Problem Solving Investigations overview

Transcription

1 Y1 Autumn 1 1 Fill the box Children fill a matchbox with items and count them Counting accurately to at least 20 accurately. Estimating up to at least 20 Y1 Autumn 1 2 Square tens Children find pairs of dominoes such that the total Number bonds to 10 number of spots is 10. Adding single-digit numbers Y1 Autumn 1 3 Sock doubles Children double numbers 1 to 5 as part of a game, and Doubling numbers 1 to 5 find which answers from 1 to 10 are possible. Recognising odd and even numbers Y1 Autumn 1 4 Flip and flop Children cut shapes from a shape and create Naming and recognising common 2D shapes symmetrical patterns. Creating and identifying line symmetry Y1 Autumn 1 5 Tricky tracks Children use reasoning and logic to play ahead in playing a game on a 1 20 track. Recognising numbers 1 20 on a track Y1 Autumn 2 6 Calculator capers Children create teens numbers using place-value Creating teen numbers using place value additions. Using addition bonds Y1 Autumn 2 7 Dotty triangle Children use trial and improvement to find different Adding three small numbers corners ways of making a given total by adding three numbers. Recognising pairs of numbers that make 3, 4 and 5 Y1 Autumn 2 8 Four towers Children arrange four towers such that the difference Comparing heights between neighbouring towers is at least two. Beginning to understand difference Y1 Autumn 2 9 Cross sums Children arrange numbers 1 to 5 on a cross to show that the row and column have the same total. Adding three single-digit numbers Y1 Autumn 2 10 Make 20 Children use coins and number shapes to make a total Recognising the value of each coin of 20. Adding single-digit numbers to numbers up to 19 1

2 Children find which numbers on a grid they can Making and saying 2-digit numbers Y1 Spring 1 11 Domino digits make using dominoes each domino can only be used Finding 2-digit numbers on a grid once. Children make loops of dominoes such that meeting Y1 Spring 1 12 Domino loop Using pairs to 5, 6 and 7 ends have a given total number of spots. Y1 Spring 1 13 Pyramid sums Children place three numbers in the bottom row of an addition pyramid and see that it is possible to end up with different numbers at the top. Adding pairs of single-digit numbers using known facts and counting on Adding pairs of numbers up to 20 by counting on Y1 Spring 1 14 Bears moving day Children make an open cube in the context of a story. Recognising the faces of a cube Y1 Spring 1 15 Trains Children use the same size carriages (rods) to make a train of 20 units. Counting in 2s, 5s and 10s Y1 Spring 2 16 Odds and evens Children use number shapes to find totals of odd and Recognising odd and even numbers even numbers, to see if they can find any rules. Adding single-digit numbers Y1 Spring 2 17 Coins in my Children use clues, and trial and improvement to find pockets different combinations of coins with a total of 20p. Adding 1p, 2p, 5p and 10p coins Y1 Spring 2 18 Make a stick Children find a collection of items which in total measure exactly one metre in length. Gaining a sense of the length of one metre Y1 Spring to 50 challenge Adding single-digit numbers to two-digit numbers Children find which numbers from 5 to 7 they can add Bridging 10s when adding repeatedly to 10 to land exactly on 50. Using number facts and patterns to add Y1 Spring 2 20 Pairs in purses Children use reasoning and logic to work out pairs of 2- digit amounts that can be made in the two purses given only ten coins. Knowing the value of each digit in a 2-digit number Showing a 2-digit number by combining groups of ten and one 2

3 Y1 Summer 1 21 Calculating Children add and subtract 1 and 10 in order to reach Add and subtract 1 to/from 2-digit numbers caterpillars targets. Add and subtract 10 to/from 2-digit numbers Y1 Summer 1 22 Domino additions Children use dominoes to generate 2-digit numbers plus Using number facts to add 1-digit numbers to 2-digit 1-digit number additions in a pattern. numbers Children roll a dice to determine how many coins they Y1 Summer 1 23 Dicey coins can take. They try to choose coins with a total of either 10p or 20p. Finding money totals to 10p and 20p Y1 Summer 1 24 Fill the bucket Children estimate then measure the capacity of a Estimating and measuring capacity in cupfuls bucket, and play a game filling it. Subtracting a small number Y1 Summer 1 25 Halving chains Children investigate which numbers from 1 to 20 will Halving even numbers up to 20 give the longest halving chain (each link must be a Recognising even numbers whole number). Y1 Summer 2 26 New neighbours Children use digit cards to make 2-digit numbers Using place value in 2-digit numbers between neighbouring multiples of 10. Ordering 2-digit numbers Y1 Summer 2 27 Balancing act Y1 Summer 2 28 Shape wheels Y1 Summer 2 29 Change challenge Y1 Summer 2 30 Stop me if you can! Children balance multiple number shapes to find equivalent multiplications. Children make a sequence of coloured shapes, changing one attribute at a time so that the sequence can end where it started, forming a circular sequence. Children find different ways of getting 1p, 2p, 3p change when buying biscuits/cakes costing 1p to 20p and using 2p, 5p, 10p or 20p coins. Children create diagonal lines on a grid by adding and subtracting 10 and 1, whilst trying to stop their partner doing the same. Counting in 2s, 5s and 10s Understanding multiplications as repeated addition Recognising 2D shapes Creating sequences Finding change by counting up Adding 10 and 1 Subtracting 10 and 1 3

