Maths and a Growth Mindset

Here is a link to an inspiring video about the power of solving maths in groups and being a problem solver: https://www.youcubed.org/solving-math-problem/

Below is a video which shows that we can all learn Maths to high levels and that even the best Mathematicians in the world can be really slow to solve problems. How you do in Maths tests does not determine your ability in Maths, believe in yourself, work hard and take your time to solve Maths problems and you will make great progress.

 

Mandala Artwork

Today we looked at how to create Mandalas and created our own creative artwork using this technique. Below is a video that explains the process.

Partitioning Numbers

Partitioning

The ability to partition is essential to be at the maths standard for Year 4.  

In Year 4 students are working towards being proficient at Strategy Stage 5 (Early Additive) in maths by the end of the year. One of the main skills of Strategy Stage 5 is the ability to add and subtract numbers by partitioning (breaking up) them rather than counting on or counting back (i.e. 5, 6, 7, 8, 9, 10, 11 … OR 12, 11, 10 9, 8…).

Partitioning numbers means we know that we can break a number up into its basic facts to help us solve problems. For example 7 can be broken up (partitioned) into two numbers:

7 = 3 + 4, or 5 + 2, or 6 + 1

partitioning_03

 

Understanding Partitioning

Year 4 = Stage 5: Early additive

Students at the Early Additive stage solve number problems by simple splitting of the numbers (partitioning) and by using groupings of hundreds, tens and ones (simple place value).

Students at this stage need to recognise that numbers can be split into parts and recombined in different ways. This is called part-whole thinking. Problems at this stage are usually limited to numbers less than 20, or where one of the numbers is a single digit.

Strategies used at this stage include:

  • using doubles
    7 + 8 as (7 + 7) + 1
  • up through a ten
    38 + 7 as (38 + 2) + 5
  • compensation
    24 – 9 as (24 – 10) + 1.

Slideshow explaining partitioning from Teacher Tools


Here is a video demonstrating Stage 5 Early Additive thinking (Year 4) by a Year 4 student.

A video explaining addition partitioning (splitting numbers up) with a tens frame and a number line

A video explaining addition subtraction (splitting numbers up) with a tens frame and a number line

Partitioning subtraction & addition worksheet

Link to: Partitioning subtraction & addition worksheet 

 

 Lesson on how to partition with three digit numbers

A lesson with a video explaining thinking behind partitioning using three digit numbers

 

Partitioning with the Tidy Number Strategies

ADDITION Tidy Number Strategy

Note: We can make either number a tidy number in the addition tidy number strategy.

Note: We do the OPPOSITE to each number, i.e. if we subtract on one of the numbers we add on the other number. The reason for this is because we take away some numbers from one of the numbers to round the other number.

For example if our addition problem was:

48 + 17 =

STEP 1: Making a Tidy Number

We first round the 48 up to 50 (because it is closest to a tidy number) by taking 2 off the 17. We are then left with the easier problem of:

50 + 15 =

The 15 is what is left after taking the 2 off the 17.

We can then partition up the numbers and add them together:

50 + 10 + 5 = 65

So we haved solved our problem:

48 + 17 = 65.

SUBTRACTION Tidy Number Strategy

Note: We only make the second number a tidy number in the subtraction tidy number strategy. By making the second number a tidy number it becomes an easier problem to solve as there are less digits to subtract from the first number.

Note: We do the SAME to each number – both sides get bigger or smaller by the same amount. We are trying to work out the distance between the two numbers so we must do the same to both numbers to keep this gap the same.

For example, if our subtraction problem was:

48 - 17 =

STEP 1: Making a Tidy Number

We first round the second number which is 17 up to 20 by adding 3 to the 17.

We need to make sure we add 3 to the 48 as well so that the  gap between the two numbers remains the same
(i.e. there is always a gap of 31 between the numbers in our example).

We are then left with the easier problem of:

51 - 20 =

STEP 2: Using our basic facts to help us solve the problem

We could now approach this problem by using our basic fact of

5 - 2 = 3
Therfore:
51 - 20 = 31

So we have solved our problem:

48 - 17 = 31

Useful Links

Here is a video explaining the addition tidy number strategy.

Here is a video explaining the subtraction tidy number strategy.

Here is a pdf that explains the tidy number strategy for addition.

Partitioning using the Tidy Number Addition Strategy (Year 3 strategy)

Partitioning using the Subtraction Tidy Number Strategy (Year 3 strategy)

 

Partitioning using the Tidy Number Addition Strategy (Year 4 strategy)

Partitioning using the Tidy Number Subtraction Strategy (Year 4 strategy)

 

Printing and Modern Cursive Handwriting

We have handwriting as part of our weekly activities in class. The style of handwriting the Ministry of Education recommends in its Teaching Handwriting handbook which develops from printing to the modern cursive handwriting style.

This term we are going to focus on printing to make sure we are forming all letters correctly.

 

Information about the handwriting curriculum and cursive writing is below.

The uppercase (capital) basic cursive script letters are the same as the basic printing uppercase (capital) letters and so don’t link to the lowercase letters. An example is below:

UppercaseCursive

The difference between the basic script alphabet and cursive alphabet are in the letters f and x and in the exits of a, d, h, i, k, 1, in, n, o, r, t, u, v, and w. (Exit refers to the stroke that forms the beginning of the link to the following letter.)

 

 

Some useful resources for practising modern cursive handwriting:

A useful website with worksheets for practise with the  for the modern cursive handwriting style is Ted Power.

A fun app for beginners to practise the modern cursive unlinked letter formations is Australian Touch and Write: Victorian Cursive app.

A useful document with great suggestions on proper grip, posture and handwriting instruction is the Handwriting South Australian Modern Cursive Handbook.

We will be looking at our grip when holding a pencil and the best position of our paper when writing in a cursive script. See the images below for examples of what we will be learning.

grip

position

We will be moving from the Year 3 printing style to cursive. The difference can be seen below:

year3script

Year 4

 

 

tableCursive