Workshops: The heart of the MagiKats Programme Every student is assigned to a Stage, based on their academic year and assessed study level. Stage 2 students are approximately 8 to 10 years old. The sheets in this pack are a small sample of what is available! These are only samples of the student s worksheets - our teaching methods include discussion and hands-on activities. Core skills sheets are also provided for independent completion by each student (usually at home). Topics offered at this level include: place value; developing number skills; ordering, comparing, estimating, rounding; fractions of numbers; working with decimals & fractions; shopping; time; measuring; area & perimeter; ratio & proportion; symmetry & reflections; drawing nets & shapes; handling data; problem solving.
Maths Stage 2: Counting On Sheet 1 Counting On Can you spot two families of numbers in the diamonds? What are they? 4 2 10 17 11 5 16 8 9 21 Pick out one family in red and one in green. 6 7 13 1 Now put all the red family in an order that starts with the smallest member and finishes with the largest. What about an order that starts with the largest and finishes with the smallest? Write it down below. 20 23 19 12 14 22 3 15 18 You have written out two sequences of numbers, one going up and one going down well done!
Maths Stage 2: Counting On Sheet 2 Using the rules that you are given, fill in the gaps in these sequences. 1) Count by 2 from 2 to 20 2 4 6 12 2) Count by 3 from 3 to 30 3 6 18 27 3) Count by 4 from 4 to 40 4 12 16 40 4) Count by 5 from 5 to 50 5 15 25 50 5) Count by 10 from 10 to 100 10 20 30 50 6) Count by 100 from 100 to 1000 100 200 300 400 7) Count by 2 from 24 to 6 2 20 18 6 8) Count by 3 from 36 to 9 3 30 21 18 9) Count by 4 from 48 to 12 4 32 28 12 10) Count by 5 from 60 to 15 60 35 15
Maths Stage 2: Counting On Sheet 3 How can we untangle a family of numbers, to give a sequence? How do we find the RULE? Look at this sequence. 7 10 13 16 19 22 25 28 31 What is its RULE? To describe the RULE of a sequence, you need to state three things. Look at the first sheets that you filled in, and the families that you sorted. Try to work out which three things are important to the RULE. What do you think are the three things you need know to be able to write the RULE? 1) 2) 3)
Maths Stage 2: Fractions Sheet 4 Equivalent Fractions Fractions 1) Colour two thirds ( 2 3 ) of this shape green. Colour four sixths ( 4 ) of this shape green. 6 What do you notice? 2) Colour three quarters ( 3 ) of this shape red. 4 Colour six eighths ( 6 ) of this shape red. 8 What do you notice? 3) Colour one half ( 1 2 ) of this shape blue. Colour six twelfths ( 6 ) of this shape 12 blue. What do you notice?
Maths Stage 2: Fractions Sheet 5 Looking back at Sheet 1 hopefully you noticed that the fractions shaded in the same colour were the same size? Different fractions which are the same size are called equivalent. So, according to Sheet 1, 2 3 and 4 6 are the same, or equivalent fractions. 3 4 and 6 8 And 1 2 and 6 12 are the same, or equivalent fractions. are the same, or equivalent fractions. How would you work this out if you were not able to draw a diagram? Like this! You need to know your tables, for a start. Do at least 3 times tables wrap-ups NOW (not 1,2,5 or 10!) Now, let s look at how 2 3 and 4 6 Look at the bottom of each fraction, What do you notice? are equivalent. 3 and 6 They are both in the 3 times table, and 3 goes into 6 twice. To convert 3 to 6 you would need to multiply by what? Whatever you do to the top of a fraction, you must also do to the bottom. So, 2 3 becomes 4 6 What does this mean?
