Hunters Hall Primary Maths Planning Guidance

Transcription

1 Fractions & Percentages Recognise half and quarter of object, shape or quantity. (Y) I can find half of a piece of paper or string, or half a shape I can find half of a small number of objects Show me half a page, half a ribbon, half of these six eggs. Give me half of the pencils in the pot. I can make whole, half and quarter turns on the spot I can fold a piece of paper into halves and quarters I can find half of a number of objects by sharing them into two equal groups I can find half of the water in a jug by pouring it into two glasses so that each glass has the same amount I can tell you when the clock says half past 2 How will you find half of that circle? How will you find half of these counters? Which shape is more than half shaded? Here is a set of 2 pencils. How many is half the set? I can find a quarter of a number of objects by sharing them into four equal groups How can I find a quarter of this strip of paper? Shade one quarter of each shape. Recognise, find, name & write /3; /4; 2/4; 3/4. (Y2) I can find three quarters of a set of objects or of a shape Take 20 counters. Can you show me one quarter? Two quarters? Three quarters? Four quarters? What do you notice? Can you write that down in some way? Here is a set of 2 pencils. How many is a quarter of the set? How many is three quarters? Find three quarters of 20 biscuits. Three quarters of 24 buttons. How will you find one quarter of that rectangle? Three quarters? If one quarter of a set of shells is 2, how many shells are in the set? Here is a pizza cut into eight equal pieces. How many pieces are needed for three quarters of the pizza?

2 Recognise equivalence of simple fractions. (Y2) Use of a variety of visual representations to understand that ½ = 2/4 Count up/down in tenths. (Y3) Use of a counting stick to count up and down in tenths: Recognise that tenths arise when dividing an object by 0 Compare & order fractions with same denominator. (Y3) Order the following fractions: 4/7 6/7 2/7 3/7 5/7 /7 Use of greater than and less than signs to compare fractions 4/7 < 6/7 3/8 > /8 +/- fractions with same denominator within a whole. (Y3) e.g. 5/7 + /7 = 6/7 Show me two fractions that add together to make 5/8 Progress to applying within increasingly complex problems to improve fluency: If I have pour 4/0 of a bottle of drink into one cup and 3/0 into another cup, how many tenths have I poured out altogether?

3 Know pairs of fractions that total. (Y3) Children to match diagrams of fractions that add to make :make : Progress mathching/adding fractions that total : ½ + ½ = ¼ + ¾ = Show me two fractions that add together to make and another and another Find fractions of an amount (Year 3) I can find a fraction of a shape drawn on squared paper I can find a fraction of a number of cubes by sharing them in equal groups How can you find of 27? Is there more than one way to shade of a 2 by 6 grid? Why?

4 I can find a fraction of an amount What numbers/shapes are easy to find one third, one quarter, one fifth, one tenth of? Why? Tell me how to find one sixth of 42. Would you rather have of 30 sweets or of 2 sweets? Why? Count up/down in hundredths. (Y4) Use of a counting stick to count up and down in hundredths: Write equivalent fractions (Y4) Equivalent Fractions have the same value, even though they may look different. These fractions are really the same: 2 = 2 4 = 4 8 Why are they the same? Because when you multiply or divide both the top and bottom by the same number, the fraction keeps it's value. The rule to remember is: "Change the bottom using multiply or divide, And the same to the top must be applied" Equivalent fractions can be represented using a variety of models:

5 Fraction Walls: Interactive fraction wall: Progress to learning the decimal equivalence of fractions using a number line:

6 Interactive tool for teaching fraction and decimal equivalence: +/- fractions with same denominator. (Y4) Step. Add the top numbers and put the answer over the same denominator: Step 3. Simplify the fraction: + = + = = 4 2 This can be represented using pizzas or other models: Calculate fractions of an amount (Year 4) I can find a fraction of an amount What numbers/shapes are easy to find one third, one quarter, one fifth, one tenth of? Why? Tell me how to find one sixth of 42. Would you rather have of 30 sweets or of 2 sweets? Why? I can find the fraction of an amount, such as of 0 Which would you rather have: of 30 or of 60? Why? Which would you prefer to receive as pocket money: of 24 or of 49? Why? Count up/down in thousandths. (Y5 Use of a counting stick to count up and down in thousandths:

7 Fraction, decimal and percentage equivalence (Y5 & 6) Children to practice matching activities/games for equivalent fractions, decimals and percentages and to be encouraged to learn them off by heart: Children to place equivalent FDP on a number line: Interactive tool for teaching fraction, decimal and percentage equivalence:

