Year 2/3 Mastery Overview Autumn Year 2/3 Mixed Year Overview Guidance Since our Year 1 to Year 6 Schemes of Learning and overviews have been released we have had lots of requests for something similar for mixed year groups. This document provides the yearly overview that schools have been requesting. We really hope you find it useful and use it alongside your own planning. The White Rose Maths Hub has produced these long term plans to support mixed year groups. These overviews are designed to support a mastery approach to teaching and learning and have been designed to support the aims and objectives of the new National Curriculum. We had a lot of people interested in working with us on this project and this document is a summary of their work so far. We would like to take this opportunity to thank everyone who has contributed their thoughts to this final document. These overviews will be accompanied by more detailed schemes linking to fluency, reasoning and problem solving. Termly assessments will be available to evaluate where the children are with their learning. If you have any feedback on any of the work that we are doing, please do not hesitate to get in touch. It is with your help and ideas that the Maths Hubs can make a difference. The White Rose Maths Hub Team © Trinity Academy Halifax 2016 [email protected] The overviews: • have number at their heart. A large proportion of time is spent reinforcing number to build competency. • ensure teachers stay in the required key stage and support the ideal of depth before breadth. • provide plenty of time to build reasoning and problem solving elements into the curriculum This document fits in with the White Rose Maths Hub Year 1 – 6 Mastery documents. If you have not seen these documents before you can register to access them for free by completing the form on this link http://www.trinitytsa.co.uk/maths-hub/freelearning-schemes-resources/ Once registered you will be provided with a Dropbox link to access these documents; please be aware some school IT systems block the use of Dropbox so you may need to access this at home. Year 2/3 Mixed age planning Using the document Progression documents The overviews provide guidance on the length of time that should be dedicated to each mathematical concept and the order in which we feel they should be delivered. Within the overviews there is a breakdown of objectives for each concept. This clearly highlights the age related expectations for each year group and shows where objectives can be taught together. We are aware that some teachers will teach mixed year groups that may be arranged differently to our plans (eg Y2/3). We are therefore working to create some progression documents that help teachers to see how objectives link together from Year 1 to Year 6. There are certain points where objectives are clearly separate. In these cases, classes may need to be taught discretely or incorporated through other subjects (see guidance below). Linking of objectives Certain objectives are repeated throughout the year to encourage revisiting key concepts and applying them in different contexts. Lesson Plans As a hub, we have collated a variety of lesson plans that show how mixed year classes are taught in different ways. These highlight how mixed year classes use additional support, organise groups and structure their teaching time. All these lesson structures have their own strengths and as a teacher it is important to find a structure that works for your class. © Trinity Academy Halifax 2016 [email protected] Within the overviews, the objectives are either in normal font or in bold. The objectives that are in normal font are the lower year group out of the two covered (Year 1, Year 3, Year 5). The objectives in bold are the higher year group out of the two covered (Year 2, Year 4, Year 6), Where objectives link they are placed together. If objectives do not link they are separate and therefore require discrete teaching within year groups. Year 2/3 Mixed age planning Teaching through topics Objectives split across topics Most mathematical concepts lend themselves perfectly to subjects outside of maths lessons. It is important that teachers ensure these links are in place so children deepen their understanding and apply maths across the curriculum. Within different year groups, topics have been broken down and split across different topics so children can apply key skills in different ways. Here are some examples: Statistics- using graphs in Science, collecting data in Computing, comparing statistics over time in History, drawing graphs to collect weather data in Geography. Roman Numerals- taught through the topic of Romans within History Geometry (shape and symmetry)- using shapes within tessellations when looking at Islamic art (R.E), using shapes within art (Kandinsky), symmetry within art Measurement- reading scales (science, design technology), Co-ordinates- using co-ordinates with maps in Geography. Written methods of the four operations- finding the time difference between years in History, adding or finding the difference of populations in Geography, calculating and changing recipes in food technology. Direction- Programming in ICT © Trinity Academy Halifax 2016 [email protected] Money is one of the topics that is split between other topics. It is used within addition and subtraction and also fractions. In Year 1 and 2 it is important that the coins are taught discretely however the rest of the objectives can be tied in with other number topics. Other measurement topics are also covered when using the four operations so the children can apply their skills. In Year 5 and 6, ratio has been split across a variety of topics including shape and fractions. It is important that these objectives are covered within these other topics as ratio has been removed as a discrete topic. Times tables Times tables have been placed within multiplication and division however it is important these are covered over the year to help children learn them. Year 2/3 Everyone Can Succeed More Information As a Maths Hub we believe that all students can succeed in mathematics. We do not believe that there are individuals who can do maths and those that cannot. A positive teacher mindset and strong subject knowledge are key to student success in mathematics. If you would like more information on ‘Teaching for Mastery’ you can contact the White Rose Maths Hub at [email protected] Acknowledgements The White Rose Maths Hub would like to thank the following people for their contributions, and time in the collation of this document: Cat Beaumont Matt Curtis James Clegg Becky Gascoigne Sarah Gent Sally Smith Sarah Ward © Trinity