Mathematics. Steps to Success. and. Top Tips. Year 4

Transcription

1 Pownall Green Primary School Mathematics and Year 4 1

2 Contents Page 1. To use less than (<), greater than (>), equals (=) 3 2. Round numbers less than 1000 to the nearest 10 or Read fractions where the numerator is greater than one 3 4. Read mixed numbers 4 5. Understand equivalent fractions 4 6. Add any pair of two-digit numbers, mentally 4 7. Subtract any pair of two-digit numbers, mentally 4 8. Column addition of two numbers less than Column subtraction of two numbers less than To know the 2, 5 and 10 multiplication tables Know the 3 and 4 multiplication tables Know the 6 and 7 multiplication tables Know the 8 and 9 multiplication tables Know the 11 and 12 multiplication tables Work out division facts to multiplication tables Find remainders after division Units of length, mass and capacity Use the correct operations to word solve problems To name polygons Say whether a polygon is regular or irregular Classify 2-D shapes Units of time Draw and answer questions about bar charts Convert cm to metres 11 2

3 and Year 4 Key Learning Objectives 1. To use less than (<), greater than (>), equals (=) Think of the symbol as a crocodile s mouth The crocodile is greedy and his mouth always opens to the larger number The less than sign is a squashed L (L for less than) 2. To round numbers less than 1000 to the nearest 10 or 100 Rounding to 10 1) Which two multiples of 10 is the number in between? 2) Choose which multiple of ten it is nearest to. If the unit is 5 or more then round up. Rounding to 100 1) Which two multiples of 100 is the number in between? 2) Choose which multiple of 100 it is nearest to. If the digit in the tens is 5 or more then round up. Memorise this poem: Find your digit (the one in the column you are rounding to) Look right next door. 4 or less just ignore. 5 or more, add 1 more. If the number is exactly in the middle, then round it up Remember High Five the number rounds up 3. To read fractions where the numerator is greater than one Remember Denominator - Down (at the bottom) Denominator = how many equal parts a whole is divided into Numerator = how many of the equal parts of the whole there are 3

4 4. To read mixed numbers e.g. 1 ¼ This is the same as reading whole numbers and fractions together e.g. 1 ½ is the same as 1 whole and a ½ 5. To understand the equivalence of simple fractions Equivalent fractions may look different, but are really THE SAME Use a fraction wall/tower or pizzas/ cakes to demonstrate 6. To add any pair of two-digit numbers, mentally 1) Add the tens digits together 2) Add the units together 3) Add both answers to find the total 7. To subtract any pair of two-digit numbers, mentally - Partitioning 1. Put the greater number in your head 2. Partition the smaller number into tens (T) and units (U) 3. Either take away the tens or the units first, whichever is easier partitioning Partitioning is best when the digits of smaller number are smaller than the corresponding digits of the larger number. - Compensation (rounding and adjusting) 1. Look at the numbers. Can any be rounded to the nearest 10? 2. Carry out the simpler calculation. 3. Adjust answer allowing for original rounding. compensation Compensation is best when the smallest number CAN be rounded up. - Counting on 1. Put the smaller number in your head 2. Count on to the next ten 3. Count up in tens, then in units 4

5 8. To carry out column addition of two numbers less than Write each digit in the correct place value column 2. Start with the units column and add up all the numbers in that column. 3. If one of the columns adds up to an answer of 10 or more: a. put the units of the answer in the column being added b. carry the tens digit to the next column on the left under the bottom line. 4. Remember to add in the digit you carried with the next column. 5. Repeat with all the columns Th H T U Write the column headings to help you. 5

