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