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Maths – How do we learn?

Maths – How do we learn?. Fractions, Decimals and Percentages. FDP Progression in School. Halving of sets of objects begins as early as EYFS and Year 1. It is vital that children know halves and quarters must be equal in size.

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Maths – How do we learn?

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  1. Maths – How do we learn? Fractions, Decimals and Percentages

  2. FDP Progression in School Halving of sets of objects begins as early as EYFS and Year 1. It is vital that children know halves and quarters must be equal in size. In Year 2 children begin to use ½ and ¼ and find these fractions of amounts ½ of £12 = £6

  3. Progression in KS2 In Year 3 we begin to use the terms denominator and numerator in writing proper fractions. We identify fractions of shapes and compare and order them. In year 4 we read and write fractions, ordering them and recognising equivalent fractions. Children also find fractions of amounts. 3/5 of 25Kg = 15Kg

  4. Progression By Year 5 children simplify fractions by cancelling. They relate fractions to decimals and percentages, and find percentages of amounts. In Year 6 we ask children to find common factors in numerators and denominators. They use these to simplify, order and make mixed numbers. Children in Year 6 convert between F, D and P and find proportions of amounts with all three forms.

  5. So why is it all so hard? Fractions, decimals and percentages are all parts of a whole, and the concept can prove confusing. These next slides will explain the progression of knowledge and how we can help children to understand at each stage. A huge focus is on what fractions, decimals and percentages look and feel like.

  6. Fractions A fraction is a part of a whole Slice a pizza, and you will have fractions: • 1/21/43/8 (One-Half) (One-Quarter)(Three-Eighths) The top number tells how many slices you have The bottom number tells how many slices the pizza was cut into.

  7. Numerator / Denominator • We call the top number the Numerator, it is the number of parts you have.We call the bottom number the Denominator, it is the number of parts the whole is divided into. • NumeratorDenominator You just have to remember those names! (If you forget just think "Down"-ominator)

  8. Equivalent Fractions • Some fractions may look different, but are really the same, for example: • 4/8 = 2/4 = 1/2 (Four-Eighths)   (Two-Quarters)   (One-Half) It is usually best to show an answer using the simplest fraction ( 1/2 in this case ). That is called Simplifying the Fraction.

  9. Adding Fractions • You can add fractions easily if the bottom number (the denominator) is the same: • 1/4 + 1/4 = 2/4 = 1/2 • (One-Quarter)   (One-Quarter)   (Two-Quarters)   (One-Half) • Another example: • 5/8 + 1/8 = 6/8 = 3/4

  10. Adding Fractions with Different Denominators • But what if the denominators (the bottom numbers) are not the same? As in this example: • 3/8 + 1/4 = ?     • You must somehow make the denominators the same.

  11. In this case it is easy, because we know that 1/4 is the same as 2/8 : • 3/8 + 2/8 = 5/8

  12. Place Value • In the number 327: • the "7" is in the Units position, meaning just 7 (or 7 "1"s), • the "2" is in the Tens position meaning 2 tens (or twenty), • and the "3" is in the Hundreds position, meaning 3 hundreds

  13. As we move right, each position is 10 times smaller. From Hundreds, to Tens, to Units   • But what if we continue past Units? • What is 10 times smaller than Units? 1/10 ths (Tenths) are!

  14. Decimals • But we must first write a decimal point,so we know exactly where the Units position is: "three hundred twenty seven and four tenths“ • but we usually just say "three hundred and twenty seven point four"

  15. The decimal point is the most important part of a Decimal Number. It is exactly to the right of the Units position. Without it, we would be lost ... and not know what each position meant. • Now we can continue with smaller and smaller values, from tenths, to hundredths, and so on, like in this example:

  16. Percentages • When you say "Percent" you are really saying "per 100" • So 50% means 50 per 100(50% of this box is green)

  17. And 25% means 25 per 100(25% of this box is green)

  18. Because "Percent" means "per 100" you should think "this should always be divided by 100" • So 75% really means 75/100 • And 100% is 100/100, or exactly 1 (100% of any number is just the number, unchanged) • And 200% is 200/100, or exactly 2 (200% of any number is twice the number)

