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Maths Terms 3 and 4

Magic Magicians

Sophie, Anthony, Kinae, Mark, Leevy, Pyper, Heidi, Katie, Noah A

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Term Four

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WEEKS 3 AND 4

LEARN:

iDENTIFY, USE, ADD AND SUBTRACT FRACTIONS WITH LIKE AND UNLIKE DENOMINATORS
USE POSITIVE AND NEGATIVE INTEGERS FOR ADDITION AND SUBTRACTIONS

Maths buddy tasks: wEEKLY REVISION

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RECAP: What are fractions? Less than a whole. Parts of a whole. It shows how many parts a whole is divided into. They have a numerator and a denominator. The line in the middle means divided by. Algebra can be used in fractions. You can turn them into a decimal or a percentage. Numbers can be fractions, measurements, shapes, money, sharing food, shares of a company.

What does simplify mean? You divide it to its simplest form, lowering it down to the Lowest Common Multiple.

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Checking our prior knowledge… Using maths talk to discuss.

What is ⅖ of 40?

21 is ¾ of A. A =?

Five people are given four bags of popcorn to share equally between them. How much of a bag of popcorn will each person get?

In the classroom there are 24 children. 1/3 like maths. How many children don’t like maths?

I had painted ⅔ of a wall in my lounge. It was 36 metres long. How many metres did I still need to paint?

It is Jo’s twelfth birthday party. Including herself there are four people at the party. If everyone gets one quarter of the cake, how many candles do they get?

Follow up FIO - print

MRS B: Draw a number line from 0 to 10 on the board (about 1 metre long). Build up the number line by getting students to write where different numbers might be. Once the whole numbers are in place, ask students to think about where numbers like 1/2 , 3/4 ,3/2 , and 4 2/3 might be. This will help students to realise how fractional numbers extend the existing set of whole numbers and can be represented on a number line in the same way.

Children: Draw a number line to show 1/2 ,1/4 , and 1/8 . Mark where you think 1/3 , 1/5 , and 1/10 would go on your number line. Explain where you placed them. Why do fractions with one on the top line get smaller as the number on the bottom gets larger, e.g. one-half is larger than one-third?

Which of these fractions is closest to one, 1/2 ,2/3 , or 3/4 ? Why?

These problems will highlight students’ knowledge of the relative size of fractions. For example, a student might find half of the distance between 0 and 1/5 to see where 1/10 should be or half the distance between 1/2 and 1 to see the location of 3/4 . The problems will also highlight their understanding of the role of the numerator (top number) as the selector of the number of parts and the role of the denominator (bottom number) as nominating how many equal parts the whole is separated into.

Tell the story of the two early birds who caught a worm. Produce a stack of one hundred Uni-fix cubes or multilink cubes joined together so that sections ten cubes long are in the same colour. Tell the students that this is the worm and when the birds measured it they found that it was very long. How long? Ask, "Suppose the two birds wanted to share the worm equally. How could they do that?" Students should use the idea of half of 100 being 50. Ask, "If they caught three worms this size and shared them out, how much would each bird get?" Record their responses using equations like 1/2 of 300 is 150.

Extend the problem. Ask, "Suppose that it took four birds to pull this worm out of its hole. How much of the worm will each bird get? What if there were five birds, ten birds?" Record the students’ strategies using symbols and diagrams

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Which is bigger?

⅓ of 90 or ¼ 0f 80?

⅙ of 120 or ⅓ of 36?

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Equivalent fractions:

Equivalent Fractions have the same value, even though they may look different.

These fractions are really the same: 1/2 = 2/4 = 4/8.

Why are they the same? Because when you multiply or divide both the top and bottom by the same number, the fraction keeps it's value.

You can make equivalent fractions by multiplying or dividing both top and bottom by the same amount.

You only multiply or divide, never add or subtract, to get an equivalent fraction.

Only divide when the top and bottom stay as whole numbers.

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Mixed fractions: A Mixed Fraction is a whole number and a proper fraction combined.

Such as 2 ⅓

Three Types of Fractions

There are three types of fraction:

You can use either an improper fraction or a mixed fraction to show the same amount.

For example 1 3/4 = 7/4. That is the whole (4/4) and the ¾ fraction together.

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Adding or subtracting fractions if the denominator is the same….

You just add the numerators and keep the same denominator:

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Solve these:

⅓ + ⅔ =

⅞ + ⅝ =

⅘ + ⅖ =

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If the denominator is different but a multiple of the other….

Make ½ and ¼’s, ⅓ and ⅙ using blocks.

½ +¼ =

⅓ + 2/6 =

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If the denominator is different ….

Watch this video - it helps you understand the concept using materials.

You need to find the lowest common denominator - which is the lowest common multiple. This is the lowest number that both numbers can go into. For example, the lowest common multiple for the numbers 2 and 5 is 10, and for the numbers 3 and 4 is 12. A key to equivalent fractions is Finding common multiples. You need to know your multiplication tables.