4 Y2 Autumn 1 1 Square order Children place four digit cards on a grid to create 2- digit numbers and order them. They move the digits around to make smaller/larger numbers. Y2 Autumn 1 2 Addition towers Y2 Autumn 1 3 Digit sums Y2 Autumn 1 4 Cut and paste Y2 Autumn 1 5 Best foot forward Y2 Autumn 2 6 Dancing digits Y2 Autumn 2 7 Make it the same Y2 Autumn 2 8 Spin the mouse Y2 Autumn 2 9 Cross additions Y2 Autumn 2 10 Coin trios Children find the total number of spots on two dice in a game context, and consider why some totals come up more frequently than others. Children find the sum of the digits in a sequence of numbers and compare the pattern found to that identified in the digits sums of the doubles. Children use Escher s method of creating tessellations from rectangles and regular triangles or hexagons and explore the patterns created. Children plot routes across the number grid by adding or subtracting 1 and 10, using arrow cards. Children use place value addition and subtraction to write chains which swap the 10s and 1s digits. Children use trial and improvement to find a way of arranging 4 coins on a square so that each row and each column add up to a constant total. They explore diagonal patterns. Children turn a mouse through a rolled number of quarter or half turns, aiming to get the mouse facing home again. Children find totals of 5 numbers less than 10 to give different totals. Children make amounts of money using three coins, speculating whether larger amounts of money can be made in more ways or not. Comparing and ordering 2-digit numbers Using knowledge about the value of each digit in a 2- digit number Adding single-digit numbers Doubling numbers to 20 Finding digit sums Identifying patterns Identifying 2D shapes and their properties Creating tessellations Add and subtract 1 and 10 from any 2-digit number Become more familiar with the number grid Understanding the value of each digit in 2-digit numbers Using place value to add and subtract Adding amounts of money Using ¼ and ½ turns Using the knowledge that two halves make a whole and four quarters make a whole Adding five single-digit numbers using number facts including pairs to 10, to help Finding totals of amounts of money 4

5 Y2 Spring 1 11 Nines to zeros Children repeatedly add 9 or 19 to numbers until they get a multiple of 10, and look for patterns. Adding 9 and 19 to single-digit and 2-digit numbers Y2 Spring 1 12 Spot the Children make 2-digit numbers using dominoes and find Finding how many more are needed to make the next difference which complements to the next 10 are possible. multiple of 10 Children use trial and improvement to arrange amounts Y2 Spring 1 13 Star of change of change from 20p along a star to give constant totals Finding change from 20p along each star line. Y2 Spring 1 14 Pink or blue? Children explore the number of quarter past and quarter to times in a day by looking at the two sides of the clock. Setting an analogue clock at quarter pastor quarter to the hour Matching analogue and digital times Y2 Spring 1 15 Near and far Children use four digit cards to make a pair of numbers far away from each other on the number line, and the same four digit cards to make a pair of numbers close to each other. Y2 Spring 2 16 Make it equal Children find pairs of numbers to satisfy an equality. Y2 Spring 2 17 Multiple madness Y2 Spring 2 18 Calendar capers Y2 Spring 2 19 Mrs Multiple s cakes Y2 Spring 2 20 One pound names Children arrange digit cards to form multiples of 2, 5 and 10. Children use squares on a monthly calendar to create an addition square. They follow a sequence of instructions and explore the patterns derived. Children arrange cakes in arrays and find which numbers between 10 and 20 can be arranged in most ways. Children add up amounts to find out how much their name is worth! They try to give themselves a new name that is worth exactly a pound. Comparing pairs of 2-digit numbers Placing 2-digit numbers on a landmarked line Multiplying and dividing by 2, undertaking this adds doubling and halving Using the equals sign Recognising multiples of 2, 5 and 10 Adding 2-digit numbers Adding a single-digit number to a 2-digit number Doubling a 2-digit number by adding it to itself Understanding and using arrays Beginning to use multiplication facts Adding several 1-digit numbers Adding two 2-digit numbers 5

