Ideas for problem solving 1. Where will the postman call next? Have a large number line at the front of the class for reference. Introduce the idea of a postman calling at houses to drop off letters. Have your postman call at regular intervals e.g. doors numbered 3, 6, 9, 12. Ask the children if they can predict where the postman will call next. Questions to ask. “Can you explain to your partner how you knew it was that house?” “Can you explain the pattern using a number line?” “Can you tell me a house number over 20 that you know he would not call at?” “How did you know that?” “What house number will he deliver his seventh / seventieth letter to?” “How could you check this?” This activity can be adapted to any age group. It can be simple patterns such as multiples of 2, 5, 10 or extended to include prime numbers or sequences such as +1 +2 +3 +4. You may want the children to solve postman puzzles that you set for them or ask them to devise puzzles of their own for a partner or the class to solve. Related NNS Objectives: See “Solving Problems” sections of the Framework. Plus… Reception Count in tens, Count in twos Year 1 Describe and extend number sequences Begin to recognise odd or even numbers. Begin to count in steps of 3 Year 2 Count in steps of 3, 4, 5 to at least 30 and back to zero. Year 3 Recognise 3 digit multiples of 50 and 100. Describe and extend number sequences Year 4 Recognise and extend any number sequence formed by counting from ay number in steps of a constant size. Recognise multiples of 3, 4, 5 and 10. Year 5 Recognise multiples of 6, 7, 8, 9. Year 6 Recognise and extend number sequences such as the sequence of square or triangular numbers. 2. Make it bigger. This activity can be adapted for any age group but if it is used for younger children then models can be many cubes high, but should only be 1 cube deep. Present the children with a multilink model of roughly 6 blocks. E.g. an “h” or “s” shape. Ask the children if they can work out how to make the model exactly twice as big. Questions to ask “Can you estimate how many cubes you will need” “Can you explain to your partner how you decided on your estimate?” “Which part of the model was the hardest part to estimate?” “Why?” ”Which part was the easiest?” “Why” “How are you going to check your answer?” “How many cubes would you need if you were going to make it 2, 3, 100 times bigger?” “How do you know?” “How could you check?” Children may want to record their predictions or findings on squared paper. NNS related objectives: Year 1 Make and describe models and patterns Use one or more shapes to make, describe and continue repeating patterns. Year 2 Explain how a problem was solved orally. Make and describe shapes using for example solid shapes. Year 3 Relate solid shapes to picture of them. 3. How many rectangles? Recap / discuss the properties of rectangles. Provide children with different lengths of string and 1cm squared paper. The pieces of string should be lengths that are multiples of 12cm in order to create the most rectangles. Ask children to investigate how many rectangles can be made from each piece of string. They should use the squared paper to help produce and record their rectangles. (This activity can also be extended to include work on area. Children can explore, using the string, the rectangle with the largest or smallest area to perimeter ratio.) Questions to ask: “What do we know about rectangles?” “How is a rectangle different from a square?” “How could we record our answers?” “How could we make sure we don’t make the same rectangle twice?” “How many rectangles can we make from a length 12cm?” “How many rectangles can we make from a length 24cm?” “How many could we make from one 120cm long?” “How could you check?” “What did you need to know / think about, when predicting how many rectangles you could make?” “If you were to do this again, what would you do differently?” “What would have made it easier?” “How did you decide what to do first?” Related NNS Objectives: Year 3 Measure and compare using standard units. Classify and describe 2D shapes. Year 4 Make shapes and discuss properties. Measure and calculate the perimeter and area of rectangles and other simple shapes. Year 5 Understand, measure and calculate perimeters of rectangles and regular polygons. 4. Wizard’s potions This worked particularly well during the Harry Potter phenomenon! Present children with different sized bottles labelled as different ingredients for a spell and with different labels of l. and ml. E.g. fairy sparkles 350ml, raindrops 10 ml, frog juice 5ml, newt jelly 505ml, bat tonic 25ml, crocodile slime 75ml Tell children that in order for wizard spells to work, they must add up to exactly 1 litre. Ask them to investigate how many different spells they can make using the ingredients. The children may need to use number lines to keep track of how much of each mixture they have used. This activity can focus on both addition and subtraction either by continually subtracting from 1000, or by adding up to 1000. You can also do this activity practically by actually using the bottles to pour liquids into a 1litre container. It can also be adapted for use with decimals or much smaller numbers for younger children. It can easily be differentiated by including more or less ingredients for the children to choose from and by introducing questions such as: “What is the fewest number of ingredients you can use to make a spell?” “What is the most number of ingredients you can use to make a spell?” “Can you use exactly 3, 4, 5 ingredients to make a spell?” Questions to ask: “Which numbers look the easiest to use?” “Why?” “Which number do you think will be most useful?” “Why?” “Are there any numbers that look tricky to use?” “Why?” “Can you spot a spell you could calculate straight away in your head?” “Can you explain to your partner how you worked this out?” “Can you explain how you are going to make sure you know what you have put into your spell?” “Can you think of a way of presenting your ingredients to prove they add up to exactly 1L?” “How could you check you were right?” “Can you think of a way of presenting your results so that someone else could follow your recipe?” Related NNS Objectives: Year 2 Use mental addition and subtraction to solve simple word problems involving numbers in real life, money or measures, using one or two steps. Explain how a problem was solved orally. Year 3 Choose and use appropriate number operations to solve word problems and appropriate ways of calculating, mental, mental with jottings, pencil and paper. Pencil and paper procedures 43, 45 Use informal pencil and paper methods to support, record or explain HTU + TU and HTU + HTU Year 4 Choose and use appropriate number operations and appropriate ways of calculating.