Academy Halifax 2016 [email protected] We are offering courses on: Bar Modelling Teaching for Mastery Subject specialism intensive courses – become a Maths expert. Our monthly newsletter also contains the latest initiatives we are involved with. We are looking to improve maths across our area and on a wider scale by working with other Maths Hubs across the country. Year 2/3 Term by Term Objectives Year 2/3 Overview Week 3 Week 4 Week 5 Week 6 Week 7 Week 8 Week 9 Week 10 Week 11 Week 12 Addition and Subtraction Multiplication and Division Time Fractions Geometry- Shape Measurement Length, weight, temperature and capacity © Trinity Academy Halifax 2016 [email protected] Statistics Assessment Place Value Summer Autumn Week 2 Spring Week 1 Four operations Year 2 and 3 Consolidation and application Year 2/3 Term by Term Objectives Year Group Week 1 Y2/3 Week 2 Week 3 Place Value Count in steps of 2, 3 and 5 from 0 and in tens from any number, forward and backward. Count from 0 in multiples of 50 and 100 Read and write numbers to at least 100 in numerals and words. Read and write numbers up to 1000 in numerals and in words. Recognise the place value of each digit in a two digit number (tens, ones) Recognise the place value of each digit in a 3 digit number. Identify, represent and estimate numbers to 100 using different representations including the number line. Identify, represent and estimate numbers using different representations. Compare and order numbers from 0 up to 100; use <, > and = signs. Order and compare numbers to 1000. Find 10 or 100 more or less than a given number. Use place value and number facts to solve problems. Solve number problems and practical problems involving these ideas. © Trinity Academy Halifax 2016 [email protected] Term Week 4 Autumn Week 5 Week 6 Week 7 Week 8 Addition and Subtraction Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100. Add and subtract numbers using concrete objects, pictorial representations, and mentally, including: a two digit number and ones; a two digit number and tens; two two digit numbers; adding three one digit numbers. Add and subtract numbers mentally, including: a three-digit number and ones; a threedigit number and tens; a three digit number and hundreds. Add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction Solve problems with addition and subtraction: using concrete objects and pictorial representations, including those involving numbers, quantities and measures; applying their increasing knowledge of mental and written methods. Solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction. Show that the addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot. Recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems. Estimate the answer to a calculation and use inverse operations to check answers. Recognise and use symbols of pounds (£) and pence (p); combine amounts to make a particular value. Find different combinations of coins that equal the same amounts of money. Solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change. Add and subtract amounts of money to give change using both £ and p in practical contexts. Measure, compare, add and subtract: lengths (mm, cm, m); mass (kg/g); volume/capacity (l/ml). Week 9 Week 10 Week 11 Week 12 Multiplication and Division Recall and use multiplication and division facts for the 2, 5 and 10 times tables, including recognising odd and even numbers. Recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables. Calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (x), division (÷) and equals (=) sign. Write and calculate mathematical statements for multiplication and division using the multiplication tables they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods. Show that the multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot. Solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods and multiplication and division facts, including problems in contexts. Solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects. Year 2/3 Term by Term Objectives All students Place Value National Curriculum Statement Fluency Continue the sequence: 2, 4, 6, 8, 10, __, __, __ 15, 20, 25, 30, __, __ 90, 80 , 70, __, __, __ 21, 18, 15, __, __ , __ Fill in the missing numbers 10 Count in steps of 2, 3 and 5 from 0 and in tens from any number, forward and backward. 20 25 30 Reasoning Spot the mistake: What is wrong with this sequence of numbers? 55, 50, 45, 35 True or False I start at 0 and count in 3’s. I say the number 14. I start at 60 and count back in 5’s. The fifth number I say will be 40. Multiples of 2 are all even numbers Multiple of 5 are all even numbers 40 Circle the odd one out: 3, 8, 13, 18, 23, 27, 33, 12, 15, 18, 20, 24 What comes next? 21 + 5= 26 26 + 5= 31 31+ 5 = 36 Investigate: which numbers appear in the 2’s, 3’s and 5’s times tables? Harry has made a sequence of numbers using six number cards. Here are three of the cards: can you think of two sequences Harry could have made? 10 20 30 A spider is climbing a 30m building. Each day it climbs 5m and slides back down 1m. How many days will it take to reach the top? Draw a picture to explain your working out Sid is counting in 2’s, Luke is counting in 3’s. Sid says ‘If we add our numbers together as we count we can make a new pattern.’ What pattern do they make? What happens if Sid counts in 5’s and Luke counts in 10’s? 20, 18, 17, 14, 12, 10 © Trinity Academy Halifax 2016 [email protected] Problem Solving Year 2/3 Term by Term Objectives All students National Curriculum Statement Fluency Continue the pattern: Reasoning Circle the odd one out. 100, 150, 200, 215, 300 Explain how you know. True or False. If I count in 100s from 0, all the numbers will be even. Convince me. 50, ___, 150, 200, ___ Problem Solving 100, 200, ___, ___, 500 Place Value Fill in the missing words: ____, ____, one hundred, one hundred and fifty Count from 0 in multiples of 4, 8, 50 and 100 Count in 10s from 0. Whenever you get to a multiple of 50 say Fizz, when you get to multiples of 100 say Buzz. If it is a multiple of both say Fizzbuzz. Using equipment, show me the fifth multiple of 50 Find the next three numbers in each sequence: 4, 8, 12, 16, __, __, __ 8, 16, 24, 32, __, __, __ © Trinity Academy Halifax 2016 [email protected] 200 400 300 Use the number cards to make a sequence. Can you make more than one sequence? Always, sometimes, never Create calculations for your friends to sort into the diagram e.g. Double 25, Half of 200 All multiples of 50 are multiples of 100 therefore all multiples of 100 are multiples of 50. All multiples of 8 are multiples of 4. Jack says ‘If I can count in 4’s, I can use this to count in 8’s.’ Do you agree? Explain why What do you notice? Al’s money is arranged in stacks. Each stack contains 50p. He has 8 stacks. How much money does Al have? Year 2/3 Term by Term Objectives All students National Curriculum Statement Fluency Place Value Match the numerals to words. 43 thirty four 62 thirty nine 39 forty three 34 Read and write numbers to at least 100 in numerals and words. © Trinity Academy Halifax 2016 [email protected] sixty two 43 Write each number represented in numerals and in words. Reasoning Dan has written the number forty four as 40 4. Is he correct? Explain how you know. How much money is there? Write your answer in numerals and words. Prove it. What number is represented in the place value grid? 1s How many different numbers can you make with four counters? Write them in numerals and words. Match the words to the numerals. Fill in the missing digits. Forty four Forty six Sixty four Thirty four True or False? The number fourteen is written as 40 in numerals. 10s Problem Solving 3 4 4 6 Can you find nine numbers in the word search? Year 2/3 Term by Term Objectives All students National Curriculum Statement Fluency Reasoning Fill in the blanks Numbers in words Four hundred and two What number is represented in the place value grid? Problem Solving Numerals 100s 10s 1s Four hundred and sixty two Four hundred and twenty six Six hundred and forty two Two hundred and sixty four Place Value 560 Three hundred and sixty six 132 Read and write numbers up to 1000 in numerals and in words. © Trinity Academy Halifax 2016 [email protected] What number is represented by the Base 10? Write it in numerals and words. 352 children were on time for school this morning. Write this number in words. Five hundred and seventy people went to the school fair. Write this number in numerals. Match the number in words to the number in numerals. Fill in the missing numbers. Using the same number of counters, how many different numbers can you make? Convince me you have found them all. Tim was asked to write the number four hundred and forty. He wrote 400 40. Do you agree with Tim? Explain why. Hannah has written the number five hundred and thirteen as 530. Explain the mistake that Hannah has made. 4 4 4 6 There are 3 cards with a digit on each. Find every 3 digit number that could be made from the cards. Write out the largest, smallest and middle number in words. 3 6 8 Work out the missing word: A number between 450 and 460. Four hundred and ______ six. Repeat this with different clues and numbers. Year 2/3 Term by Term Objectives All students National Curriculum Statement Fluency Use Base 10 or place value counters to make each number and complete each sentence. Place Value Reasoning The number ____ is made up of seven groups of ten and eight ones. © Trinity Academy Halifax 2016 [email protected] The number 89 shows __ in the tens place and __ in the ones place. Work in a pair. Partner A writes down a 2 digit number. Partner B guesses the number. Partner A ticks one of the columns in the table below and Partner B keeps guessing until they guess the correct number. Clue In the number 36 there are __ groups of ten and __ ones. Recognise the place value of each digit in a 2 digit number (tens, ones) Use manipulatives to show and then explain the value of 5 in the following numbers: 35, 56, 75 Problem Solving Use manipulatives to make 2 digit numbers where the ones digit is two less than the tens digit. What is the largest number you can make? What is the smallest number? Sally says ‘My number has 5 tens. The ones digit is less than the tens.’ What could Sally’s number be? Guess 1 Guess 2 Both digits correct Tens digit correct Ones digit correct Neither digit correct You have 0-9 number cards Using each card once, make: -Largest even number -Largest odd number - Smallest odd number -Largest multiple of 5 - Number closest to 50. How many 2 digit numbers can you make using 3 counters and the number grid below? Tens Ones Year 2/3 Term by Term Objectives All students National Curriculum Statement Fluency Reasoning Write the value of each underlined digit. Problem Solving Explain the differences in the values of 4 in the following numbers: Henry thought of a number. He thought of a two-digit number less than 50. The sum of its digits was 12. Their difference was 4. What number did Henry think of? Use the clues to find the missing digits: 318, 92, 921 Place Value H T O 473 Recognise the place value of each digit in a three digit number (hundreds, tens, ones). Find the value of statements. = 500 + 70 + 4 628 = + 20 + 8 703 = 700 + © Trinity Academy Halifax 2016 [email protected] +3 in each of these 894 546 Fill in the place value grid with counters to make 608 543 is made of 5 hundreds, 4 tens and 3 ones. It is also made of 54 tens and 3 ones. It is also made of 543 ones. Can you show 113 in these ways? Can you express 627 in the same way? What is the same about these numbers and what is different? 375 357 The hundreds digit is double the tens digit. The tens digit is 5 less than 2 x 4 The ones digit is 2 less than the hundreds digit. Claire, Libby and Katie are holding three digit numbers. They are shown below. 345 247 368 Claire and Libby give clues: Claire- My number has the smallest amount of ones. Libby- The tens in my number are 2 less than Claire and Katie’s added together. Can you work out which number is which? Year 2/3 Term by Term Objectives All students National Curriculum Statement Fluency Place these numbers on the number line. Reasoning Place 36 on each of the number lines below. Greg has made the number 24 using Base 10. Is he correct? Explain your answer. Problem Solving Match each number line to the clue that describes it. 12, 22, 5, 19 Place Value Use manipulatives to represent the following numbers. 23, 35, 53, 42 Identify, represent and estimate numbers to 100 using different representations including the number line. Place the following numbers on the number line. - 50, 23, 78 True or False? The arrow on the line below is pointing to 70. Convince me. © Trinity Academy Halifax 2016 [email protected] - The number is over half way along the number line. The number is bigger than 50. The number is between 20 and 40. Play a game of snap with cards that match 2 digit numbers with Base 10 blocks. How many different numbers can you make using 4 counters and the place value grid below? Tens Ones Year 2/3 Term by Term Objectives All students National Curriculum Statement Fluency What number is represented in each set? Reasoning Place 725 on each of the number lines below. Place Value 0 Identify, represent and estimate numbers up to 1000 using different representations. 