6 Y2 Summer 1 21 Diagonal hundreds Children use trial and improvement to place numbers in a grid to give a pair of diagonals whose sum is equal Adding two 2-digit numbers to 100. Y2 Summer 1 22 Frog s busy day Children look for numbers which have a difference of 5. Find a small difference by counting up Y2 Summer 1 23 Pyramids Y2 Summer 1 24 Ten to the kilo Y2 Summer 1 25 Jack s amazing beanstalk Y2 Summer 2 26 Lines of numbers Y2 Summer 2 27 Golden numbers Y2 Summer 2 28 Fanned fingers Y2 Summer 2 29 Left overs Y2 Summer 2 30 Sixteen rocks Children arrange numbers in a pyramid to create the largest and smallest possible totals. Children use estimation and accurate measurement skills to find exactly ten items which weigh precisely one kilogram. Children double numbers and add to a running total, and then look for patterns. Children create sequences based on Fibonacci and explore patterns of odd and even numbers, making connections with general statements about addition. Children explore which numbers are golden numbers when we are counting in steps of different sizes. Children work together to first estimate and then find an accurate measurement of the distance around their hand with the fingers fanned out or splayed wide. Children investigate which numbers leave 1 left over when divided by 5. Children arrange place value cards to make 3-digit numbers and then add the digits. They look at patterns. Adding single-digit and 2-digit numbers using number bonds and place value Choosing an appropriate way to add two numbers Estimating a weight Weighing with accuracy to the nearest 100g Doubling numbers up to at least 50 Adding single-digit and 2-digit numbers Adding two numbers mentally Identifying odd and even numbers up to and beyond 100 Multiplying and dividing by counting in steps along a number line Beginning to recognise common multiples Measuring to the nearest centimetre Choosing an appropriate method to find a distance around something Dividing by 5 Using multiples of 5 Creating 3-digit numbers using place value cards Adding three single-digit numbers Ordering 3-digit numbers 6

7 Y3 Autumn 1 1 Puzzling squares Use numbers 0 to 7 to make a total of 10 on each side Using number facts to solve puzzles of a square. Adding three single-digit numbers Y3 Autumn 1 2 Closest to 100 Children first play a game with a partner, then work Adding four numbers <100 individually or together to find a solution. Knowing number bonds to 10 Y3 Autumn 1 3 Make the Children draw on their knowledge of multiples of 2 and multiples 5 to create these using digit cards 0 9. Recognising multiples of 2 and 5 Y3 Autumn 1 4 Dodgy digital clock Children work out which times won t show correctly Reading times on a digital display because of a faulty segment in the digital display. Working systemically Y3 Autumn 1 5 Guess my number Children use their knowledge of 3-digit numbers, rounding, and properties of numbers to work out a mystery number. Rounding to the nearest 100 Using vocabulary and properties of numbers including odd and even Y3 Autumn 2 6 Fraction clues Children use their knowledge of fractions and tables to Finding half, third and quarter of numbers find mystery numbers. Recognising multiples of 2, 3 and 4 Y3 Autumn 2 7 Three coins Y3 Autumn 2 8 Litre challenge Y3 Autumn 2 9 Twisted subtractions Y3 Autumn 2 10 Mystery age Using exactly three coins, children work out how many amounts can be made between 1 and 2. Children use their knowledge of litres and millilitres to help them solve a logic puzzle. Using and labelling real jars or pots will help! Subtract a number which is the reviser of another, e.g Children use their knowledge of the 3, 4 and 5 times tables to work out mystery numbers. Place value in money Using combinations of coins to make different amounts of money Converting from litres to millilitres and vice versa Subtracting pairs of 2-digit numbers Multiplying by 3, 4 and 5 Dividing by 3, 4 and 5 with remainders Checking using the inverse 7