  19. Example: • 100% of 80 is 100/100 × 80 = 80 • Example: • 50% of 80 is 50/100 × 80 = 40 • Example: • 5% of 80 is 5/100 × 80 = 4

  20. Fractions, Decimals and Percentages Decimals, Fractions and Percentages are just different ways of showing the same value: • A Half can be written...     • As a fraction: 1/2 • As a decimal: 0.5 • As a percentage: 50%

  21. A Quarter can be written...     • As a fraction: 1/4 • As a decimal: 0.25 • As a percentage: 25%

  22. Conversions From Percent to Decimal • To convert from percent to decimal: divide by 100, and remove the "%" sign. • The easiest way to divide by 100 is to move the decimal point 2 places to the left. So:

  23. From Decimal to Percent • To convert from decimal to percent: multiply by 100, and add a "%" sign. • The easiest way to multiply by 100 is to move the decimal point 2 places to the right. So:

  24. From Fraction to Decimal The easiest way to convert a fraction to a decimal is to divide the top number by the bottom number (divide the numerator by the denominator in mathematical language) • Example: Convert 2/5 to a decimal • Divide 2 by 5: 2 ÷ 5 = 0.4 • Answer: 2/5 = 0.4

  25. Decimal to fraction First, write down the decimal "over" the number 1 0.75 / 1 Then multiply top and bottom by 10 for every number 0.75 × 100 / 1 × 100 after the decimal point (10 for 1 number, 100 for 2 numbers, etc) (This makes it a correctly formed fraction) = 75 / 100 Then Simplify the fraction 3 / 4

  26. From Fraction to Percentage • The easiest way to convert a fraction to a percentage is to divide the top number by the bottom number. then multiply the result by 100, and add the "%" sign. • Example: Convert 3/8 to a percentage • First divide 3 by 8: 3 ÷ 8 = 0.375,Then multiply by 100: 0.375 x 100 = 37.5Add the "%" sign: 37.5% • Answer: 3/8 = 37.5%

  27. From Percentage to Fraction • To convert a percentage to a fraction, first convert to a decimal (divide by 100), then use the steps for converting decimal to fractions (like above).

  28. Example: To convert 80% to a fraction Convert 80% to a decimal (=80/100): 0.8 Write down the decimal "over" the number 1 0.8 / 1 Then multiply top and bottom by 10 for every 0.8 × 10 / 1 × 10 number after the decimal point (10 for 1 number, 100 for 2 numbers, etc) (This makes it a correctly formed fraction) = 8 / 10 Then Simplify the fraction 4 / 5

  29. How do I Simplify a Fraction ? • Method 1 • Try dividing both the top and bottom of the fraction until you can't go any further (try dividing by 2,3,5,7,... etc). Example: Simplify the fraction 24/108 : ÷2 ÷2 ÷3 241262 108 54 27 9

  30. Method 2 • Divide both the top and bottom of the fraction by the Greatest Common Factor, (you have to work it out first!).

  31. Example: Simplify the fraction 8/12 : • 1. The largest number that goes exactly into both 8 and 12 is 4, so the Greatest Common Factor is 4. 2. Divide both top and bottom by 4: ÷ 4 82 12 3

  32. Fractions of amounts One of the most common SATs questions is finding fractions of amounts, such as - 1/5 of £20 = As 1/5 is one of five equal parts, all we do is divide £20 by 5, which equals £4.

  33. 4/5 of £50 = Let’s find 1/5 of £50 = £10 Then x by 4 (for the 4 parts) = £40

  34. Percentages of amounts As percent means ‘out of a hundred’ we can find 1% by dividing by 100, or 10% by dividing by 10. 30% of 18Kg = 10% of 18Kg is 1.8Kg, so 30% is... 1.8Kg x 3 = 5.4Kg

  35. Some Useful Websites http://www.teachingideas.co.uk/maths/contents_fractions.htm http://www.primaryresources.co.uk/maths/mathsB6.htm http://www.mathsisfun.com/numbers/index.html

  36. Future Maths Workshops I would like to discuss reasoning, problem solving and the importance of vocabulary in future sessions. Any other ‘hot’ maths topics?

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