0 Use place value counters or base 10 to represent the following numbers 382, 560, 905 1000 700 800 720 730 Alice says ‘The number in the place value grid is the largest number you can make with 8 counters.’ Do you agree? Prove your answer. 100s 10s Using four counters and the place value grid below, how many different numbers can you make? Eg 211 100s 10s 1s Simon was making a three digit number using place value counters. He has dropped three of his counters on the floor. What could his number be? If the number on the number line is 780, what could the start and end point of the number line be? 1s Show 450 on the number line. 1000 © Trinity Academy Halifax 2016 [email protected] Problem Solving Henry has one counter and a place value grid. He says he can make a one, two, three and four digit number. Is he correct? Show this on a place value grid. Year 2/3 Term by Term Objectives All students National Curriculum Statement Fluency Place Value Compare and order numbers from 0 up to 100; use <, > and = signs. Reasoning Order the numbers from smallest to largest. 23 32 27 30 19 41 Use <, > and = to make these number sentences correct. Order the amounts below from smallest to largest. 2 tens and 5 ones 27 2 groups of 10 and 8 ones Bill has written a list of 2 digit numbers. The digits of each number add up to 5. None of the digits are 0. Can you find all the numbers Bill could have written? Write the numbers in order from smallest to largest. 1 lot of 10 and 19 ones 33 53 37 29 34 43 Fill in the missing numbers in the grid using 1, 2, 4 and 7. 8 Use <, > and = to make these number sentences correct. 5 4 tens + 3 ones____ 3 tens + 13 ones 6 2 tens and 7 ones__ 1 ten and 14 ones 3 9 5 tens and 2 ones __ 4 tens + 15 ones © Trinity Academy Halifax 2016 [email protected] If you ordered the numbers below, which would be fourth? Explain how you ordered them. 4 tens _____ 40 ones 2 tens _____ 9 ones 4 tens _____ 44 ones Problem Solving True or False: One ten and twelve ones is bigger than two tens. Explain how you know. What numbers could go in the box below? 52 < < 56 The number in the grid is even. Which number must it be? Year 2/3 Term by Term Objectives All students National Curriculum Statement Fluency Place Value Compare and order numbers up to 1000 Compare the numbers. Use < > or = Harry puts the following numbers in order. 397 5_3 29_ 287 700 70 tens Which number would be third? 10s 278 345 Using 3 counters, like shown in the place value grid below, make all the numbers possible. Order from smallest to largest. 100s 1 3 In pairs, each child has to make a 3 digit number. They pick a 0-9 number card and decide where to write the number. Do this until they have created a 3 digit number. In each game they change the criteria they have to meet to win. Eg Make the smallest number. Make the largest number. Make a number between 300 and 500. I am thinking of a number. My number is between 300 and 500. The digits add up to 14. The difference between the largest and the smallest digit is 2. What could my number be? Order all the possible numbers from smallest to largest. Deena has ordered 5 numbers. The largest number is 845, the smallest number is 800. The other numbers all have digit totals of 12. What could the other numbers be? 7 5 5 9 0 1 368 3 2 1s Here are three digit cards. Write all the three digit numbers that you can make and order them from smallest to largest. 301 Put one digit in each box to make the list of numbers in order from smallest to largest. 2 Problem Solving 377 4 2 5 © Trinity Academy Halifax 2016 [email protected] Reasoning 5 True or False: You must look at the highest place value column first when ordering any numbers. Year 2/3 Term by Term Objectives All students National Curriculum Statement Fluency Find 10 more and less than the following numbers: 23 65 Place Value 146 192 591 2901 304 1392 1892 Fill in the missing numbers: 10 less Starting 10 number more 325 674 892 1001 © Trinity Academy Halifax 2016 [email protected] Emily has made the number: 3 0 Problem Solving 10 more than my number is 100 less than 320. What is my number? Using number cards 0-9 can you make the answers to the questions below: 5 96 What is 100 more or less than these numbers? 283 Find 10 or 100 more or less than a given number. Reasoning Write down the number that is 10 less than 305. Now write down the number that is 10 less than this new number. 10 less than 8 + 7: 10 more than 3 x 10: 100 less than 336: 100 more than 691: 10 less than 3 x 6: Explain what is happening to the number each time. What comes next? 536-10=526 526-10=516 516-10=506 What is the 10th answer in the pattern? True or False When I add 100 to any number, I only need to change the hundreds digit. I think of a number. I add 10 and then take away 100. My answer is 350. What was my number? Year 2/3 Term by Term Objectives All students National Curriculum Statement Fluency Here is a number line. The number 14 is shown. Reasoning I am less than 25. My ones digit is double my tens digit. My digits add up to an even number. What am I? Tamsin and Lila each use two of the cards to make a 2 digit number. Can you find the chosen number from the grid using the clues below? Place Value Mark the number 7 on the number line. Use place value and number facts to solve problems. Here are some digit cards. 4 1 5 Tamsin says, Jack is making numbers on an abacus. He is using 4 beads to make 2 digit numbers. I have made the largest number you can make. Lila says, I have made the smallest number you can make. Here he has made 14. How many other 2 digit numbers could Jack make using 4 beads on an abacus? © Trinity Academy Halifax 2016 [email protected] Problem Solving The digits add up to 7. The tens digit is odd. The number is smaller than 20 What is the difference between their numbers? Year 2/3 Term by Term Objectives All students Place Value National Curriculum Statement Fluency Here are two number lines. Find the difference between A and B. Can you place the numbers in the diagram below? The balloons cost 40p altogether. What is each balloon worth? Between 16 and 23 Solve number problems and practical problems involving these ideas. © Trinity Academy Halifax 2016 [email protected] Reasoning Not between 16 and 23 Digits add up to an even number Digits add up to an odd number Here is part of a number square. Add together the two numbers that would be in the shaded squares. Problem Solving Sasha is playing a game to win prizes. Each blue counter is worth 4 points. Each green counter is worth 8 points. She wins the following counters. Which of these prizes can Sasha get? 