8 Children place counters on a PV grid to make 3-digit Counter place Y3 Spring 1 11 numbers and then use logic to ensure they have made value all combinations. Y3 Spring 1 12 Does it or not? Y3 Spring 1 13 Fraction bets Y3 Spring 1 14 Y3 Spring 1 15 Don t make a triangle Pattern subtractions Y3 Spring 2 16 Testing 10s Y3 Spring 2 17 Magic 147 Y3 Spring 2 18 Mirror times Y3 Spring 2 19 Age guessing trick Y3 Spring times table wow! Children find numbers between 50 and 100 which they can divide by 4. They halve each number twice to find out. Children look at fractions and make a hypothesis of which ones are closest. They then test this out by placing fractions on a line. Game for two where strategy and identifying triangles are both crucial. Children subtract 2-digit from 3-digit numbers, by counting up, and look out for patterns in the numbers. Children multiply numbers by 10, carry out a given procedure and look for patterns in their answers. Children arrange the nearly numbers in a square so that each row and column adds to Magic 147. Children use mirrors and analogue clocks. They record pairs of times using digital format. Children subtract numbers within the same century and use this calculation to guess a friend s age. Children use the grid method to work out the 18 times table and look for patterns in the answers. Using knowledge of place value in 3-digit numbers Halving 2-digit numbers Using mental strategies to divide by 4 Writing fractions along a line Comparing fractions on a line Identifying a triangle Logical prediction Subtracting 2-digit numbers from numbers between 100 and 200 Multiplying by 10 Adding 3-digit numbers and 2-digit numbers Adding 2-digit near multiples of 10 Adding a 2-digit near multiple of 10 to a 3-digit number Telling the time to the nearest 5 minutes using analogue clocks Recording times using digital format Seeing mirror images Subtracting 3-digit numbers in the same century Adding single-digit numbers Using the grid method to multiply 18 by single-digit numbers 8

9 Y3 Summer 1 21 Magical subtractions Y3 Summer 1 22 Crack the code Y3 Summer 1 23 Threes and fours Y3 Summer 1 24 Yucky food Y3 Summer 1 25 Next-door additions Y3 Summer 2 26 Mobile towers Y3 Summer 2 27 Total 10 Y3 Summer 2 28 My square, not yours! Y3 Summer 2 29 Dog chews Y3 Summer 2 30 Step change Children subtract the digital root of a 3-digit number from that number. Magic ensues! Children work together to reason and think logically to crack a code. Children explore multiples of 3 and 4 to find divisibility patterns. Children use the skills of recording and analysing data to work out which food the class hate most! Children add pairs of 3-digit numbers and look for patterns in the digital roots of the answers. Children create four or five 2-digit numbers and add these to get different totals. Using only digits 1 9 without the 5, children are finding all possible pairs of amounts to make 10. Children draw a succession of perpendicular and parallel lines to create squares. Children find a multiple of 50 and a multiple for 4 with a given total. Children find change from two or three notes. They explore patterns in the pence. Subtracting a single-digit number from a 3-digit number Adding 3 single-digit numbers Multiplying single-digit numbers Using mental multiplication and division strategies Knowing and recalling the 3 and 4 tables Dividing numbers just above the tables range Drawing and using tables to record data Drawing bar graphs and deciding on how many items will be represented by one block Using written addition to add pairs of 3-digit numbers Adding three, four or five 2-digit numbers Estimating totals Adding two amounts of money Using number facts to add to the next 10p and to 1 Identifying and drawing perpendicular lines Identifying and drawing parallel lines Counting in steps for 50 and in steps of 4 Adding multiples of 50 and 4 Finding change by counting up Finding complements to 100 9

10 Y4 Autumn 1 1 Make 100 Y4 Autumn 1 2 No zero Y4 Autumn 1 3 Magical 9s Y4 Autumn 1 4 Timeline Y4 Autumn 1 5 Cats and dogs Y4 Autumn 2 6 Best score for me! Y4 Autumn 2 7 Odds and evens mix-up Y4 Autumn 2 8 Pencil power Y4 Autumn 2 9 Hole-y subtractions Given a pattern of four 1-digit numbers, children attempt to make a total of exactly 100. Children investigate how many numbers between one and ten thousand have a zero. Children are looking for patterns when multiplying nearly numbers by 9. Children use their knowledge about millimetres, centimetres and metres to create a scale timeline. Children work to solve a puzzle involving adding two 3- digit numbers. They find several possible solutions, and then invent their own puzzle. Children find equivalent fractions to cross numbers on a 6 6 square. They use strategies to find their highest score. Children create two 4-digit numbers one with even digits, one with odd digits and add these. They look for patterns of even/odd in the totals. Children use larger weights and numbers to find an accurate weight of one pencil by collecting data on a bar graph. Children create 3-digit palindromic numbers with a hole (i.e. a zero) in the middle. They subtract 3-digit numbers with equal numbers of 1s, 10s and 100s and identify patterns. Adding pairs of 2-digit numbers mentally, using an appropriate strategy, e.g. partitioning and recombining, doubling/near doubling, adding the nearest multiple of ten and adjusting Understanding place value in numbers with up to 4 digits Using mathematical reasoning to discover all the possibilities Multiplying nearly numbers by multiplying the multiple of ten and adjusting Identifying multiples of nine Measuring lengths in m, cm and mm Converting between m, cm and mm Placing 4-digit numbers on landmarked lines Using the language of time: year, decade, century, millennium Using expanded or compact addition to add two 3- digit numbers Reasoning about what letter can represent each number Finding equivalent fractions Using and knowledge of factors and multiples Adding two 4-digit numbers using column addition Recognising even and odd numbers Weighing objects in grams using scales Reading scales Drawing bar graphs Use counting up subtraction (frog) to subtract 3-digit numbers Identify patterns in the answers 10