Maths Stage 2: Fractions Sheet 6 Looking back again to Sheet 1, we also learnt that 3 4 and 6 8 are equivalent fractions. How would you work this out if you were not able to draw a diagram? First, look at the bottom of each fraction, To convert 4 to 8 4 and 8 you would need to multiply by what? Remember the GOLDEN RULE from the last sheet? Write it down here. So, you need to multiply the bottom number by to get from 4 to 8, so you must also multiply the top number by. So, 3 x = 4 x = 8 Looking back one more time to Sheet 1, we learnt that 1 and 6 are equivalent fractions. 2 12 How would you work this out if you were not able to draw a diagram? First, look at the bottom of each fraction, To convert 1 2 to 6 12 2 and 12 you would need to multiply by what? Remember the GOLDEN RULE from the last sheet? Write it down here. This proves that 3 = 4 6 8 So, you need to multiply the bottom number by to get from 2 to 12, so you must also multiply the top number by. So, 1 x = 2 x = 12 This proves that 1 = 6 2 12
Maths Stage 2: Subtracting in Columns Sheet 7 Subtracting larger numbers in columns Let s get warmed up! Answer these sums as quickly as you can! Do NOT use your fingers! If you need to check an answer then draw in dots to help you count on. 1) 11-5 = 2) 12-6 = 3) 12-7 = 4) 14-8 = 5) 13-7 = 6) 15-6 = 7) 16-8 = 8) 14-9 = 9) 14-6 = 10) 15-7 = 11) 18-9 = 12) 16-7 = 13) 15-8 = 14) 13-8 = 15) 16-9 = 16) 17-9 = 17) 17-8 = 18) 12-8 = 19) 13-6 = 20) 14-6 = 21) 13-5 = 22) 12-5 = 23) 14-5 = 24) 12-9 = Digits are the individual figures that make up numbers. So, digits are like letters and numbers are like words you use letters to make words, and digits to make numbers! Ex. 5238 the digits are 5,2,3 and 8, and the number is five thousand, two hundred and thirty-eight. Now, as you know, digits can mean different things depending on where they are in the number. Can you tell what the digit 3 shows in these numbers? (i.e. units, tens, hundreds, thousands.) 4321 3622. 7103. 2436....
Maths Stage 2: Subtracting in Columns Sheet 8 Break these numbers up to show what each digit represents. thousands hundreds tens units Ex. 3851 3 8 5 1 Now it s your turn! 1) 7920 2) 358 3) 6672 4) 3451 5) What are the digits in figure 1?.. 6) What is the number in figure 2?.... 7) What is the third digit in figure 3?..... 8) What are the second and fourth digits in figure 4?.. 9) Which is the biggest number?.... 10) Which has the least amount of hundreds?....
Maths Stage 2: Subtracting in Columns Sheet 9 Now you try these NB Start with the units column, work across column by column, and subtract downwards!! 1) 3 6 2 2) 5 4 7 3) 7 8-2 9-1 3 8-1 5 5) 6 3 5 6) 7 8 6 7) 4 5 6-2 2 7-7 9-1 2 5 9) 5 7 5 5 10) 9 7 6 9 0-2 4 1 6-3 4 3 2 3-1 0 2 1-1 1 2 1 2-2 0 0 1 3 If you borrow a ten and add it on to 0 units, you have These are just the start of it! Now you know the method, you can use that knowledge to help with the even harder ones.
Maths Stage 2: Subtracting in Columns Sheet 10 Start in the units column Work across column by column ALWAYS subtract downwards If you don t have enough at the top of a column to subtract downwards, borrow a ten from the next column (to the left) Add the borrowed ten to the column you need it Keep columns NEAT trust me, it makes life a lot easier! Try to use what you ve learnt so far to answer these 7 3 0-7 1 8 the units column borrow and carry 7 2 9 Do you need to borrow for the units column to work? - 5 7 6 the tens column. What do you think you need to do? 7 3 0-4 7 8 the units column.and the tens column!! Borrow and carry, borrow and carry 7 0 0-3 2 8 the units column. We don t have any tens to borrow, so how can you make the tens column bigger FIRST? Borrow and carry, borrow and carry..
