Posts tagged logic

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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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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Olympic Puzzles

www.nrich.maths.org have gone with an Olympic theme this month, so I have uploaded a couple of puzzles I wrote a while ago linked to this theme. My class have this theme in the summer term, so I will produce more puzzles nearer the time.

Olympic rings:

Winter Olympics

We did quite a bic mathematics topic based on the Winter Olympics. I have added some of the activities below. The first set are based on logical problem solving activites adapted from the draft materials published by Primary Strategy for year 4.

  • Winter Olympic medal tables

This first activity is has four puzzles that lead the children to draw graphs to show how many gold, silver and bronze medals won. I asked the children to complete the graphs so that each column had three colours indicating gold, silver and bronze so that they could see the total number of medals won also.

  • Summer Olympic Medal Tables

These are similar to the Winter Olympic medals puzzles, but based on the summer games.

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Christmas puzzles

We have finished our ‘How to train your dragon’ topic and have turned our attention to Christmas. I have put together some maths puzzles to end the term, which revisit all the puzzles the children have been introduced to over the term. (Click on the pictures to access the puzzles)

  • 12 Days of Christmas

  • Mazes

  • Presents

  • Wangdoodles

I have added simple, whole pound examples, and more difficult decimal examples. Children in my class are in transition between guess and test strategy and more systematic tick chart method explained in the draft logic problem materials for kieran’s cats.

Shape puzzles

 

  • Maisie Mouse

  • Zids and Zods

  • Nicknames

I have also uploaded Christmas themed digit cards, which can be use to solve problems such as magic square puzzles, card sharp puzzles, e.g.

You can also access smartboard files and further ideas and activities linked to digit cards here.

Year 2 activities: http://www.tes.co.uk/teaching-resource/Year-2-Christmas-Maths-6146500/

Year 4 activities:http://www.tes.co.uk/teaching-resource/Key-stage-2-Christmas-Maths-Puzzles-6147071/

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African animals

Last year, following a trip to South Africa over the half term, I did a topic on African animals. I found the nuffield D and T unit on ‘how will your beast move its mouth very helpful. I have already uploaded several of the activities I used, but I have organised them all here under 1 post. I have also added smartboard files to accompany activities onto TES website:

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Telling the time, reading timetables and working together.

Telling the time is something that quite a lot of my class need to practise often. I have already uploaded some of the activities I have written this year, but here is a few more. On this revisit we are focusing on 24 hour clock, reading time tables and collaborating to solve problems. Because we are working on block D, I have tried to make links to other block D objectives, so there is a bit of coordinates and a bit of finding the difference between times.

24 hour coordinates grid

Nicknames puzzles

  • time logic (one of these is inspired by edhelper.com. For more information follow the link below).

Collaborative puzzles

Collaborative puzzles inspired by edhelper.com

I adapted two time puzzles I found on edhelper.com to make them collaborative. To find the original puzzles click here.

Below are some useful telling the time websites that we will visit.

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Susie Snake, Maisie Mouse and other remainder puzzles

This type of puzzle is one of my class’s favourites. We tried it for the first time as an optional puzzle when we were learning about the Viking history of Gainsborough. It proved to be so popular that we have revisited a few times since in different contexts. Because the strategy to solve it requires you to talk about grouping and remainders, it is an excellent, concrete context for teaching division by drawing groups, and reinforcing the link between division and multiplication.

The class have got quite sophisticated now, that for most of them it is about number sequences more than division, and they can confidently work with multiples up to 10, with remainders up to 9 and with grouping numbers up to 100.

Here are the contexts we have met the problem in so far. Notice the first puzzles use the clues from Susie snake, the second uses the clues from Maisie mouse.

Vikings

African animals

Christmas

Robots

Healthy eating

Skeletons

Tudors

In writing these puzzles, I found this interactive on Nrich.maths.org very helpful. Click on the picture to follow the link.

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Kieran’s Cats, Weighing Wangdoodles and Arithmagons.

These three puzzles are one I return to often. I began year 4 solving these problems using equipment, e.g. shape cards, weighing scale pictures, digit cards etc. We then moved to using a finding all possibilities approach. Children solved the problems by writing ordered lists.  Now most of my current class can use the method suggested in the Logic draft materials booklet. It is a terrific approach because it develops data handling skills, adding three numbers using a mental or written method, halving two or three digit numbers and finding the difference.

The puzzles are easily adapted to almost any curriculum area, I have added a few that I have produced for classes over the years.

Place value

Pirates

The next three links open documents that make the link between arithmagons and ‘Kieran’s Cat’ type clues. There are some interactive arithmagons on the Nrich website which you can access by clicking on the picture above or following this link.

Kandinsky

Wizard of Oz

Arithmagons

Vikings

Tudors
Robot Wars

Sports day

These next few puzzles all require children to put objects in a row. The row contains either 3, 4 or 5 objects. When there are three objects, I have used ‘Kieran’s Cats’ type clues. When there are 4 in a row I have used either ‘Esmarelda’s coins’ clues. For 5 objects, I have gone to ‘Row of Coins’ for inspiration. All these puzzles can be found in the challenging more able children book.

Shapes

African animals

Angles

Measuring Cylinders

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Coordinate grids

These next activities are very popular with my class. I began by using them as ‘information gap’ or ‘mystery’ activities, where children worked in pairs or small groups sharing clues and solving the problems together. I have moved over the year to children solving them individually as they have solved them so many times. Hope you like them. Again, like the nicknames problems, we have revisited these problems in lots of different contexts to fit in with the different cross curriculat themes. They lend themselves to shape, space and measure objectives. I have used all of these with my year 4 class this year.

Instructions.

  1. Children cut up the pictures to be sorted onto grid. My class have found it helpful to put their initials on the back of each picture.
  2. Read through all the clues.
  3. Where a clue tells you exactly where a picture is to be placed, place it there.
  4. Tick off the clues as you solve then.
  5. When puzzle is solved, make sure solution fits all the clues.

Shape

Telling the time

Units of measurement

Angles

Tudors

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