Bean bag shot problem
Teacher's notes
- Finds the lowest and highest total.
- Lists total from scoring 2 three times as the 'middle score'.
- Works systematically: 'all scores the same' and then 'two scores the same'.
- Continues to find 9 of 10 possible scores.
- Omits the total from scoring 1 + 2 + 5 from 'one of each score'.
Next steps
Find out which numbers between the lowest and highest totals cannot be made with scores from three bean bags.
Daniel's own bean bags problem
Teacher's notes
- Sets a new problem to challenge a friend.
- Chooses larger scores.
- Finds 9 of 10 possible total scores.
- With support of probing questions, finds tenth possibility, one bean bag in each bucket to give 4 + 8 + 9 = 21.
Numbers on a line
Teacher's notes
- Draws an empty 0–100 number line and positions 25, 50 and 75 with reasonable accuracy.
- Places markers appropriately for his secret numbers, 33, 47 and 61.
- Decides his friend's estimates of 49 and 65 are reasonable.
- Explains that the estimate of 45 for his '33 marker' is not good 'because 45 would be closer to 50 not 25…and 33 is about halfway between'.
What the teacher knows about Daniel's attainment in Ma1
When breaking into a problem, Daniel suggests ways to get going. He becomes very focused when he pursues a line of enquiry and is keen to work through to draw conclusions. He can sustain his interest over a number of days.
When solving problems like the bean bag problem, Daniel works systematically to find possible scores. He records clearly and in an organised way. He perseveres to find as many scores as possible. He checks and explains how he knows there cannot be other scores. He appreciates the nature of problems he is given and sets challenging examples for his friends to solve.
He solves problems in a range of contexts, most successfully when working with numbers, money and measures. For example, he measures heights accurately to find out which children in the class could go on a ride at the theme park, where there is a minimum height requirement of 1 m 45 cm. To solve the problem, he explains, 'We don't need to know how tall each person is. We just need to measure whether they are as tall as the 1 m 45 cm mark and put them on the list: "Can go on the ride/Can't go on the ride"'. Daniel thinks about others' solutions and comments on whether they are appropriate or feasible.
Summarising Daniel's attainment in Ma1
In class discussion, Daniel suggests ways to approach problems. He works mentally as he solves problems but records clearly and is beginning to appreciate different purposes for recording, for example to remember what he has done so far, to check his work and to share and compare solutions. He is beginning to work systematically and this is reflected in the way he organises his recording. He uses and interprets a range of diagrams and mathematical symbols such as +, -, ×, ÷ and =. In discussion he demonstrates his reasoning, for example by finding an example to match a general statement given by the teacher.
His performance in this AT is best described as working securely in level 3. To make further progress within level 3, Daniel needs to experience a range of problems involving shape, position and movement as well as number problems and investigations.