Maths Stage 2: Classification of Polygons Sheet 11 Polygons Polygons are named according to the number of their sides or angles. Number of Name Example Sides or Angles Name Example F Number of Sides or Angles triangle 3 heptagon 7 quadrilateral 4 octagon 8 pentagon 5 nonagon 9 hexagon 6 decagon 10 The end points of the lines that form each angle is called the vertex. The plural of vertex is vertices. A, B, C etc are vertices in each of these polygons. A D A B C C B A B E D A regular polygon has all its sides the same length. C
Maths Stage 2: Classification of Polygons Sheet 12 Fill in the names in the table below: Name Example Number of Sides or Angles Name Example Number of Sides or Angles 3 heptagon 7 quadrilateral 4 8 5 9 6 10 Carefully set up your compasses. To do this, fix the (sharp) pencil in the holder so that the compass point and pencil point touch the table together when the compass arms are together. Now open the compasses to 5cm (use your ruler to get this right). On a blank sheet, carefully draw a straight line 5cm long. Put your compass point on one end and draw one or two arcs. Now repeat this with the other end of your line. Join each end of your line to a point where two arcs cross. You have drawn a regular (an equilateral) triangle. See if you can use the same idea to draw a regular polygon with more than three sides.
Maths Stage 2: Classification of Polygons Sheet 13 Identify the polygon that matches the following descriptions. 1) a six-sided figure. 2) a rectangle that has equal sides. 3) a five-sided figure. 4) a quadrilateral that has all sides equal with no right angles. 5) quadrilaterals that have two pairs of equal sides. 6) quadrilaterals that have all equal sides. 7) a quadrilateral that has only one pair of opposite sides parallel. 8) quadrilaterals that have all right angles. 9) quadrilaterals that have both pairs of opposite sides parallel. 10) quadrilaterals that have only opposite sides equal. 11) Draw all the lines of symmetry. a) b) c) d) e) f)
Maths Stage 2: Classification of Polygons Sheet 14 Name each triangle and say if it is equilateral, isosceles, scalene, or right angled. 1) 2) B Q 3cm 3cm 2cm 4cm A 3cm C 3) 4) X W P 5cm R 10cm 6cm 4cm 4cm V 8cm X Y 2cm Z Name each triangle and say if it is acute, right, or obtuse. 5) 6) Q R L 50 J 45 45 40 K M S V 7) 8) 30 22 130 28 50 100 N P U W
Maths Stage 2: Division with Remainders Sheet 15 Division with Remainders Look at this sum 15 3 = Read this as 15 divided by 3 Another way of saying this is 3 times what is 15? Think about your 3 times table. 3 x 5 = 15 so 15 3 = 5 Suppose the sum is 17 3 = Read this as 17 divided by 3 - how many 3s in 17? Think about your 3 times table. Blow! 17 isn t there. Let s investigate! Just how close can I get to 17 in the 3 times table? Well. 5 x 3 = 15 and 6 x 3 = 18 We want to know how many lots of 3 are in 17. 6 lots make 18 so this is too big. The best choice is 5 lots of 3 which makes 15. If I have 17 all together and 15 is packaged up in 5 lots of 3 then that leaves 2 over. x x x x x x x x x x x x x x x x x So 17 3 = 5 remainder 2 This would be written as 5 r2 Now try the question sheets!
Maths Stage 2: Division with Remainders Sheet 16 Try these questions, writing in a remainder when necessary. The first question is answered for you as an example. 1) 29 5 = 5 r 4 2) 25 4 = 3) 18 3 = 4) 22 3 = 5) 30 5 = 6) 19 2 = 7) 49 5 = 8) 8 4 = 9) 27 4 = 10) 21 2 = 11) 33 5 = 12) 28 4 = 13) 20 5 = 14) 6 3 = 15) 30 4 = 16) 18 2 = 17) 3 3 = 18) 24 3 = 19) 20 5 = 20) 23 4 = 21) 55 5 = 22) 32 3 = 23) 8 2 = 24) 19 5 = 25) 3 2 = 26) 24 3 = 27) 20 2 = 28) 47 4 = 29) 15 4 = 30) 18 4 =
Maths Stage 2: Division with Remainders Sheet 17 A different way of dividing Sums like 15 3 = 5 or 17 3 = 5 r 2 are quite straight forward. It is harder with big numbers, e.g. 123 3 = unless you know your 3 times table this far! I bet you don t! Make it easier look at this method: Write the sum this way 3 ) 1 2 3 Work it out bit by bit First say 3 into 1 : it won t go 3 ) 1 2 3 Move along: say 3 into 12 = 4 Write it in! 4 Put it in the right place above the 2 3 ) 1 2 3 That s the 12 done so move on to the 3. 4 1 3 into 3 goes 1: write it in 3 ) 1 2 3 ANSWER 4 1 3 ) 1 2 3 You did it! Well done! How do you think you do remainders?