Once you have found the lowest common denominator and made the equivalent fractions, the addition and subtraction part is very easy. The next step is to check to see if you can simplify your fraction.

SEE THE NEXT SLIDE FOR ANOTHER EXAMPLE

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Example:

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WATCH THE FOLLOWING VIDEOS

Adding like fractions

Changing improper fractions to mixed fractions

Simplifying fractions

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WATCH THE FOLLOWING VIDEO

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Solve this

¼ + ½ =

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Example 2:

⅜ + ½ =

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WALT: About integers

An integer (pronounced IN-tuh-jer) is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043. Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14, .09, and 5,643.1.

Practise here

Game

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WALT: About integers

An integer (pronounced IN-tuh-jer) is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043. Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14, .09, and 5,643.1.

Practise here

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WALT: About integers

An integer (pronounced IN-tuh-jer) is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043. Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14, .09, and 5,643.1.

Practise here

Watch this

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WALT: About integers

Practise here

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WALT: About integers

Practise here

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Statistical investigation

LEARN:

Write questions for statistical investigations and design a method of collection of data
Display collected data in an appropriate format
Make statements about implications or possible actions based on the results of an investigation
Make conclusions on the basis of statistical investigations.

Dragon maths follow up:

Green pages 102-129

Red Pages 112 - 130

Maths buddy tasks: Statistics

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Statistical Investigation

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Statistical Investigation

The problem is about formulating a statistical question, what data to collect, who to collect it from and why it is important. It is important to think about what data to collect - much like fair testing in science. What is your initial hypothesis?

The plan section is about how the data will be gathered, what to measure and what the variables are.

The data section is about how the collected data is managed and organised. How will you record your data? You could try a table or a tally chart.

The analysis section is about exploring and analysing the data, using a variety of data displays and numerical summaries, and reasoning with the data.

The conclusion section is about answering the question in the problem section and giving reasons based on the analysis section. Refelct on your hypothesis.

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LEARN: statistical investigation

Introduce statistical studies - Child poverty in NZ. This is an example of how statistics is reported = large scale. Here is an example of an investigation from Griffin.�watch this�What do we know…�Heidi-It is a way collection of information put into a graph to see things and understand things in an easier way.�Leevy: A statistical investigation is a way of collecting data and finding answers to your questions.�Anthony: A statistical investigation consists of A hypothesis, Data and graphs. Put into a informative D.L.O.�Sophie: For a statistical investigation you need to have a question and collect and organise the data, and pick a type of display for your data. Such as a frequency table, dot plot, double column graph, stem and leaf plot, or a sector graph. Then after collecting all the data then you use your data and show the results on your display. Also add this all with writing to explain what you did.�Pyper: In a statistical investigation you start with a question, then hypothesis and in the hypothesis you need to ad a why or because. Then collect you data by testinga and put it into a graph that works well. Lastly, you need to have a evaluation and conclusion. Also add photos and videos if posible.�What do we want to know…�Leevy: To analyze the data�Pyper: How to analise data.�Sophie: How to analyze data.

Anthony:How to collect and analyze data in the best way

Katie: How to analizy tha data and choose a good graph.

Heidi-How to use google sheets for this information.

Katie: That we start with a Question, then a hypothesis, then you write the method. Next you collect the data and put it into different graphs (choose which is best). After that analyze the data and also turn into percentage if needed. Then see if there are any questions that follow your analyzation. Then write a conclusion and evaluation

I want to know what it can be used for and i know that you can use it for finding out stuff about things the are going. And i wont to leran how to use google sheets

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LEARN: statistical investigation

Whole class lesson (teacher led) model of investigation- collect data (could be measure height, eye colour, hair colour, how we travel to school) - demonstrate how to collect data - tally chart or table. Discuss and identify variables. Come up with the investigative questions

How to turn data into a graph - watch which graph do I use.

Try a stem and leaf and one other kind of graph to show your data. Create our graphs using sheets.

Together analyse and make conclusions about the data.

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WALT: statistical investigation

Our own investigation (make sure this is in your mathematics folder - begin a new slideshow/DLO).

1 decide on a question - I wonder if…

2 Plan how to gather information - Tally charts, other ways?

3 Gather information

3 decide how to show it STATSGraphs Use at least 2 different graphs to show it

4 look at the information and work out what it is telling you.

5 Report your findings and share

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WALT: statistical investigation

Link your investigation here:

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Term three

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Week 5 remember our strategies

LEARN: To use a number of strategies to solve addition and subtraction problems

Mentally solve whole number addition and subtraction problems using:

compensation from tidy numbers including equal additions
place value
reversibility
use appropriate recording techniques.

You have 2-3 minutes to solve this IN YOUR HEAD:

Sarah has $288 in the bank. She then deposits her pay cheque for $127 from her part time job at PetCare. How much does she have now?

