Multilink cubes. strävorna

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1 Multilink cubes p r o b l e m s o lv i n g c o n c e p t s n u m b e r sense a l g e b r a g e o m e t r y Product description Cubes in 10 bright colours. Use them from early stacking, sorting and counting exercises to fractions, geometry, statistics and algebra. One cube is 2 cm x 2 cm x 2 cm. Counting Let every pupil take a hand full of cubes. How many are red? blue? white? Who has most yellow cubes? Build something with 4, 7, 10 cubes. What have you built? Put cubes on a string and use them for skip counting. Let every pupil put cubes together. Hold the stick behind the back. Mingle around Hi! Break the stick and show one part. The friend tells how many cubes are left behind the back. Check it together! Works well with the youngest pupils, 6 8 years old when they are a bit restless and need to move. A nice way to practise the use of number bonds for ten and at the same time a socializing activity. Double and half Double One pupil takes a hand full of cubes. The friend picks up twice as many. Check together! Half One pupil takes a hand full of cubes. The friend picks up half as many. Check together!

2 Concepts Some activities that practise concepts as on, in front of, behind, between, in the middle Put a number of small objects on the table, one is a cube. Ask a pupil to describe where the cube is placed: In front of the apple. Between the car and the sheep. Ask a pupil to put the cube in a specific place: In front of the cow. Behind the ball. Put some objects in a row, one is a cube. Ask a pupil to describe where the cube is placed, e.g.: it s in the middle it s in the third place from the beginning it s first it s the last but one. Patterns Patterns with colour Ask the pupils to slot the cubes together e.g. where every other cube is red. New patterns Ask them to slot the cubes and make any pattern they think of. Let the pupil ask a friend if he/she can find and describe the pattern. Fractions Make an exhibition: The pupils use cubes to show fractions as 1/2, 1/3, 1/4,, 1/10. They write the corresponding number on a piece of paper. More in the exhibition: The pupils use cubes to show e.g. what a half can look like in three different ways.

3 Percent Make an exhibition: The pupils use cubes to show percent numbers as 100 %, 80 %,, 1 %. They write the corresponding number on a piece of paper. More in the exhibition: The pupils use cubes to show e.g. what 50 % can look like in three different ways. Fractions and percent Compare the exhibitions: What conclusions can be drawn? More: Take a hand full of cubes (you may correct the numbers if necessary): What fraction shows the yellow, blue or black cubes? How many percent are black, blue and yellow? and more: Decide how many percent you have picked up and ask how many more cubes you need to pick up to get 100 %. This is 75 % This is the same, but organized I will need 25 % to get 100 %

4 Space Length Use the edge of a cube as an unstandardized length unit. Measure objects in the classroom. Put 10 cubes together, measure A way to introduce tenths. Area Use the side of a cube as an one area unit. Let the pupils draw a large shape, like a stain, on paper and use the cube to measure it. How big is the area? In other words: how many cubes do you need to cover the shape? Discuss how precise this method is. Volume Use the cube as an one volume unit. Let the pupils build a number of solids with precise volumes, e.g. 5 solids with the volume 12 v.u. Discuss if it matters in what direction you look at the solid when you are supposed to decide the volume. Algebra A secret number Put some cubes under a box. Write X, + and = on post-it notes. Place the materials as in the photo. How many cubes are hidden under the box? Check it! Another secret number Use two boxes and arrange as in the photo. Explain that you have put the same number of cubes under the boxes. What is x? Check it!

5 Statistics Let the pupils make a survey, e.g.: What kind of pets, and how many, do you have? Use the cubes to build a bar chart. If the same survey is made in a number of groups, in the end all groups can easily put their bar charts together to one large bar chart. dog aquarium cat bird frog snake guinea pig Combinatory logic If you have two cubes in different colours, there s only one way to combine them. How many pairs of cubes, in different colours, is it possible to make when you have three colours? Four colours? Five colours? Try, in your own words, to formulate a rule for an increasing number of colours. I can choose the first colour in n ways and the second in n 1 ways multiply and then divide with 2 since the order doesn t matter. Try to translate the rule to a formula. n (n 1) / 2 Chance To pick cubes from a paper bag (better than envelope) Idea from 100 Ideas for Teaching Mathematics, Mike Ollerton. Links & literature A useful link about linking cubes: Linking Cubes and the Learning of Mathematics Making Algebraic Structure and Mathematical Thinking Accessible to Learners of all Ages, Paul Andrews, Association of Teachers of Mathematics

6 Multilink cubes Material Double sided dotted paper and multilink cubes. Instructions Try to build these figures. The numbers in the brackets show how many cubes are needed. Turn the paper over. Build your own figures and draw them. The numbers in the brackets show how many cubes are needed Turn the paper over Try to build these figures The numbers in the brackets show how many cubes are needed Turn the paper over Build your own figures and draw them Build your own figures and draw them Try to build these figures The numbers in the brackets show how many cubes are needed Turn the paper over Build your own figures and draw them