P3, P4 and P5 Workshop for Parents Mental Maths and Problem-Solving October 2018

Aims of the workshop To gain an insight into what we mean by Mental Maths and Problem-Solving To provide you with some ideas to support your child at home. Good evening everyone, I am Rachel Thompson and I am the Numeracy Coordinator here is St Mary’s on the Hill. I would like to welcome you all to an informal information session in which Mr Conway and I hope that we will help you gain an insight into what the children are doing in school when they say they have been doing mental maths and /or problem-solving. We also want to give you some tips and ideas about what you can do at home.

Before we start … https://www.youtube.com/watch?v=3icoSeGqQtY Before we start I want to show you a little clip that is really important about how we feel about getting things wrong as adults and for the children as well. Mr Conway and I have already heard a few people say oh I hope I don’t get asked anything or I don’t want to have a go in case I get it wrong. This clip is from a talk by Jo Boiler who is one of the leading figures in maths education and it is just for you to see the importance of making mistakes. STOP AT SO 12.56

Why do Mental Maths? Essential part of managing everyday events e.g. planning what to watch on TV, cooking, shopping Ability to calculate in your head Rapid recall of number facts Use a range of different strategies Solve calculations, with the most efficient strategy, quickly and accurately Mental maths can be described as the the rapid recall of number facts, for example, knowing your times tables off by heart or knowing, without having to work it out, that 4 and 6 will make 10. It is a vital skill that once learnt, your children will be able to use for the rest of their lives in recipes for quantities or in the shops for change. The aim of mental maths is to help children feel equipped for their maths work.  

Number Sense Number sense is children’s “fluidity and flexibility with numbers” (Gersten & Chard, 2001). A sense of what numbers mean, understanding their relationship to one another, able to perform mental math, understands symbolic representations and can use those numbers in real world situations.  Number sense is the children’s ability to play with numbers and it is what we would like to develop in all the children Read slide CC talk about tests

P3, P4 & P5 children should… Learn that there are many ways of getting an answer Have opportunities to explore and share different strategies Realise some strategies are more efficient than others Share thinking to consolidate understanding Reflect on and explain calculations To develop number sense we focus on metal maths. Our mental maths sessions should help the children develop a range of different strategies. Its about being equipped with a number of different ways of working out the answer- getting the answer is great but knowing a different way of doing it is even better. The focus is on the strategy rather than on the answer.

Teaching Mental Maths Short 10 min sessions at the start of each maths lesson Variety of activities Develop the use of mathematical language Gives pace to the lesson Encourages fun

Mental Maths Strategies Counting On & Counting Back Re-Ordering Rounding and Adjusting Partitioning Inverse Operations There are a number of different strategies developed in Mental Maths throughout the school. In P3, P4 and P5 we mostly focus on READ SLIDE What we plan to do is go through each strategy and have a go at them … remember the video clip from the beginning!

Let’s have a go! Count on and back; https://www.topmarks.co.uk/learning-to-count/helicopter-rescue So here is an example of an online game of counting on and counting back. You can see you can pick the range and we will have a go at this one. Just shout out the answer. Mr Conway is going to do a clapping rhythm with you. This helps consolidate the tables. In P3 the children are introduced to the 2, 5 and 10 x tables. In P4 the children work on developing a rapid recall of the 2, 5, 10 , 3 and 4 x tables. In P5 the children are expected to know all the tables.

Counting on Counting back Give the next two numbers in each sequence. Here are a few other ways the children practice counting on and back. You need to id the rule – does it go up / down - in what steps - develop mathematical language such as counting in multiples of 2 Just shout out the answer Year 4

2 4 6 8 10 12

Re-ordering This is when we rearrange the order of the numbers in a calculation to make it easier to do. USE WHITE BOARDS

Re - Ordering Give the total of each strip of numbers. Year 3 Write your answer and turn it around to show me. Year 3

32 4 2 6 20 What ways did you reorder your number? I started with the biggest number 20 I then made a pair to 10 - 4 + 6 Then I added on the 2 20 + 10 + 2 = 32 Anyone do this another way?