11 Y4 Autumn 2 10 Mystery multipliers Children work out which single-digit numbers and multiples of 10 have given products in order to solve a puzzle. Multiplying single-digit numbers by multiples of 10 Dividing 2-digit and 3-digit multiples of 10 by multiples of 10 and single-digit numbers 11

12 Y4 Spring 1 11 Tell the teacher Y4 Spring 1 12 Wonderful 1089! Y4 Spring 1 13 Foodie fractions Y4 Spring 1 14 Tremendous tiles Y4 Spring 1 15 Race to 200 Y4 Spring 2 16 Magical square decimals Y4 Spring 2 17 Present prices Y4 Spring 2 18 Time to reflect Y4 Spring 2 19 Y4 Spring 2 20 Mobile subtractions Rocking remainders Children consider whether given calculations are harder or easier to work out a scoring system. Children add two 3-digit numbers and subtract a pair of 3-digit numbers to find patterns. Given fractions of amounts, children work out how many friends are at a picnic. Children explore creating patterns of tiles with three asymmetrical blocks. They look for and identify lines of symmetry, creating patterns with at least two lines of reflective symmetry. Children apply knowledge of factors within the 2, 3, 4, 5, 9 and 10 tables. Children use the arrangement of digits on a magic square to create 1-place decimals. They try to demonstrate that they have found all the possibilities. Children will use logic and addition, along with some trial and improvement to solve this problem involving money. Children apply their knowledge of 24 hour digital clocks. Children select three contiguous numbers from a mobile phone display and create a subtraction. Children divide 11, 22, by 3, 4, 5 and look for patterns in the remainders. Adding and subtracting 1s, 10s, 100s and 1000s to/from 4-digit numbers, including crossing 10s, 100s and 1000s Adding two 3-digit numbers using written addition Subtracting one 3-digit number from another using column subtraction Finding unit and non-unit fractions of quantities using multiplication and division Using an inverse operation to find a missing number Recognising line symmetry Creating patterns with two lines of symmetry Recognising or deriving multiples of 2, 3, 4, 5, 9 and 10 Choosing methods for mental addition Dividing numbers by ten to create 1-place decimal numbers Adding amounts of money using expanded and compact addition Telling the time on a digital clock Subtracting 3-digit numbers Adding 3 single-digit numbers Dividing 2-digit numbers by numbers 3 up to 12, finding remainders 12

13 Y4 Summer 1 21 Magic chains Y4 Summer 1 22 Decimal detective Y4 Summer 1 23 Table digital roots Y4 Summer 1 24 Soma cube Y4 Summer 1 25 Target timings Y4 Summer 2 26 Set square Y4 Summer 2 27 Subtraction trios Y4 Summer 2 28 Coordinate patterns Y4 Summer 2 29 Testing 10s Y4 Summer 2 30 Fancy fractions Children use knowledge of inverse operations to quickly work out a sequence of calculations. Children use clues to find a number with two decimal places. Children find the digital roots of multiples of 2, 3, 4, 5, 6, 7, 8, 9 and 10. They identify patterns and relate these to what they know of numbers. Children create specified 3D shapes using 2D representations and then combine these to create other 3D shapes including a cube. Children add or subtract ones, tenths or hundredths to reach a target number. They use mathematical reasoning to choose the best strategies. Use digits 1 9 once only to complete a calculation grid with given answers for each row and column. Children look for patterns in answers when subtracting 3-digit numbers from 4-digit numbers with consecutive digits. Children draw rectangles with a given area, and one fixed vertex. They label the other coordinates and begin to work them out. Children divide numbers by 10, carry out a given procedure and look for patterns in their answers. Children find non-unit fractions of multiples and look for patterns. Adding and subtracting 1, 10, 100 and 1000 to/from 4-digit numbers Using knowledge of inverse operations Using place value in numbers with two decimal places Rounding to the nearest tenth and whole Recalling times tables facts to Recognise and create 3D shapes from 2D representations Recognise a cube and cuboid and understand their properties Identifying the place value in a 2-place decimal number Adding or subtracting ones, tenths and hundredths to or from a 2-place decimal Calculating using a mix of all four operations Using mathematical reasoning to explain findings Using column subtraction (or Frog) to subtract 3-digit numbers from 4-digit numbers Labelling coordinates Finding areas by counting squares Dividing by 10 Adding on a number with one decimal place Finding non-unit fractions of amounts Listing multiples 13

