Place Value Progression and Activities

I have also produced progression documents for place value.

  • Place Value

Remember, if you click on the picture, you will access the full document, however the hyperlinks won’t work. To download the zipfile, click here (Mediafire) or here (4share):

If you do download the zipfile, be patient it takes a while. You will need to unzip it, open the folder and locate the word document: LT Place Value. Everything hyperlinks from there.

I have attached a step by step guide for unzipping the folder. click here

And here are 3 Place Value activities as a taster…

  • 5 digit number mystery
  • Fast Track

Year 4 Digit Sum (plan)

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Shape, Angle and Position Progression and Activities

I have uploaded several shape activities already and you can download activities and smartboard files from the tes website by following this link.

I have also produced progression documents for 2D shapes, 3D shapes, angles and position and movement.

  • 2D shape
  • 3D shape
  • Angles
  • Position and Movement

Remember, if you click on the picture, you will access the full document, however the hyperlinks won’t work. To download the zipfile, click here (Mediafire) or here (4share):

If you do download the zipfile, be patient it takes a while. You will need to unzip it, open the folder and locate the word document: LT 2D shape, LT 3D shape, LT angles or LT position and movement. Everything hyperlinks from there.

I have attached a step by step guide for unzipping the folder. click here

  • 2d shape mobiles puzzles (zids and zods)
  • Reflective symmetry in regular polygons

And here is a great pentomino activity…

  • Pentomino

Click on the picture to link to an interactive file from NGFL CYMRU.  When I introduced it to my class, I began with this activity:

Children invetsigated all by finding all 12 pentominoes using square paper provided below, then sorted onto Venn diagram: Net of open cube, at last 1 line of symmetry. Finally, they solved the attached puzzles:

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Finding All Possibilities Progression and Activities

Do you remember the problem solving materials that were produced looking at the progression in finding all possibilies problems?

 

Here is the document I produced to support teachers with developing the skills neededs to solve finding all possibilities problems. If you click on the picture, you will access the full document, however the hyperlinks won’t work.

To download the zipfile, click here (Mediafire) or here (4share):

If you do download the zipfile, be patient it takes a while. You will need to unzip it, open the folder and locate the word document: LT Finding All Possibilities 1. Everything hyperlinks from there.

I have attached a step by step guide for unzipping the folder. click here

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Finding Rules and Describing Patterns Progression and Activities

A while ago, some draft materials were produced that looked at the progression in finding rules and describing patterns.  The birthday candles problem fits in well with the consecutive number activities discussed in the challenging more able children post.

Because I am interested in trying to develop problem solving right across the school, I used the primary framework for mathematics to support teachers at school get a better understanding of progression by pulling out examples for each year group. I then produced a document that linked the progression documents to guidance materials and activities.

The result is a series of word documents that hyperlink to smartboard files, worksheets and interactive teaching materials to help plan and teach maths in a more systematic way throughout school.

Here is the document I produced to support teachers with finding rules and describing patterns.If you click on the picture, you will access the full document, however the hyperlinks won’t work. You need to click here, then download the complete zipped file.

To download the zipfile, click here (Mediafire) or here (4share):

If you do download the zipfile, be patient it takes a while. You will need to unzip it, open the folder and locate the word document: LT patterns, sequences and rules. Everything hyperlinks from there.

I have attached a step by step guide for unzipping the folder. click here

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Space Activities

With the success of ‘Stargazing Live’ and the finding of a new planet by Chris Homes from Peterborough, I have uploaded some space themed activities I wrote for a year 5 class I taught a few years ago.

I have uploaded smartbord files accompanying these activities to the tes website.

  • Planet information gap

Information gap activities require children to work in pairs and share information verbally.

  • Planetary Routes 
  • Distance from the moon and diameter of the Earth (mysteries for 4)

  • Interplanetary football
  • Sum and difference rockets

I used this template explore the relationship between to the sum and difference between two numbers. When these two values are added, the number in the cone of the rocket is always twice the bigger number on the bottom. We continued to explore this by questions such as:

  • I think of 2 numbers.
  • When I add them, I get _____, one is ______ more than the other.
  • What are the two numbers?

We then explored why this is the case using paper strips, before moving into the realms of algebra.

  • Planet sequences
  • Planet Polypod (zids and zods)

 

  • Moons of Vuv
  • Four Planets
  • Word Problems

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Challenging more able children

As well as teaching year 4 children, I also set regular puzzles for more able children in years 5 and 6. I will post examples of activities I have used and web pages I have found which have helped generate ideas.

www.nrich.maths.org is always the first place I look for ideas. Here is an example of a puzzle I found there, and how I adapted it to take the learning further.

