Published about 2 years ago by Ann Baker
Use this DOES IT MATTER slide to initiate conversations about what order to subtract and add these numbers.
Download a copy here, to use with your class if needed: DiM4 Subtraction1
We spend a lot of time learning how to read and write from left to right, in a set order. All of a sudden students are expected to look at a number sentence or question such as those presented in this DOES IT MATTER and decide whether to simply read left to right and carry out the operations in the order presented or to chunk particular parts together first.
In the examples given here it is important to know that the changing the order in which the two operations are worked out will create 2 different outcomes and to be able to explain why that is so. Many students come to understand that addition is commutative and then over generalise commutativity to questions such as the ones presented above.
We can see that each question has 2 possible answers depending on the order in which the operations are worked out in For 8 – 3 + 1
Students need time to explore and explain why this is so. More importantly though they need to match which interpretation to use in a particular situation. For example: a) l had $8 in my purse. I spent $3 and then found a dollar coin. How much money do I have now? as opposed to: b) I had $8 in my purse. I spent $3 on a notebook and $1 on a pencil. How much money do I have left?
The next step is to be able to link the number sentence to match the intent: a) (8 – 3) + 1 b) 8 – (3 + 1)
Maybe we over complicate things when we explain and should listen to and watch how students can come to make sense of things.
Allow time for students to compare answers and talk about what they notice and encourage them to use brackets to 'chunk' parts to match a word problem that they have created with the numbers and operations given.
Remember that these discussions are intended to lead to deepening understandings so it is important that students and teacher both listen to the ideas and reasoning of others and challenge thinking respectfully and constructively. Only under 'safe and respectful' conditions can students take a risk and explore ideas as they make mistakes, clarify thinking and test the validity of their reasoning.
This second DOES IT MATTER looks like the first one except that the questions only use subtractions. This time the order in which the operations are carried out doesn’t matter and using a collection of objects may help to make this clear.
Download a copy here, to use with your class if needed: Does It Matter 1 - subtraction-2
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