14 Y5 Autumn 1 1 Y5 Autumn 1 2 Magic star additions Durer s Magic Square Y5 Autumn 1 3 Get to the root Y5 Autumn 1 4 Digits of time Y5 Autumn 1 5 Persistent answers Y5 Autumn 2 6 Long as you like Y5 Autumn 2 7 Excellent eights Y5 Autumn 2 8 Billiard angles Y5 Autumn 2 9 Fraction pictures Y5 Autumn 2 10 Reverse digits, same product Children explore addition patterns on a star derived from a simple magic star. Children use Durer s Magic Square and create 2- or 3- digit numbers and find the difference between different pairs. They identify patterns. Children use their fluency in mental multiplication to explore the patterns of digital roots in multiplication. Children find out how many times the digit 9 is used on the 24-hour digital clock between noon and midnight. Children subtract numbers with consecutive digits from numbers with identical digits and record the different possible answers. Children create chains of numbers by finding factors and multiples. Their aim is to create the longest chain possible. Children explore patterns when multiplying numbers with consecutive digits by 8. Children use a knowledge of angles to draw lines of incidence and reflection on billiard tables of differing proportions. They identify patterns and make predictions. Children use knowledge of equivalent fractions to work out what fraction each shape is as part of the whole picture, and which shapes are the same size. Children find the product of a pair of 2-digit numbers then reverse the digits of both numbers and find an identical product. Adding 4-digit numbers mentally or using written addition Exploring patterns generated Adding mentally, choosing an appropriate strategy Subtracting mentally, choosing an appropriate mental method Multiply 2-digit numbers by 1-digit numbers using mental strategies Add single-digit numbers using number bonds Telling the time on a 24-hour digital clock Using column subtraction to subtract pairs of 4-digit numbers where moves from 1000s, 100s and/or 10s are necessary Finding factors of 2-digit numbers Finding multiples of 2-digit numbers Using trial and error to improve their results Using grid multiplication to multiply large numbers by a single-digit number Using short multiplication if appropriate Drawing lines at specified angles Plotting lines of travel on a grid Recognising that angles in a triangle add up to 180 degrees and using this fact to calculate missing angles Identify fractions as part of a whole Using knowledge of equivalent fractions Multiplying a 2-digit by a 2-digit number using long multiplication or grid method Using tables facts 14

15 Y5 Spring 1 11 Lost digit Y5 Spring 1 12 Four of the best Y5 Spring 1 13 Prime differences Y5 Spring 1 14 Weights in a line Y5 Spring 1 15 Decimal differences Y5 Spring 2 16 Dozen divisions Y5 Spring 2 17 Riveting reversals Y5 Spring 2 18 Polygon dissections Y5 Spring 2 19 Fraction fireworks Y5 Spring 2 20 Big domino additions Children explore 6-digit numbers using a trick based on reduced numbers (casting out nines). Children use an incomplete magic square to explore patterns in the addition of four numbers. Children find out if prime numbers become less frequent as we consider sets of larger numbers. Children use systematic working to calculate the number of possibilities of making weights using just two set weights, and then look for patterns using line graphs. Children subtract pairs of numbers with consecutive digits and different numbers of decimal places, and look for patterns in their answers. Children use short division to divide 3-digit numbers with consecutive digits by 12. They reverse the digits in the 3-digit number and repeat, then find the difference between the two answers. Multiply 4-digit numbers with consecutive digits by a single-digit number; reverse the 4-digit number and repeat. Find the difference between the two answers. Children cut squares, rectangles and regular polygons into two parts and see what new shapes they can make by putting the two parts together in different ways. Children find the answers to a sequence of fraction multiplications and look for patterns in the answers. Children follow a logic to convert arrangements of dominoes to numbers and then perform a giant addition. They then create their own domino additions. Identifying the place value of any given digit in a 6- digit number Adding and subtracting single-digit numbers Adding 1-place decimals mentally Using column addition to add decimal numbers Subtracting small numbers Using number facts Ordering a search for combinations Plotting points accurately on a line graph Counting up to subtract numbers with different numbers of decimal places Using short division to divide 3-digit numbers by 12, writing the answer as a mixed number where there is a remainder Finding the difference between mixed numbers and whole numbers Using short multiplication to multiply 4-digit numbers by single-digit numbers Find the difference between 4- and 5-digit numbers Recognising quadrilaterals and polygons Multiplying mixed numbers by whole numbers Adding pairs of 5-digit numbers Adding several 3-digit and 4-digit numbers or towers of 2-digit numbers Pence and pounds Children find patterns in the differences when pounds Finding a difference between two amounts of money Y5 Summer 1 21 reversed and pence are reversed. Identifying multiples of nine 15