Maths Stage 2: Division with Remainders Sheet 18 Applying division skills Fill in this 100 square. 1 Cross out 1. Colour all numbers that are divisible by 2, but not 2, the same colour. Colour all numbers that are divisible by 3, but not 3, the same, new colour. Colour all numbers that are divisible by 5, but not 5, the same, new colour. 100 Colour all numbers that are divisible by 7, but not 7, the same, new colour. Make a list of all the numbers that are not coloured or crossed out. What is special about these numbers?
Maths Stage 2: Pictograms, Venn Diagrams, Carroll Diagrams Sheet 19 Bar Charts You need to understand all the bits of a bar chart. First, remember that the height of each bar shows the frequency of the item. You read across from the bar to find the number of people on each bus. There were 12 people on the 7:50 bus. The labels tell you what the chart is about. 7:50 8:30 9:00 11:00 1:00 3:00 Bus times 1) How many people were on the 8:30 bus? 2) Which bus had the most people on? 3) Which bus had the fewest people on? 18 16 14 12 10 8 6 People 4 travelling 2 Look at the bar chart on the right and answer these questions on it: 4) What was the favourite pancake topping? 5) What was the least favourite pancake topping? 6) How many people s favourite topping was lemon? 0 50 45 40 35 30 25 20 15 10 5 0 Number of people on each bus to Grimsby on Tuesday Number of People Favourite Pancake Toppings Pickled Onions Lemon Maple Beef & Sugar Syrup Mustard Pancake toppings Gravy 7) How many people s favourite topping was beef and mustard? 8) How many more votes did maple syrup get than pickled onions?
Maths Stage 2: Pictograms, Venn Diagrams, Carroll Diagrams Sheet 20 When creating a bar chart, Use a ruler to find the top of the bar. The frequency chart (below) shows the different animals I found in my garden last week. I ve started putting the results into a bar chart. Type of Animal Frequency Cat 10 Badger 2 Hedgehog 4 Monkey 3 Blue Whale 1 Kangaroo 5 The highest number is 10, so the bar chart scale only needs to reach 10. 2 badgers were spotted, so the top of the badger bar goes at 2. 1) Fill in the rest of the bar chart. 2) Which animal did I find fewest of? 3) This is a table showing 30 people s favourite octopus names. Draw a bar chart of the results in this table. Favourite Name Frequency Ollie 15 Orrid 6 Oscar 8 Obi 4 Offul 5 Orvil 2 Number of Animals 10 9 8 7 6 5 4 3 2 1 0 Cat Animals Spotted in my Garden Badger Hedge Monkey Blue -hog Whale Type of Animal Kanga -roo 4) What is the least popular name? 5) What is the most popular name? 6) How many votes did Orvil get?
Maths Stage 2: Pictograms, Venn Diagrams, Carroll Diagrams Sheet 21 1) Working together, and with the help of your tutor, write a survey on favourite television programmes to carry out in your workshop. Decide on six programmes that should be in your short-list. Go round your workshop and ask each student and staff member to choose their favourite programme. Draw these results as a bar chart, then answer the questions at the bottom of this page. a) What was the favourite programme? b) What was the least popular programme? c) How many people are in your workshop today? d) How many people took part in your survey? e) How many people took part is an important piece of information. Why do you think this might be?
Maths Stage 2: Pictograms, Venn Diagrams, Carroll Diagrams Sheet 22 Venn Diagrams Venn Diagrams show the groups things are in. 1) This diagram splits up even numbers and numbers over 30. Using the diagram, write down: Even Over 30 a) the even numbers: b) the numbers over 30: c) the numbers that are not even and not over 30: d) the even numbers over 30: 2) Fill in this Venn diagram with odd numbers and numbers under 10. Pick 2 odd numbers that are under 10 and 2 that are not under 10. The numbers outside the 2 circles can t be odd or under 10. Make sure that anything in both circles is odd and under 10. 3) Choose 2 other types of numbers and then put them on this diagram. Don t use something like numbers over 20 and numbers under 20 or there won t be any overlap. 12 33 50 24 41 Odd Under 10 19 If you really can t think of anything yourself, try using numbers in the 3 times table for one of them.
