Dewch i Feddwl Mathemateg (9 i 11 oed) Gwers 7 Anghenfilod Rhif
Lesson Plan
Abstract 
Introduce the class to the notion of children who are fussy eaters and what this means. Tell them that there are some very fussy monsters who prefer to eat certain types of numbers and the task today is to try to work out how they are choosing their numbers. The monsters are coming to dinner and they must provide them with the numbers they like to eat. 
Episode 1 
Intro Draw a grid on the board with the headings ‘eaten & noteaten’. In the lefthand column write 10 and in the righthand column write 17. Explain to the children that you want to know: ‘Which numbers the monster does eat’ and ‘How he chooses which ones to eat’ and scribe these two phrases on the board. Ask the children in pairs: ‘Can you give me another number that will go in the ‘eaten’ column?’ Respond to their suggestions by writing numbers in the correct column but without giving reasons. (This monster eats any multiples of 5.) After several numbers appear in the grid it is important to challenge the children to think about why the numbers are ‘eaten’ rather than continuing to take random suggestions. Ask them to think about a rule for the numbers which are allowed to be ‘eaten’. Ask them to choose numbers which will prove or disprove these rules. Tell the class that they are now ready to find out about the Sameosaurus. In a new grid write 4 and 10 in the ‘eaten’ column and 2 and 12 in the ‘noteaten’. (This monster eats only multiples of 3 plus 1, or 3n + 1.) Children now have a few minutes to work in pairs to decide how this monster is making his choices. Ask them to volunteer a number he will/will not eat initially without giving a reason and write it in the correct place on the grid as in the previous activity. 
Group Discussion Once all pairs have made a suggestion and their numbers have been recorded ask the children to work in groups of four to refine their reasoning and agree on a rule. Give the children marker pens and A3 paper so that they can copy and reorganise the numbers in the grid as they look for patterns. Do not spend too much time on discussion as the children need to be challenged over the final table of eaten and not eaten numbers that results from this activity. The confusion here for many children arises over the way they will explore additive links without looking for a multiplicative solutions. Many will suggest strange additive links like + 18 which will work due to the change each time being 3. It may help to move the children on by choosing numbers that challenge their initial ideas. 
Sharing Allow each group to share their reasons without suggesting any new numbers. Once all ideas have been noted down encourage them to explore and test each one. As they suggest ideas always relate them back to the numbers as a good test. It is also fruitful to explore the numbers he dislikes and to look for patterns here. Many children will latch upon the sense of 3ness present here and depending upon how near or far they are you may wish to list the numbers, in order, he likes above those which he does not like to develop the perception of multiplying by 3 and adding. A good suggestion is to write all of the numbers from 1 – 20 in a line but to underline or ring the numbers eaten. Many children will have difficulty with the fact that they are dealing with a twostep relationship ie x 3 and then adding 1. Explore different ways of writing this rule: a) One more than the three times table b) times by 3 and add 1 c) x 3 + 1 d) Any number times by 3 and add 1 e) n x 3 + 1 or (n x 3) + 1 f) 3 x n + 1 or 3 x n + 1 g) 3n + 1 Note that it is not necessary to come up with a classic ‘algebraic’ description as in c to f above. However, if the children only describe it using model a, you might with to ask them ‘So, if I take any number, how can I turn it into a number that he will eat?’. This will shift them into using a sentence like d and then into shortening it to statements like e to g. [Numbers eaten: 4, 7, 10, 13, 16, 19, 22, 25, etc] 
Episode 2 Number monster, ‘Changeosaurus’ 
Intro Give the name of this monster and draw the grid to include two ‘eaten’ and two ‘noteaten’ numbers i.e. 10, 17 and 4, 9. (This monster eats only square numbers plus 1 or n 2 + 1.) Children now have a few minutes to work in pairs to decide how this monster is making his choices. Ask them to volunteer a number he will/will not eat initially without giving a reason and write it in the correct place on the grid as in the previous activity.

Group Discussion The children work in groups of four to suggest other eaten numbers and how the monster is choosing (as per the previous activity). Again, the children may want to use marker pens and A3 paper to make notes and test hypotheses. 
Sharing The children consider and discuss the variety of ways to think about and describe the number patterns: Times by itself and add 1 (n x n) + 1 n 2 + 1 [Numbers eaten: 2, 5, 10, 17, 26, 37, 50, etc] 
Episode 3 
Intro Ask the children why they think the monsters are named the way they are – take some suggestions and explore their reasons. Tell the class that we are going to put the numbers onto a number line to see why they got their names. 
Group Discussion Ask the children to use Resource Sheet A to plot the numbers for Sameosaurus and Changeosaurus onto a number line to see the patterns they make. The children can label and join strips together to create representations of the two number patterns. They need to discuss what the number line enables them to see. 
Sharing The children discuss what the number line enables them to see about the two number patterns and how this helps them think about the names of the monsters: • Sameosaurus: three every time, the jumps/spaces/gaps are the same; • Changeosaurus: different sized jumps/spaces/gaps each time. 