8 Recognise mixed numbers & fractions & convert from one to another. (Y5) You can use either an improper fraction or a mixed fraction to show the same amount. For example 3 / 4 = 7 / 4, as shown here: Converting mixed numbers to improper fractions: To convert a mixed fraction to an improper fraction, follow these steps: Multiply the whole number part by the fraction's denominator. Add that to the numerator Write that result on top of the denominator. Example: Convert 3 2 / 5 to an improper fraction. Multiply the whole number by the denominator: 3 5 = 5 Add the numerator to that: = 7 Then write that down above the denominator, like this: 5 Converting improper fractions to mixed numbers: To convert an improper fraction to a mixed fraction, follow these steps: 7 Divide the numerator by the denominator. Write down the whole number answer Then write down any remainder above the denominator. Example: Convert /4 to a mixed fraction. Divide: 4 = 2 with a remainder of 3

9 Write down the 2 and then write down the remainder (3) above the denominator (4), like this: 2 x 5 = Multiply proper fractions by whole numbers. (Y5). Turn the whole number into a fraction by putting it over : 2 x 5 = 3 2. Multiply the numerators with each other and the denominators with each other: Answer: x 5 = 2 x 5 = x 0 Calculate fractions of an amount (Y4/5) I can find fractions of numbers using division. For example, to find of a number, I divide it by 3 What operation must you do to find one seventh of a number? One sixth of a number is 3. What is the number? What calculation would you key into a calculator to find of 403. of 75 is 25. Write this as a division statement. What operation would you key into a calculator to find of 256? One seventh of a number is 4. What is the number? Find of 3km. Tell me how to find three quarters of 60. Add & subtract fractions with different denominators & mixed numbers. (Y6) + = 3 6. You need to make sure the denominators of both fractions are the same: (x2) + =

10 3 (x2) = Add the top numbers and put them over the denominator: 2 + = 2 + = Simplify the fraction: 3 = = 2 + = 3 = Example problem: You are going to make and sell cupcakes: A friend can supply the ingredients, if you give them / 3 of sales And a market stall costs / 4 of sales How much is that altogether? Multiply simple pairs of proper fractions, writing the answer in the simplest form. (Y6 Example: x _2_= 2 5

11 . Multiply the numerators 2. Multiply the denominators x 2_= x 2 = x 5 0 Simplify if needed: 2 = 0 5 This can be illustrated using pizzas: Divide proper fractions by whole numbers. (Y6) Step. Multiply the denominator of the fraction by the whole number Step 2. Simplify the fraction (if needed) 2 3 Step. Multiply the bottom number of the fraction by the whole number = Step 2. Fraction is already as simple as possible. 3 = 2 6 Calculate fractions of an amount (Year 6) What is two thirds of 66? What is three quarters of 500? Three-quarters of a number is 48. What is the number?

12 Extend to finding fractions of numbers up to,000,000. Progress to expressing one number as a fraction of another: What fraction of 6 is 3? What fraction of 6 is 6? What fraction of 9 is 6? What fraction of 90 is 60? Shade 0% of this grid. Calculate % of whole numbers (Y6) Which is bigger: 65% or 3 4? How do you know? What percentage is the same as 7 0? Explain how you know. What is 3 00 as a percentage? Which is a better mark in a test: 6%, or 30 out of 50? How do you know? What percentage of the bar is shaded? 40% of a class of children are boys. What percentage are girls? Rick says that 3% is equivalent to 3 0. Is he right? How do you know? A test has 50 marks. Rory gets 40 marks. What is his percentage score? Find 75% of 200 ml. How did you do this? What percentages can you easily work out in your head? Talk me through a couple of examples. Kate says: To find 0% of an amount, you divide it by 0. So to find 20% of an amount, you divide it by 20. Is Kate correct? How do you know? What calculations would you do to find 5% of 50? What percentage of the whole numbers from to 0 are even? Explain the steps you would take to find 35% of an amount without a calculator. How would you find 35% of an amount using a calculator? Three-quarters of a number is 48. What is the number? What is twenty per cent of sixty pounds? What is two percent of three hundred? What is twenty out of forty as a percentage? Make up some more questions like this for me to answer. You must tell me whether I am right or wrong. What percentage of 8 is 2? What percentage of 4 is 6? Tell me two amounts where one is 25% of the other. Now give me two amounts where one is 5% of the other. What about 40%?