1. Starter – 5 minute maths (ARW)
Every day 5 minutes (after lunch register maybe) pupils complete a ladder.
Can be made more complex and easier as needed, we could put up a 3 differentiated ladders.

2. Whole School Approach to Word Problems.
Singapore Bar Models
Whole School Approach to Word Problems.

3. Singapore 3 Part Approach
Number sense is the overall understanding of a number. Mental math helps to develop this.
Place Value is a student’s understanding of a digit’s position in a number.
Model Drawing is a visual method of turning a word problem into a diagram with unit bars that represent values.

4.  In Singapore, children are encouraged to use visual models such as ‘bar models’, ‘ten frames’, arrays and place value charts. We are going to focus on the ‘bar model’ which is specifically used to help children make sense of word problems.
The approach is meant to reveal the structure of the mathematics in the problem.
It is not a tool for performing a calculation.

5. PROBLEM SOLVING WITH MODEL DRAWING
The model drawing approach takes students from the concrete to the abstract stage via an intermediary pictorial stage.
Students create bars and break them down into “units.” The units create a bridge to the concept of an “unknown” quantity that must be found.
Students can learn to use this strategy in the primary grades and continue with it through the middle grades.

6. Benefits of Model Drawing
Students have one strategy for solving every problem.
Process work for most of word problems.
Students have a visual to associate with numbers that can be abstract.
Unit bars help visualization.
Students learn to translate the English into math and then back into English.
Model drawing builds a bridge between word problems, equations, and solutions.
7 steps work for 80% of word problems. Unit bars help visualization. Model drawing builds a bridge between word problems, equations, and solutions. Model drawing emphasizes the relationships between values in the computation.
Students start to see the relationship behind numerical values.
Model drawing emphasizes the relationships between values in the computation

7. 4 Steps for Model Drawing
Read the problem. Identify the variables(the who and the what – do we know the whole?).
Draw a unit bar or bars/Use Practical Equipment.
Chunk information by rereading the problem one sentence at a time, and adjust the unit bar or bars to match the information.
Work the computation.

8. Question 1
Ben spent 2⁄5 of his money on a CD. The CD cost £10. How much money did he have at first?
How would your children cope with this?
If this appeared on a KS2 SATs paper how many Year 6 children would confidently attempt it?

9. Using Practical Equipment
Ben spent 2⁄5 of his money on a CD. The CD cost £10. How much money did he have at first?
How could you use Unifix Cubes? ?
£10

10. Bar Method (Pictorial Method)
Ben spent 2⁄5 of his money on a CD. The CD cost £10. How much money did he have at first?
1) Draw a Bar
2) Divide into 5ths
3) 2/5 = £10
4) One 5th = £5
5) So 5 * £5 = £25

11. What do you think?
Did that help make the problem easier to understand?
Did this open up the problem- show what you are required to do?
Do you think this would support less able mathematicians?

12. Can you use both methods?
Have a go…
 1)Peter has four books. Harry has five times as many books as Peter. How many more books does Harry have?
Can you use both methods?
Peter’s books
Harry's books 
Harry has 16 more books.

13. Can you use both methods?
Have a go …
2)There are 32 children in a class. There are 3 times as many boys as girls. How many girls?
Can you use both methods?
Each square is 8, so there are 8 girls and 24 boys

14. Can you use both methods?
Have a go…
3)Sam had 5 times as many marbles as Tom. If Sam gives 26 marbles to Tom, the two friends will have exactly the same amount. How many marbles do they have altogether?
Tom’s marbles Same
Amount
Sam’s marbles
So each part is 13, so 78 marbles altogether
Can you use both methods?

15. Can you use both methods?
Have a go…
4) A computer game was reduced in a sale by 20% and it now costs £48. What was the original price?
Can you use both methods?
Each part is £12, so the original price was £60

16. What do you think?
Did that help make the problem easier to understand?
Did this open up the problem- show what you are required to do?
Do you think this would support less able mathematicians?

17. Starting with basics
We may not be able to jump straight to complex problems and we must make sure pupils understand the method before challenging with more complex mathematical ideas?
In Reception and KS1, simple calculations are be explored practically and when the children are ready they could also be represented pictorially.

18. KS1 examples
Using red and blue cars set this problem: Rasheed had 5 red cars and 3 blue. How many more red cars does he have?
This becomes a generalisation where a whole will represent 5 and not distinct squares:

19. KS1 Example
Rosie had 4 pencils. Samir had twice as many. How many pencils did Samir have?

20. Final Question (5th Grade Singapore)
Ext)Sophie made some cakes for the school fair. She sold 3⁄5 of them in the morning and 1⁄4 of what was left in the afternoon. If she sold 200 more cakes in the morning than in the afternoon, how many cakes did she make?
5th grade = 10 – 11 years old
Starting Point
There are five more morning parts than afternoon parts, so each part is 40 (200 ÷ 5).
She made 400 cakes

21. This model shows the part- whole relationship with addition and subtraction

22. This model shows how the larger and smaller quanities are related in an addition/subtraction comparision problem. This model can easily support an additional step of figuring out the total of the two quantities.

23. This model shows how the part and whole are related through multiplication and division. I could show that if I had 15 stickers and I divided them evenly among 3 kids, each kid would get 5 stickers. Later we can use this diagram to model fraction relationships. This picture shows that the part is 1/3 of the whole.

24. This picture shows a multiplicative relationship between 2 quantities
This picture shows a multiplicative relationship between 2 quantities. The larger quantity is 5 times as large as the smaller quantity. Later this same picture can be used to show comparision with fractions. The smaller quantity is 1/5 of the larger quantity.

25. Model Drawing is NOT the answer to every problem.
Courtney starts with 12 birdhouses. She makes three new birdhouses each week. Which pattern shows the number of birdhouses Courtney has at the end of each week?
Give one way that a cone and a cylinder are alike. NO
One month Tony’s puppy grew 7/8 of an inch. The next month his puppy
grew 5/8 of an inch. How many inches did Tony’s puppy grow in two months? Y
Which spinner has a probability of 0 for landing on a star, ?
What transformation changed shape 1 to shape 2?
Mrs. Thomas gave the store clerk $25.00 for a pair of jeans. She received
$2.88 back in change. What was the price of the jeans?