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.

Singapore Bar Models

Whole School Approach to Word Problems.

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.

• 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.

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.

Benefits of Model Drawing

• Students have one strategy for solving every problem.

• Students have a visual to associate with numbers that can be abstract.

• Students learn to translate the English into math and then back into English.

• Students start to see the relationship behind numerical values.• Model drawing emphasizes the relationships between

values in the computation

• Process work for most of word problems.

• Unit bars help visualization.

• Model drawing builds a bridge between word problems, equations, and solutions.

4 Steps for Model Drawing

1.Read the problem. Identify the variables(the who and the what – do we know the whole?). 2.Draw a unit bar or bars/Use Practical Equipment. 3.Chunk information by rereading the problem one sentence at a time, and adjust the unit bar or bars to match the information. 4.Work the computation.

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?

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?

?£10

How could you use Unifix Cubes?

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?

5) So 5 * £5 = £254) One 5th = £5

2) Divide into 5ths

3) 2/5 = £101) Draw a Bar

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?

Have a go… 1)Peter has four books. Harry has five times as many books as Peter. How many more books does Harry have?

Peter’s books  Harry's books  Harry has 16 more books.

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?

Each square is 8, so there are 8 girls and 24 boys

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?

Have a go…4) A computer game was reduced in a sale by 20% and it now costs £48. What was the original price?

Each part is £12, so the original price was £60

Can you use both methods?

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?

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.

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:

KS1 Example

• Rosie had 4 pencils. Samir had twice as many. How many pencils did Samir have?

There are five more morning parts than afternoon parts, so each part is 40 (200 ÷ 5). She made 400 cakes

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?

Starting Point

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 puppygrew 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?