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 Use < > or = to compare the numbers. Jack has 10 more points than Sasha. He uses his points on 2 prizes. Which 2 prizes does he choose? Year 2/3 Term by Term Objectives All students National Curriculum Statement Fluency Reasoning Complete the part whole models. 20 13 Place Value 9 Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts to 100. © Trinity Academy Halifax 2016 [email protected] 16 + Play a game for 2-4 players. Give each player 2 ten frames. Each child takes turns to roll a die and they place that amount of counters on their ten frame. They must then say how many counters they have altogether and how many more counters they need to make 20. Continue until one player has completed their two ten frames. Fill in the so the sum of the numbers on each line is 20 How is this pattern the same and different as this one? 9 = 10 – 1 8 = 10 – 2 7 Complete the missing numbers. Use two ten frames to help you. Continue the pattern. 90 = 100 – 10 80 = 100 – 20 Problem Solving Here is a hundred square. = 20 20 = 15 + 6 20 = 12 Here are ten tens. How many ways can you split them between the two circles to make different number bonds to 100? One has been done for you. 9 Sam colours in the numbers 1 – 30. Tom colours in the numbers 31 – 60. How many squares are not coloured in? Kim says ‘ If I know 9 + 1 = 10, I can work out 90 + ____ = 100’ Find the missing number and explain how Kim knows. 4 Can you complete the boxes so each row and column adds up to 100? 20 50 30 40 Year 2/3 Term by Term Objectives All students National Curriculum Statement Fluency Reasoning Calculate: True or False? Problem Solving Take 3 consecutive numbers that are neighbours when you count. Eg 4, 5, 6. Add them together, what do you notice? Choose 3 more neighbour numbers up to 10. See if there is a pattern as you add them. Lily has 3 dogs. When you add two odd numbers together you always get an even number. + Convince me. Place Value Add and subtract numbers using concrete objects, pictorial representations, and mentally, including: a 2 digit number and ones; a 2 digit number and tens; two 2 digit numbers; adding three 1 digit numbers. Owen has 45 football cards, he gives 20 to his friend Jack. How many does he have left? Use the bar model to help you. 2 + 5 = 87 How many ways can you do it? Show me. 45 20 ? Work out the total of each row and column. 5 3 5 © Trinity Academy Halifax 2016 [email protected] What digits could go in the boxes? 4 7 7 2 8 3 Sam says I am thinking of a two digit number, if I add ones to it, I will only need to change the ones digit. Explain how Kim knows. A B C Dog A and B weigh 7kg. Dog B and C weigh 8kg. Dog A and C weigh 11kg. What does each dog weigh? Take five coins: 1p, 2p, 5p, 10p, 20p. Put them in a row using these clues. The total of the first three coins is 27p. Year 2/3 Term by Term Objectives All Students National Curriculum Statement Fluency Addition and Subtraction Calculate: 153 + 6 153 + 60 153 + 600 Are these number sentences true or false? 396 + 6 = 412 504 – 70 = 444 556 + 150 = 706 Justify your answers. Calculate: 356 – 9 356 – 90 356 – 200 Add and subtract numbers mentally, including: a threedigit number and ones; a threedigit number and tens; a three digit number and hundreds. © Trinity Academy Halifax 2016 [email protected] Fill in the missing numbers Start Add 5 Reasoning Add 50 Add 500 Always, Sometimes, Never When you add 7 to a number ending in 8 your answer ends with 5. Explain your answer. Problem Solving Always, Sometimes, Never - 2 odd numbers add up to make an even number. - 3 odd numbers add up to make an even number. - Adding 8 to a number ending in 2 makes a multiple of 10. Three pandas ate 25 bamboo sticks. Each of them ate a different odd number of bamboo sticks. How many bamboo sticks did they each eat? Find as many ways as you can to do it. A magician is performing a card trick. He has eight cards with the digits 1-8 on them. He chooses four cards and the numbers on them add up to 20. How many different combinations could he have chosen? Which questions are easy, which are hard? 342 322 246 Complete the bar models 453 + 10 = 493 + 10 = 930 – 100 = 910 – 120 = How many different ways can you complete the part whole model? 70 Year 2/3 Term by Term Objectives All Students National Curriculum Fluency Statement Addition and Subtraction Use the grid to solve the calculation below. 355 +426 Reasoning Find the missing numbers in the addition. 6 2 © Trinity Academy Halifax 2016 [email protected] Write down three numbers that add up to make 247. __+__+__= 247 Write down a different set of numbers that add up to 247. Harry has 357 stickers, John has 263. How many do they have altogether? If Harry gives John 83 stickers, how many do they have each now? The answer to the addition is 201. All the digits used are either 1 or 9. Fill in the boxes. 4 + 2 Add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction. Problem Solving Dan saved £342 in his bank account. He spent £282. Does the subtraction below show how much he has left? Explain your answer. 282 -342 140 Find the errors in the calculations and correct them to find the right answer. Calculation Error Correct solution 256 + 347 2907 63 - 38 35 201 = + + Can this be done more than one way? Convince me. Roll a 1-6 die, fill in each of the boxes and try to make the smallest total possible. Repeat and try to find different answers. Could you have placed the digits in a different place to make a lower total? + Molly went swimming every day for 5 days. She swam 80 lengths during the 5 days. Each day she swam 4 less lengths than the day before, how many lengths did she swim each day? Year 2/3 Term by Term Objectives All Students National Curriculum Addition and Subtraction Statement Solve problems with addition and subtraction: using concrete objects and pictorial representations, including those involving numbers, quantities and measures; applying their increasing knowledge of mental and written methods. © Trinity Academy Halifax 2016 [email protected] Fluency There are 32 children in Class 2. 