What is it that we need for teaching Stage 5 division? Bk6 Pg2 A focus needs to be on asking questions in different ways. This makes asking the task 'richer'. Rate problems, comparison problems, (not just thinking of groups) Multiplicative thinking. (Bk 6 Pg5) All of these types of questions can be modeled, simplified and taught at Stage 5. I know this is a weakness of mine. I currently have been focusing on 'Equal Groups' & 'Rectangular Area'. Cartesian Product - Looking at a probability tree. How many different products? 3 t-shirt colours & 3 shorts colours. Are there enough combinations for 10 people to all wear something different? Division When we know how many groups - use 'Shared' into. 12 kids shared in 6 cars. How many kids in each car? When you know how many groups they are it is related to fractions. EQUIPMENT - plates & beans/counters 12 kids going to the museum in groups of 6. How many cars do we need? 12-6-6 (until you get to 0) When you know how many in a group they are it is related to subtraction. This one is suited for a number line. EQUIPMENT - number lines & pegs Students need to use both ways. Both these equations are written the same way. IT IS THE WORD PROBLEM which tells us what type of problem it is. Goal Spend time teaching each type independently - with word stories. Then progress to mixing them & students to work out what type of question it is. When teaching division - it HAS to be a word story so it can be modeled & taught the same way. Teacher Modeling - DivisionFast maths - Slow maths - Really slow maths Fast maths Animal strips - groups of? 4 How many groups? 5 How many 5s can I put over? If we do it in a line? Do we still have the same number of animals? What can we say about this? 4x5= 20 = 5x4 Here are 2 questions. There are 2 more questions here. If we have 20 animals shared into groups of 5? 20 animals shared into groups of 4? Model of family of facts. This lesson is solely a lesson for teaching the knowledge of family of facts. Give each student 2 different types of animal strips. Now can you make a family of fact to show this? This is more powerful than teaching 'swap the numbers' around. What do you have here? 4 lots of 6=24 What's underneath? 6 lots of 4=24 If they have 24 on top - what are they sharing them into? Groups of 6. Spend a few days getting the students to reinforce this learning.
Slow Maths Building a new super gym for kids. 18 kids. There are 3 kids on each swing. How many swings do we need at the super gym. (This is suited for number line & pegs. Rather than asking 18 kids & 3 swings which involves sharing) Use a number line & pegs to 'peg out the problem' Quick scan of group - start with group that has the least/lowest understanding. Support - where would you start? 18 Then what would you do next? 1 group said they just use their eyes - do you agree? Students read each number - 2, 4, 7, 11 Is this right? How many need to be each swing? 3? Division is about the same sized groups. This group started at 3 and skip counted. How many lots of 3s? 3x?=18 These guys started with 18 and then took away 3, then skip counted backwards in 3s until they got to 0. Today we are going to practise subtracting. Ask each student what their next step is. What about if we had 24 but with 8 on each swing? What about 47 kids and 9 on each swing? How many swings? How many kids miss out?
Teach take 10 and then put 1 back. so 47, 37 (38), 28 (29), etc. Teach the kids to put their hand between the pegs to count the number of groups (swings) - This prevents them counting the pegs which represents the 0 point as well. These students a reliant on the number line & pegs to then transfer this onto their own number line. Repeat this a few more times for independent. To round up the lesson - summarise what we have learnt. How would we do a question like 34÷groups of 4? = Use repeated subtraction to solve any division question.
Bar Model is a way of thinking that describes a way of modeling out a problem so you can see what maths is needed.
Look for the information to make a model.
Basic Facts/Knowledge=tools / Bar Model/Strategies= House
Our job is to teach the children to pick the right tool to solve the problem. This is done through APPLICATION. There are lots of games & resources in our Dinah Folder:
When selecting games to teach/practise it is PARAMOUNT that it is taught at the right stage.
Below is the linear plan for teaching Stage 5 Division:
Below is the shared bubble map of the same plan:
My key learning - the importance of solving division problems using a word problem/context as this affects the strategies for solving. Teach through their mistakes - don't just tell & kids copy. Show a little, then kids have a go, observe mistakes & teach. Let the kids fall in the pit! Don't teach 'me', teach 'us' - community of learners. Scaffold learning - help them help themselves. Algebra Anything to do with = (balance/not answer) E.G. 14=9+5=16-2 or 9+5=16-2 8+5+?=18-2 Don't put a word story with algebra learning. That will just add confusion. Common error 8+5=13 +6 Students need to learn that equal just means it is balanced on BOTH sides. Making our learning visible Focus on Algebra - what does = mean, any number of numbers & symbols can go on either side. Make algebra patterns richer by setting a challenge - E.G. make the 12th item in the sequence a square. You get more out of a lesson when the teacher gives less. If the teacher shows how to do it. The children will just copy. Celebrate the different strategies and help each child to progress at their level. When it comes to algebra - make sure we don't just focus on 'patterns'
My classes have started already this year. I am finding we are speaking a lot more than last year - which is what I need.
In class I am teaching te reo for:
For my own development I am increasing my kupu hou using Memrise (see below). I have now completed 2 levels and I am currently in 2nd place!
Today we had a successful lesson on how we can solve multiplication problems using repeated addition and skip counting using animal strips.
They found it challenging as they were unable to count on through tens. This will be our next warm up 'Hot Spot'. I will use tens frames "how many more make 10?" Once I have modeled it, they can practise independently at their own pace.
I thoroughly enjoyed collaborating with Joy to plan this week. The focus of the week was all about relating to others and working as a team. For many students these activities were a first. It was great to see the students working with a variety of other students.
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