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.
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:
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.
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.
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.
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.
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.
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!!)
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.
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.
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.
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:
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.
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.
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.
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.
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.
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.
On day 17, we shift our focus to the Statistics topic looking at Mean, Median, Mode and Range. We take a look at how to calculate the three averages and when it might be necessary to calculate each average.
Mean - When you want to include all the data. Median - When you want to eliminate extreme values (outliers) from the data set. Mode - When you are dealing with categorical data (either Quantitative or Qualitative). Range - Is not an average but a measure of spread.
Day 16 takes a look at Sequences. With sequences you will be required to know what is happening between each term in a sequence, using that information to carry on the sequence as well as find a general rule to find the value of any term in the sequence. We start off with simple sequences and the processes required to find the general rule (known as the nth term) and move onto the more advanced quadratic sequences.