17 are girls. How many are boys? On Monday, Jack swims 12 lengths. On Tuesday he swims 13 lengths. How many does he swim altogether? Reasoning Sam and Zoe are working out some subtractions. After Wednesday, Jack has swum 40 lengths in the week. How many lengths did he swim on Wednesday? The length of the school hall is 21 metres. Tilly runs from one end to the other and then back again. How far has she run? Problem Solving Aron has some balloons. Fiona has 12 more balloons than Aron. In total they have 40 balloons. How many balloons has Fiona got? Yasmin has 3 jars of bugs. Sam’s answer is double Zoe’s answer. What could Zoe’s question be? Always, sometimes, never. odd number + odd number + odd number = even number Use number cards to make numbers to test out if this statement is true. There are 7 more bugs in the first jar than the second. There are 3 less bugs in the third jar than the second. There are 40 bugs in total. How many bugs are in the first jar?? Year 2/3 Term by Term Objectives All Students National Curriculum Statement Fluency Addition and Subtraction Rich and Georgia have the same number of stickers. Reasoning If Problem Solving In the pyramids, the two numbers below add to make the number above. Complete these two pyramids. Rich gives 15 stickers away. Georgia gives 32 stickers away. How many more stickers does Rich have than Georgia? Solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction. Work out: Choose either < > or = to complete the number sentences. Lucy has some balloons. Andy has 12 more balloons than Lucy. In total they have 40 balloons. How many balloons has Lucy got? What is the value of the blue box? Put the numbers 6, 7, 8, 9, 10 and 11 into the boxes. You can only use each one once. How did you get your answer? © Trinity Academy Halifax 2016 [email protected] Year 2/3 Term by Term Objectives All Students National Curriculum Statement Fluency Addition and Subtraction Complete the number sentences. Reasoning True or False? These four calculations have the same answer. 1+4+2 2+4+1 4+2+1 4+1+2 Problem Solving Use the number cards below to make as many addition and subtraction sentences as you can. How many can you make? 3 Explain your answer. Show that the addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot. Use = < or > to complete the number sentences. 64 + 13 13 + 64 23 – 12 12 – 23 Here is a fact family. 12 + 5 = 17 5 + 12 = 17 17 – 5 = 12 17 – 12 = 5 Use these numbers to create your own fact family. 11 © Trinity Academy Halifax 2016 [email protected] 27 16 True or False? These four calculations have the same answer. 7–3–2 2- 3- 7 3–2–7 7–2–3 Write the missing symbols + - and = in the number sentence. Can you complete it in two different ways? 40 23 17 40 23 17 10 4 What could the values of the circle and triangle be? 12 Use cubes to help to explain your answer. 7 + = - = 12 How many number sentences can you write to describe the part whole model? 50 27 23 Year 2/3 Term by Term Objectives All Students National Curriculum Addition and Subtraction Statement Fluency If I know 34 + 20 = 54, what other addition and subtraction sentences can I write? How many number sentences can you write to describe the ten frames? Reasoning Write a number sentence to find the value of the ? in each of the bar models. Problem Solving 36 In the pyramids the two numbers below add to the make the number above. Complete these two pyramids. ? 25 36 11 ? Recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems. ? Make a number on a ten frame using two different coloured counters. Challenge a friend to write number sentences to describe your ten frames. What do you notice? Dan calculates 67 + 8 = 75 Use a subtraction to check his answer. 25 11 What is the value of the blue box? What is the greatest whole number that can fill the box? How did you get your answer? © Trinity Academy Halifax 2016 [email protected] I think of a number. I take away 7 and add 2. My answer is 15. What is my number? Year 2/3 Term by Term Objectives All Students National Curriculum Statement Fluency Addition and Subtraction Estimate the answer to a calculation and use inverse operations to check answers. © Trinity Academy Halifax 2016 [email protected] Make an estimate: Which of the following number sentences have an answer between 50 and 60? 274 - 219 533 – 476 132 - 71 34 + 45 = 79 Use a subtraction to check the answer to the addition. Reasoning Niamh estimates the answer to 489 + 109 as shown: Problem Solving 489 + 109 ≈ 500 Do you agree with Niamh? Explain your answer. Leonie says: ‘ 353- 26 = 333 because 300 – 0 = 300, 50 – 20= 30, 6 – 3= 3 so 353-26 Hannah has baked 45 cakes for a bun = 333’ sale. She sells 18 cakes. How many does she have left? Double check Do you agree with her answer? your answer by using an addition. Prove your answer by using an addition calculation. Sam has used the bar model to find 113 + 134 = 247 Can you write a subtraction to check his answer? Colin says ‘If I add two numbers together I can check my answer by taking them away afterwards. So to check 3 + 4, I can do 4 -3.’ Is he right? Explain Colin’s thinking. Is it magic? Think of a number. Multiply it by 5. Double it. Add 2. Subtract 2. Halve it. Divide it by 5. Have you got back to your original number? Is this magic? Can you work out what has happened? Using the idea above (Is it magic?). Create your own set of instructions where you think of a number and end up back at the original number. I think of a number. I divide by 2 and add 98. My answer is 100. What was my number? Year 2/3 Term by Term Objectives All students National Curriculum Statement Fluency Addition and Subtraction Here is a table of money that three people have in pounds and pence. Can you fill in the blank boxes? Name £ p Total Phil 4 £4.65 Sue 3 95 Gary 115 £6.15 Jackson went to the shop to buy milk and bread. 49p Recognise and use symbols of pounds (£) and pence (p); combine amounts to make a particular value. © Trinity Academy Halifax 2016 [email protected] Reasoning Anna has 3 silver coins in her hand. Larry says, “I have more than you because I have a £1 coin.” Is he correct? Explain why. Problem Solving Jamie has 5 silver coins in his hand. How many different ways can he make £1 or more? Patrick visits an arcade. He has £5. He wants to go on at least 4 games. Always, sometimes, never. You can make £1 using an odd number of coins. Convince me! Game Whack-a-rat Donkey Derby Bingo Grab-a-prize Dance mania Deal or no deal True or false 5 copper coins can be worth more than 1 silver coin. 90p Which games can he go on? Will he have any change? Can you find more than one combination of games? How much money does he need to pay without receiving any change? Tara has 2 ten pence coins, a five pence coin and a fifty pence coin. How much money does she have altogether? Tim has 5 coins in his wallet. The total amount is £1. Which coins could he have? Price 70p 90p £1 50p 85p £1.25 How many ways can you make £1 using an unlimited amount of coins? Year 2/3 Term by Term Objectives All students National Curriculum Statement Fluency Addition and Subtraction Make 50p three ways using the coins below. You can use the coins more than once. Reasoning Charlie tells her friend Sam she has only silver coins in her hand. She says she has 43p. Sam thinks that’s impossible. Do you agree with Sam? Explain why. True