Strategies used:Place value

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Week 5 remember our strategies

LEARN: To use a number of strategies to solve addition and subtraction problems

Place value:

288 + 127 is just like 288 + 100 +20 +7. So that’s 388… 408… 415.

Tidy numbers:

If I tidy 288 to 300 it would be easier. To do that I need to add 12 to 288, which means I have to take 12 off the 127. So that’s 300 plus 115.

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Week 5 remember our strategies

LEARN: To use a number of strategies to solve addition and subtraction problems

Any other strategies you can think of?

Sarah has $466 in her bank account and spends $178 on a new phone, how much money does she have left in her bank account?

Discuss strategies:

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Week 5 remember our strategies

LEARN: To use a number of strategies to solve addition and subtraction problems

Reversibility:

$466 - $178 is the same as saying how much do you need to add to $178 to get $466. $178 plus $22 makes $200, plus $200 more makes $400 plus $66 makes $466. If you add up $22 plus $200 plus $66 you get $288.

Tidy numbers using equal additions:

You round the $178 to $200 by adding $22. $466 - $200 is $266. Then you put on $22 to keep the difference the same, so it’s $288.

There is a strong possibility that some students may misapply the addition tidy numbers strategy to subtraction problems. When using tidy numbers in subtraction the difference between the numbers in the equation must remain the same, so if you add an amount to one number, you must also add it to the other number. This is the opposite to addition, where the sum of the two numbers must remain unchanged when using a tidy numbers strategy, meaning that if you add an amount to one number you must subtract it from the other number. Some students may solve subtraction problems like 63 – 28 by tidying 28 to 30 (adding two), and 63 to 61 (subtracting two). The student has failed to keep the difference unchanged.

In this situation the students’ beliefs may need to be challenged by posing a conflict situation, using a simple example. For example, misapplying the tidy numbers strategy to 20 - 8 will leave the students with the problem 18 - 10. The situation can be modelled using Cuisenaire rods or a ruler.

As different strategies arise ask the students to explain why they chose to solve the problem in that way. Accept all the strategies that are elicited at this stage, recording them to reflect upon later in the unit (perhaps in a modelling book).

Ask students to reflect on the strategies that have been discussed in the session and evaluate which strategies that they personally need further work on, perhaps using thumb signals - thumbs up - confident and competent with the strategy, thumbs sideways - semi confident, thumbs down - not yet confident.

Use this information to plan for your subsequent teaching from the exploring section outlined below.

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Week 5 remember our strategies

LEARN: To use a number of strategies to solve addition and subtraction problems

Room 9 are selling muesli bars at lunchtime to raise money for their camp. They had 434 at the beginning of lunchtime and sold 179, how many did they have left to sell?

Ariana has scored 739 runs for her cricket club this season. Last season she scored 294, how many did she score in total in the last two seasons?

Farmer Dan has 1623 sheep and he sells 898 sheep at the local sale. How many sheep does he have left?

Copy these onto a google drawing and record yourself telling me how you solved it using tidy numbers or equal additions.

568 + 392

661 - 393

1287 + 589

1432 - 596

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Week 6 remember our strategies

https://nzmaths.co.nz/resource/addition-and-subtraction-pick-n-mix

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Week four - Learn: Scale is important

Consolidation of our learning:

Go to this site for Scale practise

Go to this site for ratio practise

Go to this site for scale drawing practise

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Week one - Learn: Scale is important

How to make a scale model

Estimate the height width, and length of our classroom (including room 5).

Our estimates: Anthony height 4m width 8m length 22m

Noah a and marko 11 width 4.3 height 27 length and its in meters.

Noah S 28 length 8 height highest point 18 width all in metres

Leevy L & Heidi length: 17m, width: 6m, Height: 4m

Pyper, Katie & Kinae: Height: 4, Length: 19, Width 7.

Sophie: Height:4, Length: 18, Width:9

Discuss the students’ estimates of the height and length of their building and how they arrived at these estimates.

Discuss how the actual length and height of the buildings can be measured. The length can be measured using a metre ruler or a tape measure. Elicit some ideas from the students as to how they might measure the height indirectly (they can’t climb the buildings!).

What is the actual height and length?

�Was there a large difference between the estimated height or length of your structure and the actual measurement? Why?

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Our measurements.

Heidi & Anthony-Length,Capiter wheel-23m. Ruler-23m�Width-Capiter wheel-10.5m. Ruler-10.5m

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Week one - Learn: Scale is important

What scale can we use for our models that will work for these heights and lengths?

So what would the measurements of our model be?

Create: apply this to building your Utopian model

Complete this as follow up:

Scale worksheet

Ask Mrs B for a paper copy

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Introduction to Ratio

1st lesson Ratio - Mrs B to print

2nd Lesson on ratio

Class ratios - Mrs B to print