5 6 5 39 55 Write down your answer on the whiteboard then 3 2 1 show me What was your strategy? I started with 39 I doubled 5 to get 10 39 + 10 = 49 I split / partitioned the 6 into 5 and 1 49 + 1 = 50 and then 50 + 5 = 55

Rounding and Adjusting The rounding rap: 1, 2, 3, 4 round down to the 10 before 5, 6, 7, 8, 9 up to the next 10 on the line. Your going to need your number fans for this one. Rounding is a great skill to develop when out shopping. My class use this rhyme to help them. Let’s try a few rounding to the nearest 10 -- 20 36 - - 40 99 - - 100 11 - - 10

Rounding and Adjusting 38 + 15 round 38 to 40 to make 40 + 15 = 55 Subtract 2 55 – 2 = 53 Or 40 + 13 = 53 We can use rounding to work out calculations We need to adjust by subtracting or adding the amount we changed when rounding the first number The key to this is talking about your strategy.

Partitioning Partitioning is when we split a number up to understand and see it value – H T U or to make calculations easier.

Partitioning This is when children use their knowledge of their number bonds to help them make calculations easier. It shows their number sense. They work by thinking how to get to the next 10 and splitting up / partitioning the number they are working with to do this. e.g. They use their knowledge of number bonds to 7. They know 7 is made up of 2 + 5. By splitting the number 7 into 2 and 5 they can add 2 to 8 to make 10 and then add 5 to make 15.

Inverse Operation This is an important strategy It simply means using the opposite calculation + becomes - x becomes divide It highlights the connection between the operations It is a simple way of checking numbers e.g. 6 + 4 = 10 10 – 4 = 6 It is a good strategy to use when working out missing numbers

Find the missing number in each In or Out Find the missing number in each function machine. T Year 3

24 + 4 28 IN OUT What is the inverse operation? So we work backwords 28 – 4 = 24

76 IN - 6 OUT 70 Again, using the inverse, we are adding 6 to get the starting point of 76

Problem-solving

Problem-solving Children should be solving problems, as the point of learning maths is to be able to solve problems. Learning those rules and facts is important, they are the tools with which we learn to do maths fluently. Now turning to problem-solving Children asked what is maths – calculations Mathematicians see maths as problem-solving for a purpose e.g. calculating orbits for space programmes. READ SLIDE It is similar to the way that learning the scales is an important part of learning to play music fluently but there’s more to music than playing scales.

What are the strategies? One strategy that we have introduced is Bar Modelling to solve word problems. Bar modelling is a visual representation of a word problem. A word problem is when the children have to figure out what calculation they need to do and then apply this skill. Children learn by using concrete materials - such as cubes – then move on to drawing a pictorial representation before moving to the abstract concept of numbers and symbols. Bar modelling is drawing out the info .

Bar modelling https://vimeo.com/83488437 This is a short video of children using a bar model to solve a word problem. Start at 2.08 and finish 4.12

Bar Modelling Talk through the steps on WHITE BOARD.

Question to try Ben spent 2/5 of his money on a CD. The CD cost £10. How much money did he have at first?

Bar model

What are the other strategies? Look for patterns 2. Draw a picture 3. Act it out Make an organised list 5. Make the problem simpler Make a table 7. Work backwards Predict and check 9. Use trial and improvement 10. Make a general statement

Draw a picture The Draw a Picture Strategy is a problem-solving technique in which the children make a visual representation of the problem.

Please turn to the back of your handout. Draw a picture Please turn to the back of your handout.

Make an organised list / table This will help you to: display information in a particular order Organise a lot of information Examine patterns Compile possible combinations

Make the Problem Simpler It can be a useful strategy to begin by solving a simpler problem of the same type. Once a method for solving this type of problem has been established, a solution for the more difficult example can be worked out. One way of applying this strategy is to replace larger numbers in the problem with smaller numbers, so that the calculations are easier.

Tom and Anne found 527 bugs on Wednesday Tom and Anne found 527 bugs on Wednesday. On Thursday, they discovered 374 bugs. How many more bugs did they find on Wednesday than Thursday? Difficulty with the numbers or the vocabulary Look at a simpler problem. Simplify things by changing the numbers from 527 and 374 to simply 5 and 3. See that 5 is 2 more than 3 on a number line Use subtraction

https://www.youtube.com/watch?v=6dvQ91PelHs

Ways to help at home Be positive and celebrate the maths your child can do Maths is not always about being right or wrong – can your child explain the strategy they used to get their answers Don’t panic if your child has a different way of working out from you You don’t have to know all the answers Stop when your child begins to lose interest Remember the video clip from the beginning – mistakes make the brain grow!

Ways to help at home Encourage your child to have a go – remember making mistakes will help them to improve List of websites & link to ‘Let’s Count on Numeracy’

Important Remember to ask your child to explain how he or she worked out the answer. Expect good results aim high!!!