or false: 4 five pence coins are worth more than 2 ten pence coins. Explain why. Find different combinations of coins that equal the same amounts of money. I have £1.45. Can you find or draw the coins I could have to make this? Paul has £2 and Tony has £1.20. Which coins could Tony add to his pile to make his and Paul’s amounts equal? Emily finds a 20p coin and thinks she now has enough for a ride on the ghost train. She puts it with her other three 20p coins. The ghost train costs £1. Is she correct? Explain why. Problem Solving Hanna and Ste both claim to have 90p. Hanna has 3 coins and Ste has 4 coins. Are they correct? Which coins could they have? Emily has £3.40 and Katie has £2.20. How much does Emily need to give Katie so they have the same amount? Here is a price list. Jay has £2.20 What can he buy? Item Chicken sandwich Ham sandwich Turkey sandwich Salad Jacket potato Panini Soup Sauce Can of pop Bun Chocolate bar Price £1 £1.50 £1.20 30p £1 £1.30 £1.60 10p 60p 60p 50p Can you find a different set of items he can buy? © Trinity Academy Halifax 2016 [email protected] Year 2/3 Term by Term Objectives All students Addition and Subtraction National Curriculum Statement Fluency Benji spends £1.35 in the shop and pays with a £2 coin. How much change will he receive? True or false: you can make 51p using just 2 pence coins. Write an explanation with your answer. Arun buys an ice lolly from the ice cream van. It costs 90p. He pays in 10 pence coins. How many 10 pence coins does he use? Alex has 90p. He bought a rubber for 30p and wants to buy a pencil. Solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change. © Trinity Academy Halifax 2016 [email protected] Reasoning 70p – 50p = 5p + Odd one out. Look at the coins below. Which one is the odd one out and why? 2p 3p 5p 7p Frankie bought candyfloss at a fayre. She paid with 6 coins. How much could the candyfloss have been? Which answer do you think is the most reasonable? Colin has 5 coins in his pocket. How much money might he have? The shopkeeper will not sell him the pencil. Can you explain why to Alex? Marie went to the shop and spent 20p. She bought at least one of each sweet. Which item did she buy two of? Munchy Sweetie Choccy bar Spotty eggs 70p Fill in the missing box: + 40p = £1 – 30p Problem Solving Year 2/3 Term by Term Objectives All students Addition and Subtraction National Curriculum Statement Fluency Reasoning What is 2 pounds and fifty pence less than 9 pound? Mary buys these two items. These items are sold in a shop. Problem Solving Mo is saving for a book. 16p 19p Add and subtract amounts of money to give change, using both £ and p in practical contexts. Ray buys three items. Two of them are the same item. He spends £23 What items does Ray buy? How do you know? 16p She pays with a 50p coin and is given a 10p and 5p coin as change. Has she been given the correct change? Complete the part whole diagram. 126p His mum gives him a quarter of the money. How much more does he need to save? Mike buys these items and it costs him 30 pence. Which is worth more? 90 ten pence coins or 9 pound coins. Explain why. Olga buys these items and it costs her 42 pence. 68p How much does a ruler cost? © Trinity Academy Halifax 2016 [email protected] Year 2/3 Term by Term Objectives All students National Curriculum Statement Fluency Addition and Subtraction How long is the pencil? If I have 3m of ribbon and cut it into 50cm lengths, how many lengths can I cut? Convince me. Abigail’s ruler has broken. How could she still use it to measure things? Find the length from A – B, find the length from B-C. Which is longer? How much longer? Problem Solving A coach is three times as long as a car. A train is 6.5m longer than a coach. The train is 36.5m long. How long is the car? (It may help you to use bar modelling) Which of the following statements could be true? A Measure, compare, add and subtract: lengths (m/cm/mm). © Trinity Academy Halifax 2016 [email protected] Reasoning - B Harry is measuring the length of this pencil. Explain what he is doing wrong. Check them and correct the false ones by using measuring equipment. Can you create some for a friend? Insert <, > or = below. 13cm 140mm 1m 90cm 1m – 10mm Half a metre A chair is about 120mm tall. A ruler is about 300mm long. The length of a swimming pool is 50m. Miss Jones swims 2000m every morning. How many lengths is this? Year 2/3 Term by Term Objectives All students Multiplication and Division National Curriculum Statement Recall and use multiplication and division facts for the 2, 5 and 10 times tables, including recognising odd and even numbers. © Trinity Academy Halifax 2016 [email protected] Fluency Use towers of cubes to calculate: 4 x 5= 20 ÷ 2 = 6 x 10= 25 ÷ 5 = A flower has 5 petals. How many petals do 5 flowers have? Circle the odd numbers. 12 13 17 18 21 Look at Numicon up to 10 Which numbers are odd? Which are even? What’s the same about the even numbers? What’s the same about the odd numbers? Reasoning Which has more? 4 bags of sweets with 5 in each or 3 bags of sweets with 10 in each? Explain your reasoning. 20 = x What numbers could go in the boxes? Prove it. I have 35p in my pocket in 5p coins. How many coins do I have? Draw a picture to prove your answer. Problem Solving Tubes of bubbles come in packs of 2 and 5. Holly has 22 tubes of bubbles. How many of each pack could she have? How many ways can you do it? Sally and Katie want to share sweets out equally between them. They can buy bags of 17, 18 or 21 sweets. Which bag should they buy? What other packs of sweets could they buy? Fran and Lily had a tub of lollies. When they shared them between them they had one left over. Just as they had finished sorting, three of their friends came and wanted some lollies so they shared the same lollies again. This time they had 2 left over. How many lollies might have been in the tub? Year 2/3 Term by Term Objectives All students National Curriculum Statement Fluency Multiplication and Division How many altogether? Reasoning Tom says ‘I can use my 4 times table to help me work out my 8 times table’. Is he correct? Convince me. What pair of numbers could be written in the boxes? × Recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables. © Trinity Academy Halifax 2016 [email protected] Use cubes to show me 8 groups of 4 Tell me what division and multiplication facts you can find from this. True or false? Put these statements into two piles. Explain why. Start this rhythm, clap, clap, click, clap, clap, click. Carry on the rhythm, what will you be doing on the 15th beat? How do you know? What will you be doing on the 20th beat? Explain and prove your answer. Megan has a box of pop that are in packs. Some packs have 4 cans in them, some packs have 8 cans in them. The box contains 64 cans of pop. How many packs of 4 cans and how many packs of 8 cans could there be? Have you found all the possibilities? = 24 3 × 4 = 0 + 12 5×8>6×8 28 ÷ 4 = 2 × 4 Complete the bar models. Problem Solving Can you sort the cards below so that they would follow round in a loop? The number at the top is the answer, then follow the instruction at the bottom to get the next answer. 