You have 13 cents to spend at the store on gifts for your friend's birthday. Show by writing and/or drawing what you would choose to buy from the product list if you spent all 13 cents. (See the product list below for items.) Can you show more than one way? Write number sentences that show your answer(s).
This task was given to students who have experience finding the sum of several addends and who had been working with money. This task has 13 or more solutions, so it allows students to experience a task with multiple correct answers. It shows a child's ability to think mathematically as they combine numbers to equal a set answer. It also shows the accuracy of students' computation. The task also helps students to discover the commutative property of addition. The students will draw models of choices to demonstrate possible combinations of choices equal to 13 cents. The students will often check their choices to see if they total 13 cents. The completeness, correctness and the number of answers will determine the student level of performance. Less than one hour The time needed will vary due to mathematical ability, artistic talent, concern for neatness and number of choices found. This task can be given on the day a student in your class is having a birthday. It can be given during a unit on shopping, money or a holiday in which gift giving is involved. It is important that children be given experience in solving open-ended problems in both guided and cooperative group settings before given a problem like this to work on independently for assessment purposes. Items in the task can be adapted along with their prices to support a different theme or higher level of calculation skill.
- Coins
- Manipulatives
- Drawing paper
- Photocopies of the objects that can be purchased (for the students to cut apart)
7 + 6 = 13 (a trumpet and a boat) 7 + 5 + 1 = 13 (a trumpet, a balloon and a pinwheel) 7 + 4 + 2 = 13 (a trumpet, a top and a whistle) 7 + 3 + 3 = 13 (a trumpet and two party horns) 6 + 6 + 1 = 13 (two boats and a pinwheel) 6 + 5 + 2 = 13 (a boat, a balloon and a whistle) 6 + 4 + 3 = 13 (a boat, a top and a party horn) 5 + 5 + 3 = 13 (two balloons and a party horn) 5 + 4 + 4 = 13 (a balloon and two tops) 4 + 4+ 4 + 1 = 13 (three tops and a pinwheel) 3 + 3 + 3 + 3 + 1 = 13 (three party horns and a pinwheel) 2 + 2 + 2+ 2 + 2 + 2 + 1 = 13 (6 whistles and a pinwheel) 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 13 (13 pinwheels) These are just a few of the acceptable answers. All solutions, which total 13 cents, are acceptable. It is important that students know that 6 + 7 is the same as 7 + 6.
The Novice is unable to apply a strategy to this situation. A drawing and words are present, but they may be unrelated to the problem or the solution. Little or no math language is used to communicate.
The Apprentice will display some understanding of the problem, but the solution contains computation errors or does not equal 13 cents. There are random and weak explanations for decisions made and there is little use of math language.
The Practitioner understands the problem and comes up with at least one accurate solution. Inaccurate solutions are indicated by the student if any are present. The student uses appropriate mathematical language and clearly presents the solution.
The Expert will come up with several correct solutions. The Expert will have an appropriate equation for each and the objects purchased will be communicated clearly. The Expert may make mathematically relevant comments such as 6 + 7 is the same as 7 + 6 or that you can buy two party horns for the same price as one boat.
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