Maths in Year Six
Thursday 4th February: Negative Numbers
Today we practised adding and subtracting using negative numbers. What we need to remember is to think "make more" when we see the addition (+) sign and "make less" when we see the subtraction (-) sign.
Example 1:
5 + -6 =
5 [make more] [negative] by 6 =
If we make a number more negative, we are going to move left on a numberline. We start on 5 and move 6 places to the left. The answer will be -1.
Example 2:
-2 - 7 =
-2 [make less] [positive] by 7
If we make a number less positive, we are going to move left on a numberline. We start on -2 and move 7 places to the left. The answer will be -9.
Hey diddle diddle
The median's the middle
You add then divide for the mean
The mode is the one that happens the most
And the range is the difference between
(the biggest and the smallest)
Area and Perimeter
Compound shapes might look like this:
To find the area of the shape we normally do length x width, but we first need to split the shape into two quadrilaterals.
We know that 5cm - 2cm = 3cm, so this will be our missing measurement.
The area of the first shape (rectangle) will be 5cm x 2cm = 10cm^{2}
The area of the second shape (square) will be 3cm x 3cm = 9cm^{2}
To find the area of the whole compound shape we need to add them together (9cm^{2} + 10cm^{2} = 19cm^{2})
Perimeter is the length of the sides of the shape, so we need to add them:
2cm + 5cm + 5cm + 3cm + 3cm + 2cm = 20cm
Area is a squared (^{2}) measurement because we are measuring space. Perimeter measures length.
To find the area of a triangle, multiply the base by the height and then halve your answer.
The area of a parallelogram is the base multiplied by the height.
Extra: To find the area of a trapezium:
1. Add the lengths of the parallel sides.
2. Multiply this by the height.
3. Halve your answer.
Fractions, Decimals and Percentages
There are some equivalent proportions which are useful to learn off by heart. Key equivalent fractions, decimals and percentages to learn are:
Fraction | Percentage | Decimal |
1 |
50% | 0.5 |
1 |
25% | 0.25 |
3 4 |
75% | 0.75 |
1 10 |
10% | 0.1 |
1 5 |
20% | 0.2 |
1 3 |
33.33...% | 0.3333... |
2 3 |
66.66...% | 0.6666.... |
1 8 |
12.5% | 0.125 |
1 whole | 100% | 1 |
1 100 |
1% | 0.01 |
Converting Percentages and Decimals
Percentage means out of 100.
As you can see from the table, to get from a decimal to a percentage we have multiplied by 100. When we multiply by 100, we move two places (two zeros) to the left (think Beyonce "to the left"):
T Tens | O Ones/Units | . | Tth Tenths | Hth Hundredths |
0 | . | 5 | ||
5 | 0% | . |
0.5 x 100 = 50%
If we want to get from a percentage to a decimal, we do the opposite and divide by 100.
50 ÷ 100 = 0.5
Converting Percentages and Fractions
Percentage means out of 100.
A fraction means out of the bottom number (denominator).
So 50% is 50 out of 100 or:
50
100
We can then simplify this fraction.
50 = 5 = 1
100 10 2
If we want to convert from a fraction to a percentage, we need to make the fraction out of 100.
Remember, when we are finding equivalent fractions, whatever we do the bottom, we have to do the top.
1 = 10
10 100 (We have multiplied the denominator by 10 by 10 to get to 100)
10 out of 100 is 10%
Factors and Multiples
To help us remember the difference between factors and multiples, we have been singing our "factors go in, we make multiples" song with actions.
E.g. factors of 20 are:
1 and 20
2 and 10
4 and 5
because they go into the number 20.
(We write them in order to ensure we are systematic).
We make multiples so multiples of 20 are numbers we make by multiplying 20:
20, 40, 60, 80, 100 ...
A prime number only has two factors.
E.g.
factors that go into 5 are 1 and 5 (2 factors). It is a prime number.
factors that go into 6 are 1 and 6, 2 and 3 (4 factors). It is not prime number.
The only factor that goes into 1 is 1 (1 factor). It is not a prime number.