1 8 2 1 1 5 8 -5 5 1 0 2 0 × 1 4 4 × 1 2 3 7 × × Year 2/3 Term by Term Objectives All students Multiplication and Division National Curriculum Statement Fluency 5 x 3= 15 Write a division sentence using the same numbers. Write these addition sentences as multiplication sentences. Reasoning Calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (x), division (÷) and equals (=) sign. © Trinity Academy Halifax 2016 [email protected] 5 + 5 + 5+ 5= 5 x 4 2+2+2= 10 + 10 = Can you write 4 number sentences to describe the array? Fill in the missing boxes 12 ÷ 12 ÷ 3x 4x =4 =3 = 12 = 12 Use the number cards to make multiplication and division sentences. How many numbers up to 20 can you make? 1 One has been done for you. Problem Solving 2 3 4 5 Each purple block is 8cm long. Each green block is 6cm long. eg 1 x 1 = 1 Use the picture below to think of multiplication and division sentences using x , ÷ and = How long is a blue block? Write a multiplication and division sentence for each step of working out you do. Year 2/3 Term by Term Objectives All Students National Curriculum Statement Fluency Multiplication and Division Reasoning Use place value counters to multiply a two digit number and one digit number together. Always, sometimes, never A two digit number multiplied by a one digit number makes a two digit answer. Fill in the missing boxes. Problem Solving Using the digit cards in the multiplication below how close can you get to 100? 2 3 4 10 5 40 × 23 x 4= Write and calculate mathematical statements for multiplication and division using the multiplication tables they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods. © Trinity Academy Halifax 2016 [email protected] = Explain your answer. Set up a grid with 4 rows as we are finding 4 lots of 23. Make 23 in each row using the place value counters. Add up each column, starting with the ones to find out your answer. Hassan is calculating 32 x 5. He writes his answer 15010. Can you work out Hassan’s mistake and write an explanation of how he could do it correctly? Fill in the missing digits in the multiplication below: 2 3×5= Complete this statement and use this to solve the multiplication below: 3 × 50 = 30 × 5 = 5×3 = 3 × 4 1 Solve: + 0 Year 2/3 Term by Term Objectives All Students National Curriculum Statement Fluency Multiplication and Division Write multiplication sentences for the bars below. What do you notice? 4 5 Show that the multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot. © Trinity Academy Halifax 2016 [email protected] Reasoning 4 4 5 4 5 4 5 Fill in the gaps: X 3 = 15 3 x = 15 Here are some number cards. Use them to fill in each number sentence below. 2 10 Circle the incorrect number sentence. Explain your reasons. 4 x 5 = 20 5 x 4 = 20 20 ÷ 5 = 4 5 ÷ 20 = 4 20 __ x __ = __ __ = __ x __ __ ÷ __ = __ __= __ ÷ __ True or False? 2x5=5x2 2 x 5 = 10 x 1 2 x 5 = 1 x 10 What do you notice? The rectangle is made of 2 rows of 4 and 4 columns of 2. Can you write 2 multiplication sentences to show this? What do you notice about the numbers? Problem Solving Use the number cards to make multiplication and division sentences. How many can you make? 20 2 10 5 4 Cassie has 4 bags with 5 sweets in each. Rachel has 5 bags with 4 sweets in each. How many do they have each? Can you split the sweets into different numbers of bags so they both still have the same number Year 2/3 Term by Term Objectives All Students National Curriculum Statement Fluency Multiplication and Division Use the pictures to fill in the missing numbers. groups of Solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods and multiplication and division facts, including problems in contexts. © Trinity Academy Halifax 2016 [email protected] Reasoning Compare the number sentences using < > or = 3+3+3+4 3x4+4 5x4+2+2 5+5+5+5+2+2 = + + = 12 Addition sentence: + = 12 Multiplication sentence: = = I have five 10p coins, exactly enough to buy a chocolate bar. Here are some apples. Class 2 are asked work out the total. Here are four different ways they do it. Fill in the missing blanks. ….. + ….. = 10 ….. + ….. + ….. + ….. + ….. = 10 …… × …… = 10 …… × …… = 10 I need 1 more 10p to buy bottle of pop. How much is a bottle of pop? Problem Solving If + Erik bakes 5 trays of muffins. Each tray contains 6 muffins. + + + + =4 = 30 + = 20 Complete the addition He sells 16 muffins and eats 5 How many muffins does he have left? + + = Year 2/3 Term by Term Objectives National Curriculum Statement Fluency Fill in the boxes: 5x Multiplication and Division All students Reasoning 12 buns are shared between 3 boys. 16 buns are shared between 4 girls. Who gets more buns, boys or girls? Explain your answer. For every 3 boys in class there are 2 girls. Which of the combinations of boys and girls could be correct? = 15 Problem Solving Use the numbers 1 - 8 to fill the circles below: Lottie is counting the number of legs in her house. People and cats live in Lottie’s house. People have 2 legs, cats have 4 legs. If there are 26 legs altogether, how many cats and people might there be? William has 3 t-shirts and 4 pairs of trousers, how many different outfits can he make? X 4 = 32 48 Solve problems including missing number problems involving multiplication and division, positive integer scaling problems and correspondence problems in which n objects are connected to m objectives. © Trinity Academy Halifax 2016 [email protected] =8 Jemima has a toy car measuring 8cm. Aisha has a toy train that is 8 times as long as the car. How long is the train? 18 boys and 12 girls 15 boys and 10 girls 21 boys and 9 girls 12 boys and 8 girls Kainat is making buns. For every 40g of flour she needs 1 egg. Show your thinking using a picture. If she uses 5 eggs, how many grams of flour does she use? If she uses 400g of flour, how many eggs does she need? 4kg of cereal costs £4.80. How much does 6kg cost? How many kg of cereal can I get for £8.40 How many different combinations of numbers can you find that would fit in the empty boxes? 5x = 10 x True or false, explain why. For every 50g of flour, 40g of sugar is needed. Kay says ‘if I use 125g of flour then I need 100g of sugar’
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