6 9. To carry out column subtraction of two numbers less than Write the greatest number on top, line up the digits in the place value columns. 2. Start by subtracting the units column, taking the bottom number away from the top. 3. If the top digit is less than the digit you are going to subtract, you need to exchange with a digit in the column to the left. Make the left neighbour 1 less, write the 1 beside your digit on its left) H T U Keep everything in the correct columns. If there is a decimal point (e.g. money), make sure the decimal point is lined up. Exchange if necessary. When exchanging, cross out digit you are exchanging from and take away one from it. Write the new number above it. Remember you cannot take away from 0 so you need to exchange from the next column to the left. First to make 10 then exchange a 1 and a leave a 9 in that column. 10. To know the 2, 5 and 10 multiplication tables TopTips For x2 tables - Count up in 2s, remember all answers are even and end in 2, 4, 6, 8 or 0. For x5 table - numbers in the x5 table always end in 5 or 0 For x10 table - numbers in the x10 table always end in 0 6

7 11. To know the 3 and 4 multiplication tables To multiply by 4, just double the number and then double it again. 12. To know the 6 and 7 multiplication tables The 6 times table is double the 3 times table. Remember 5,6,7,8 so 56 = 7x8 13. To know the 8 and 9 multiplication tables The 8 times table is double the 4 times table etc. Remember 5,6,7,8 so 56 = 7x8 The sum of the digits in multiples of 9 add up to 9. Remember finger trick for the 9 times tables. 14. To know the 11 and 12 multiplication tables The 11 times table digits are the same up to 9 x11 The 12 times table is double the 6 times table etc. 15. To work out division facts to multiplication tables Link to multiplication tables e.g. 2 x 3 = 6, 3 x 2 = = 3, 6 3 = 2 Circle sets to demonstrate 7

8 16. To find remainders after division 1. Divide into the greater number, one digit at a time, starting from the LEFT (It s the opposite side from when you are adding, subtracting and multiplying) 2. Put the result of each division directly above, on the top of the bus stop 3. If the small number won t go into a digit exactly, carry the remainder across (to the next digit on the right). If it won t go at all put a 0 on top and carry the whole digit. 4. Work out how many are left over. Show this as a remainder. e.g 24 divided by 3 = 7 r 3 Extend bus stop analogy to numbers that are out in the rain and sheltered numbers. Use your multiplication facts to help. 17. To know and use the links between familiar units of length, mass and capacity There are three types of metric measures length, mass and volume (capacity). Each one has a base unit: Length = metre Mass = grams Volume = litres Each type of metric unit has smaller and larger units which are either 10, 100, times smaller or larger. The size of the unit compared to the base unit is shown by adding a prefix. Deci = 1/10 of the base unit (10 times smaller) Centi = 1/100 of the base unit (100 times smaller) Milli = 1/1000 of the base unit (1000 times smaller) Kilo = 1000 time larger than the base unit 8

9 18. To choose and use the correct operations and ways of calculating (mental, mental with jottings, pencil and paper) to solve problems 1. Read and understand the problem. 2. Underline key information. 3. Decide what you need to work out. 4. Estimate 5. Calculate 6. Answer in a sentence 7. Take time to check your answer Break your method down into clear steps Use mathematical language to explain your method 9

10 and Shape, Space, Measures and Data Handling - Year 4 Key Learning Objectives 19. To name polygons, using criteria such as number of right angles, whether or not they are regular, symmetry properties Steps to success- Symmetry 1) Copy shape on to paper and cut out 2) Fold the shape to check if both sides fold exactly on top of each other A shape may have more than I line of symmetry A line of symmetry is also called a mirror line 20. To say whether a polygon is regular or irregular Polygons have straight sides Regular polygons also have sides of equal length 21. To classify 2-D shapes using criteria such as number of right angles, regular and irregular, lines of symmetry Use correct vocabulary such as right angle, faces, vertices, edges and practise by playing Guess the Shape (describing properties of each shape) or using a feely bag. 10

11 22. To know and use the relationships between units of time Remember these facts 365 days/12 months = 1 year days = 1 month 7 days = 1 week 1 day = 24 hours 1 hour = 60 minutes 1 minute = 60 seconds 23. To draw and answer questions about bar charts 1) Draw the horizontal and vertical axis on the line 2) Calculate the scale required 3) Mark equal points/numbers on axis on the line 4) Carefully plot information on graph, across first then up 24. To convert cm to metres Remember 100 cm = 1 metre Divide the number of cm by 100 to convert to metres Multiply number of metres by 100 to convert to cm 11