16 Y5 Summer 1 22 The eights have it Y5 Summer 1 23 Alternating chains Y5 Summer 1 24 Y5 Summer 1 25 Y5 Summer 2 26 Y5 Summer 2 27 Triangle coordinates Exasperating 80 grand Big triangle of fractions Remainder runners Children multiply numbers starting with 9 by 9 and add single-digit numbers in a decreasing sequence. They identify and describe the patterns and start to explain them. Children create chains of alternating positive and negative numbers and look at the patterns in their totals. Children draw different types of triangle on coordinate grids and reflect these in the y-axis. Children use the digits 0 to 9 only to create pairs of 5- digit numbers, with a total as close to 80,000 as possible. Children add fractions with related denominators and find equivalent fractions to identify patterns. Children divide 1234, 2345, 3456 by 3, 4, 5 and look for patterns in the remainders. Y5 Summer 2 28 Guesstimate Children work out the capacity of their classroom. Y5 Summer 2 29 Martian numbers Y5 Summer 2 30 What an odd thing! Children explore the facts that Arabic numbers use a base of 10, we can write numbers using a base of 3, and Roman numbers have no base. Children create a triangle of odd numbers and identify the patterns when rows are summed or their end numbers are averaged. Multiplying numbers with 1, 2, 3, 4 or more digits by 9 Adding single-digit number to 5-digit or 6-digit numbers Adding positive and negative numbers Drawing shapes on a coordinate grid and writing their coordinates Reflecting shapes in the y-axis and noting the coordinate pattern Using column addition to add pairs of 5-digit numbers Estimating totals Finding an equivalent fraction to non-unit fractions (denominator 12) Adding fractions with related denominators Using short division to divide 4-digit numbers by numbers 3 up to 12, finding remainders Converting cm3 to millilitres Converting millilitres to litres Writing numbers using Roman numerals Writing numbers as Martian numbers (i.e. in base 3) Adding several 2-digit numbers Halving numbers with 2 or 3 digits Recognising square and cube numbers 16

17 Y6 Autumn 1 1 Crack the code Children use logical thinking to solve a mathematical puzzle involving multiplying by 10 and 100 and adding decimal numbers. Y6 Autumn 1 2 Decimal pyramids Y6 Autumn 1 3 All at 6s and 7s Y6 Autumn 1 4 Annoying clock Y6 Autumn 1 5 Nine AGAIN! Y6 Autumn 1 6 Riveting reversals Y6 Autumn 2 7 Noughts and negatives Y6 Autumn 2 8 Geometry genius Y6 Autumn 2 9 Awesome answers Y6 Autumn 2 10 Percentage puzzles Y6 Autumn 2 11 Fraction frenzy Children add numbers with three decimal places to give a number with two decimal places, then add numbers with two decimal places to give a number with one decimal before finally adding numbers with one decimal place to give a whole number. Children try to make every number to at least 10 using 6s, 7s and sometimes 2 and 3, and any operations. Children apply their knowledge of time to solve a multi-step problem involving dates and organised reasoning. Children subtract 5-digit numbers and look for patterns in the digital roots. Multiply 3-digit numbers with consecutive digits by a 2- digit number; reverse the 3-digit number and repeat. Find the difference between the two answers. Children play an adapted game of noughts and crosses, aiming to get negative number answers. Children use what they know about how to find the areas of triangles and parallelograms to find the areas of rhombi, kites and trapezia. Using a magic square to generate 3-digit numbers, children create divisions with dividends containing specified fractions. Children work systematically to find equivalent percentages of different amounts. Children multiply proper fractions by whole numbers in a multiplication grid and look for patterns. Multiplying by 10 and 100 Adding decimal numbers using number bonds to 10 Adding numbers with 1, 2 and 3 decimal places Using knowledge of numbers bonds to add decimals Using knowledge of the order of operations and brackets to carry out calculations Knowing and using facts about time, e.g. how many minutes are in an hour and how many days are in a year Using a calendar Using 24-hour clock format Subtracting 5-digit numbers to find a difference Choosing an appropriate method to find a difference Using long multiplication or the grid method to multiply 3-digit then 4-digit numbers by numbers between 10 and 35 Find the difference between 4-, 5- and 6-digit numbers Subtracting single-digit numbers to give zero or negative answers Finding areas of parallelograms and triangles Writing formulae Dividing 3-digit numbers using short division Recognising fractions and writing these in their simplest form Finding multiple of 10 percentages of different amounts of money Using fraction and decimal equivalents Multiplying fractions by whole numbers Converting improper fractions to mixed numbers 17