Maths Stage 2: Standard Units Sheet 23 Measuring Weight Often we need to know how heavy things are, or their weight. For this we use scales. There are different types.. Some are digital, and just show the weight in a screen. These are the easiest to use. Some have a dial with a scale, and a moving pointer shows you the weight. Some have a pair of trays, and you must make them balance with weights. These are the hardest ones to use. A gram (g) is a very small measurement of weight. A teaspoon of sugar weighs about 5g. There are 1000grams in 1kilogram (kg). A kilogram is the weight of a bag of sugar. How many grams or kilograms do you think these things weigh? a) A bus b) An orange c) A jar of preserve d) A pencil
Maths Stage 2: Standard Units Sheet 24 1) What weight is shown on these digital scales? Write the weight in words. 540g a) 54kg b) 45kg c) 2) How many g in one kg? 3) How many g are in: a) 2kg b) 17kg c) 38kg 4) Write the following as kg and grams. a) 2474g = kg g b) 4190g = kg g c) 8390g = kg g d) 8003g = kg g e) 248g = kg g f) 10900g= kg g 5) Put these weights in order, starting with the lightest. a) 3kg 400g 34kg 3kg 34g 430g 3kg 44g b) 1kg 554g 15kg 4g 1kg 504g 15kg 400g 1kg 540g c) 25kg 3g 2kg 320g 152kg 5g 15kg 32g 15kg 230g
Maths Stage 2: Standard Units Sheet 25 Draw in what the scales would show if you had these items in the pan: 350g flour 170g raisins 210g margarine 29kg sand child weighing 27kg 33kg rock Now try these questions. 1) Sophie puts 350g butter, 400g flour, 275g margarine and 50g cocoa powder in a bowl. How much do the ingredients weigh altogether? Write your answer in g. 2) Mark weighs 7 1 2 kg more than his brother Jack. Jack weighs twice as much as his little sister, who is 15kg. a) How much does Mark weigh? b) How much would they weigh if they all got on the scales together? c) Their Dad weighs 84kg. What is the difference between his weight and their combined weight?
Maths Stage 2: Standard Units Sheet 26 Measuring Capacity Weighing is often used in cooking, but what if the ingredients you need to measure include some milk? You wouldn t weigh milk! For this we need another type of measurement capacity. You will probably have seen litres written on the side of milk or drink bottles. You might also see another measure ml (millilitres). We should drink about 2 litres of water every day. A can of coke holds about 330 ml. A bucket holds about 6 litres of water. A small car holds about 35 litres of fuel. 1) How many ml in: There are 1000 millilitres in 1 litre. a) 2 litres = ml b) 14 litres = ml c) 30 litres = ml 2) Write the following as l and ml. a) 2340ml = l ml b) 4030ml = l ml c) 10000ml = l ml d) 6670ml = l ml e) 2090ml = l ml f) 8030ml = l ml
Maths Stage 2: Standard Units Sheet 27 Summary Questions Now you have learnt about the different types of measure, try to answer these questions. 1) Which of these units is a unit of weight: ml, g, m, cm, pint, kilometre, kg? 2) Which of these units is a unit of length: mm, g, m, cm, l, gram, ml, km? 3) Which of these units is a unit of capacity: cm, pint, kg, ml, l, g, m, mile? 4) What units would you use to measure the length of a car? 5) What units would you use to measure the distance from Cardiff to London? 6) What units could you use to measure the capacity of a mug? 7) What units would you use for these: a) the length of a spider? b) the capacity of a teaspoon? c) the weight of a chocolate bar? d) the weight of a man? e) the capacity of a bucket? 8) What would you use to measure the weight of a chair? 9) What would you use to measure the length of an ant? 10) What would you use to measure the length of a table? 11) What would you use to measure the length of a house? 12) What would you use to measure the capacity of a cola bottle? Well done set finished!