  • Fitted is an activity that appeared in the key stage 3 section in November 2011. I slightly adapted it because the class teacher was working on area and perimeter in class.

“Nine squares with side lengths1,4,7,8,9,10,14,15 and18 cm can be fitted together with no gaps and no overlaps, to form a rectangle. What is the perimeter of the rectangle?”

In the next session I used www.mathspickle.com because it has a terrific video section that takes the same idea a bit further, but allows you to explore balanced equations in a practical context.

Although the website has worsheets for the activities, I rearranged them to save paper and to concentrate on area and perimeter (click on the picture). 

We stuck with the idea of multiplying numbers together to find products, but used a calculator to explore products from consecutive numbers and square numbers. I have this activity in the context of area and in the context of mountains. I have attached resources for both.

 The final activity we looked at linked to square numbers also came from nrich. I posted the recording sheet under multiplication activities. With the more able children we concentrated on multiplication using the grid method and using algebra to find the reason why the difference increases in square numbers.

 Sticking with an algebra theme we are now investigating Fibonacci sequences. I found these resources.

(http://www.teachfind.com/national-strategies/fibs-and-truths) and adapted them to produce these.

Next week we are going to revisit problems introduced in year 4. The strategy taught then was based on a guess and test approach. We will be refining this to using an algebraic approach to solve them more efficiently. 

Leaf Pyramid Algebra

  • See the rainforest post for a picture, or click here to download resources.

We investigated the possible totals that could be made when the numbers on the bottom of the pyramid were consecutive. When solving the three layer pyramid, children noticed that the numbers in the top row were all multiples of 4, and that the number was always four times the middle number on the bottom row.

I then challenged them to find the bottom four numbers if the top number was 100. This led to some children dividing the top number by 4. We then tried to complete the pyramid using algebraic terms with the bottom row being: n, n+1, n+2 and discovered the top number was 4n+4. If the top number = 100, then 4n+4=100. The children were able to manipulate this to calculate that n was 24. They then tried to complete the pyramid given different top numbers, before moving onto 4 layer pyramids.

Adding consecutive numbers (the Guass way).

Sticking with consecutive numbers…

Johann Carl Friedrich Gauss (30 April 1777 – 23 February 1855) was a very famous German mathematician. One well known story about him happened after the he misbehaved in primary school. His teacher, J.G. Büttner, gave him a task: add the numbers from 1 to 100. The young Gauss produced the correct answer within seconds, to the astonishment of his teacher. Can you find a quick way of adding all the numbers that he might have used?

 Solving this puzzle with children reminded me of other consecutive number puzzles we have solved over the years. I always teach the children the strategy:

  • draw loops to join first and last number and find total.
  • repeat for second and second last numbers. what do you notice about the ‘loop’ total?
  • repeat, joing all numbers in sequence and record all ‘loop’ totals.
  • Record information systematically in table with the following headings:

last number :     how many loops :   loop total  :  overall total

  • explain the relationships in the table, how many loops is always 1/2 the last number, the loop total is always 1 more than the last number, the overall total is always the product of loops x loop total. This leads the children the algebraic formula.

Handshakes (link to NGFL CYMRU interactive)

 PS there are other brilliant interactive introductions to interesting investigations on this website; I particularly like the tower of hanoi puzzle and the leapfrog puzzle, which like the last two puzzles require the children to use a table to collect data, then analyse data to find patterns before expressing relationships algebraically.

 Totalling consecutive numbers (taken from the Nrich website)

 I like to do this activity early on in year 4 to introduce the idea of adding sequences of numbers by linking them together as described above. Although it takes determination and perseverance, the more able childrenfind the solution that you cannot make the powers of 2 (1, 2, 4, 8, 16, 32, 64). I then challenge them to use these powers of 2 to make different totals, which can link to Egyptian Multiplication and to this puzzle from the blue problem solving book.

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Rainforest Maths

My topic for this term is Rainforests. We have bought into the International Primary Curriculum resources, so my planning will be alongside this. I will try to update the blog weekly with ideas that I have used in the class, so here is the first activity.

  • Birds eggs.
  • Travelling to a rainforest

I used this website to find how far it was from Morton in Gainsborough to different rainforests around the world. htp://www.mapcrow.info/ then made up some puzzles like this:

  • Addition Leaf Tree

I am using the addition pyramid to revisit mental addition strategies, before teaching children column addition adding units first.

  • Rainforest Animal wangdoodles
  • Venn diagram puzzles
  • Easy
  • Harder

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