18 18

19 Y6 Spring 1 12 Mobile differences Children use trial and improvement to find the largest and smallest possible differences using numbers selected to given criteria. Y6 Spring 1 13 Mixed up fractions Y6 Spring 1 14 Stunning squares Y6 Spring 1 15 Ellipse in a circle Y6 Spring 1 16 Talisman Squares Y6 Spring 1 17 Magic multiplication squares Y6 Spring 2 18 Dicey differences Children add a pair of fractions, multiply the same pair, then find the difference between the two answers, looking for patterns. Children explore patterns in the squares of numbers with reversed digits to find pairs of stunning squares. Children draw a circle and then use straight lines and angles to construct an ellipse within it. Children find differences between adjacent numbers on a 4 4 grid and then explore arrangements on a 3 3 grid. Children complete a magic multiplication square. They then explore factors and multiples to create a new multiplication magic square. Children use two dice with decimal numbers to find largest and smallest possible differences and use mathematical reasoning to calculate the probability of getting close to a specified target. Y6 Spring 2 19 Mean score Children design a dice such that the mean score is 5. Y6 Spring 2 20 Cycling coordinates Y6 Spring 2 21 Why is it so? Y6 Spring 2 22 Stars and crosses Children use a sequence of coordinates to create quadrilaterals. Children identify a pattern in the division of a total of six numbers created using the same 3 digits. They then use algebra to explain why it is so. Children find totals of the numbers in shapes on a grid, make generalisations and then write a formula to find the total of any similar shape on the grid. Subtracting 5-digit numbers to find a difference Choosing an appropriate method to find a difference Adding, multiplying and subtracting pairs of fractions Multiplying 2-digit numbers by 2-digit numbers Multiplying 3-digit numbers by 2-digit numbers Multiplying 3-digit numbers by 100 Drawing a circle with a given radius Drawing rays from a point Drawing lines perpendicular to those rays Subtracting two 1-place decimal numbers Multiplying three numbers choosing appropriate methods Finding factors and multiples Subtracting numbers with 2 decimal places from numbers with 1 decimal place using counting up Finding the mean of a set of numbers Adding six numbers and dividing by 6 Using coordinates Recognising different types of quadrilaterals Adding towers of 2-digit numbers Performing long and short division Making generalisations and writing formulae Finding totals of three, four, five or more 2-digit numbers 19

20 Year Term Week Investigation title Y6 Summer 1 23 NO INVESTIGATION TO ALLOW TIME FOR SATS PREPARATION Y6 Summer 1 24 NO INVESTIGATION TO ALLOW TIME FOR SATS PREPARATION Y6 Summer 1 25 NO INVESTIGATION TO ALLOW TIME FOR SATS PREPARATION Y6 Summer 1 26 NO INVESTIGATION TO ALLOW TIME FOR SATS PREPARATION Y6 Summer 2 27 NO INVESTIGATION TO ALLOW TIME FOR SATS PREPARATION Y6 Summer 2 28 NO INVESTIGATION TO ALLOW TIME FOR SATS PREPARATION Y6 Summer 2 29 NO INVESTIGATION TO ALLOW TIME FOR SATS PREPARATION Y6 Summer 2 30 NO INVESTIGATION TO ALLOW TIME FOR SATS PREPARATION 20