MATHEMATICAL CONTENT KNOWLEDGE -
In mental computation, students are greatly tested on their knowledge on the relationship of the
four operations and their basic facts. For example, how addition and multiplication refer to
combinations where both addends or both factors are less than 10, and subtraction and division
facts correspond to addition and multiplication facts. These basic fact concepts should be learned
n the first grade and mastered in grade 2. Strategies to master basic facts include memorisation,
using patterns, and learning strategies that are reinvented by students.
PEDAGOGICAL CONTENT KNOWLEDGE -
In addition and subtraction, the JUMP strategy can be used as it requires the user to keep one
number unchanged, break up the other number, and add or subtract parts.
Example of subtraction: 76 - 33
The student might jump down from 76 to 46 (subtracting the 30 from 33), then
take away 3 more to achieve 43.
Another strategy used in addition and subtraction is the SPLIT strategy, where the user breaks up
both numbers, adds or subtracts the place value parts, and recombine the added parts to make
the sum.
Example of addition: 45 + 38
The student might add (40 + 30) to get 70, then add (5 + 8) to get 13. Then 70 + 13 = 83.
A third strategy for addition and subtraction is the COMPENSATE strategy, where the user will adjust
one number (building up or down), add or subtract parts, and adjust the sum (difference).
Example of addition: 36 + 19
The student might think 36 + 20 (rounded 19 to a 20) to get 56, then -1 again to achieve 55.
Strategies in mental computation in multiplication can include:
- Doubling E.g. x2, x4, x8
- Multiplying with multiples of 10/using place value E.g. x10, x100, x20
- Multiplying with 5 or 50 E.g. x5, x50
- Using a known fact
- Doubling and halving E.g. 4x6 can be halved and doubled into 2x12
- Using compatible pairs or using factors
- Multiplying front first
- Rounding and adjusting
Strategies in division can include:
- Using multiplication E.g. 45/5 = 9 because the quotient is 9 since 9x5 = 45
- Halving E.g. 60/2, half of 60 is 30
- Expanding the dividend E.g.
- Doubling or multiplying both numbers
Reference: (Van et al., 2015)
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Activity - Doubles Bingo
Year Level - 2
Classroom Context -
To cater to students with sensory needs, provide graphic representations or picture cues to help
them understand the doubles concept. Either draw pictures or search up pictures from the
internet that can help students visualise the concept of doubles better.
Content Descriptor -
Solve simple addition and subtraction problems using a range of efficient mental and
Learning Objectives -
This fun activity will allow students to learn the addition strategy of adding doubles using
mental computation. There are many real-life examples of ‘doubles,’ such as objects that
come in pairs. This game will help students understand and recall their double facts.
Resources -
Key Mathematical Language:
Double, add, total, altogether
Hands-on Manipulatives/materials:
Whiteboard, pens, dice, counters, doubles bingo charts
Prior Knowledge -
Students should be familiar with the concept of addition as well as basic addition facts
Students can recognise simple patterns in everyday contexts
Students can copy simple patterns
Students can build and subtract numbers by using objects or fingers
Instructions -
- With the whole class together, list double factors up from 1 to 10 and write them on the whiteboard as ‘1+1=2, 2+2=4’ etc.
- Ask students to contribute by asking them to give examples of what comes in twos, fours, and so forth. E.g. A pair of shoes, a dog with 4 legs, a pack of 6 soft-drink cans, a spider with 8 legs, 10 fingers, a dozen of eggs, etc.
- Split students into small groups for a game of doubles bingo.
- Starting with one student, they will roll a dice and whichever number it lands on, they must double it and place a counter on the number on the game chart.
- Go around the circle for each student to take turns. Challenge them to see whoever achieves 5 counters in a row on the chart. Let them play until every student gets 5 in a row or until time runs out for the session.
Questions to ask -
What are doubles?
How can doubles help us answer other addition problems?
What are some real-life examples you can think of, of double factors?
Enabling Prompts -
For student who find this game challenging to play, sit them down and give them two dice.
Allow them to roll one dice and match the other dice with the same number. Ask them to
figure out the total of the two dice added together.
Extending Prompts -
For fast learners, give them an extra activity. Give the student two dice. They must add the total
of the two dice and double that.
E.g. Student will roll a 6 and then roll a 4. The total of this is 10. The double of 10 is 20.
Images -
Students will roll their dice, count the number, double it, and put a counter over
the number on the chart.
Reflection -
In week five, we focused on mental computation and how to teach it. The importance
of mental computation has been identified by a significant amount of research, resulting
in the finding that 80% of all calculations by adults are carried out mentally, and that making
estimations are quite frequent (AAMT). Research also indicates that an emphasis on mental
computation can improve students’ development of number, and the teaching approaches of
this should reflect on everyday life. The big ideas of mental computation include key number
knowledge, generalising patterns and relationships, developing fluency and flexibility and
thinking strategically. This is reflected in the above activity, as I chose to create a simple, fun
and engaging activity for children of the younger grades, that aids them in building fluency and
patterns by carrying out calculations in their heads (AAMT). I personally had the opportunity to
carry out this activity with my students from a previous placement, and the results of it were
really successful. The students were engaged, challenged and competitive. It pushed them to
think strategically and allowed them to use strategies from some previous doubles lessons that we had.
References -
Australian Association of Mathematics Teachers. (2018). Mental computation.
Retrieved from https://www.aamt.edu.au/Topdrawer/Mental-computation
Van, D. W. J. A., Karp, K. S., & Bay-Williams, J. M. (2015). Elementary and middle school
mathematics: teaching developmentally, global edition. Retrieved from https://ebookcentral-proquest-com.ezproxy.library.uq.edu.au
