A Halloween Problem

Ann was running a demo lesson with the year 3s at Crestmead Primary School this week. Ann told the class that she wanted to make 12 trick or treat bags for a Halloween party but didn’t know what to put in them. The students were quick to identify the quintessential ingredients for the bags. The problem that emerged is shown below along with a few student samples that demonstrate a wide range of strategies.

12 bags

Each bag will have:

6 sour worms

2 sets of vampire teeth

5 bubble gums

4 jelly snakes

10 mini- marshmallows

3 lolly pops

13 little chocolates

How many of each type of sweets will that be?

How many sweets will that be to fill the bags altogether?

Student Work

This problem had just the right amount of desirable difficulty for the class who were engaged readily and who persisted with the problem solving process. As is usual with these problems there was a broad range of approaches allowing students multiple entry points into the problem.

Not all students answered all parts of the problem as can be seen in Hayden’s work sample. Hayden however demonstrated that he had interpreted the problem as a multiplicative situation and linked the multiplications to two different representational forms for multiplication. He is developing a firm foundation for connecting these strategies to the more formal strategies of multiplication. You can also see that Hayden was applying fix up strategies as he worked.

Roania’ work sample shows that she is able to use known multiplication facts flexibly. She has used the distributive property to split 12 into 10 and 2 because she ‘knows her 10s and knows how to double’. The realism of the problem connected to her and is manifested by her idea of presenting each type of sweet in its own box so that it could be used as a shopping list.

Roma’s strategy though not fully correct or complete (she was working on her fix up strategy when time eluded her) focussed on the second question rather than the individual parts. She worked out 43 sweets in each bag and began to carry out a repeated addition with chunking. As she began chunking her answers, place value problems became visible. As formative assessment these types of problematised situations make visible gaps and error patterns that might otherwise go over looked.

The following work sample shows how one student checked the reasonableness of his answers, giving ticks before moving onto the second question, how many altogether. As a work sample that shows the working out and steps involved this one really makes the student’s thinking visible.

And last, the next sample shows counting in 2s, 3s and 5s as well as the use of tallies, with the totals being rearranged to make good use of friendly numbers.

Over all the samples give a snap shot of the range of strategies and levels of development that can be seen in any class. We’d like to say thank you to this class and the teachers involved. The students were AWESOME.