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"Use Me", says Calculator
Hi, I am the Calculator. In the adult world, I'm fairly ubiquitous, in fact quite indispensable for many. But I miss children terribly. Also, I feel sad because when a child picks up me (a calculator), immediately I am put down as somebody who will spoil the child's mathematical abilities and habits.
I do not really blame the adults for such a biased perception of my role in life and utter ignorance of my role in learning. After all computation, mental math and speed are considered of prime importance by many. However, according to me, the essence of mathematics is in conceptual understanding (and not in procedural competence). Hence, a mere tool like me can only aid in understanding of concepts. Also used judiciously I can also help build procedural abilities.
I am not going to argue the above case - rather I will show you examples of how you can use me to build both - conceptual understanding and procedural competence - that too in children in their pre-primary and primary years. I think once you see real example of "how to" get fun and learning value from using me - I hope I will find my rightful place in mathematical development.
Before we start - please realise that I will be required to be given to and used by children only when they are doing these activities / games. They need not "have it' all the time. Also for most of the activities mentioned here, a simple calculator is what is required (not the advanced one or one available in mobile phones). Typically a school can have enough common calculators as activity resource in their math labs.
For Pre-Primary years (3-4-5 years)
- Explore Calculator - this is more like a pre-activity. The idea is to just give me (the calculator) in children hand and let them press whatever keys and see what happens. Obviously, you'll know - no matter what key combination they press - they cannot harm me!
- Counting Scorecard - This is used for simple counting (upto 8). For example one child aims a ring over an object and every time he "rings", another child records success (score) by pressing any digit once. So if the child presses digit 8 five times, he can count and call the score as "five". We have interestingly used this to find out how many times, in a day, a child went to toilet (just for the fun of statistics :).
- Dice Digits - A game to reinforce the count (quantity) and digit (symbol) relationship. Use a dice with dots only. Child rolls -counts - and then enters the corresponding digit. Since they are not forced to write - the children here can focus on the correct digit rather than correct way of writing it. If required, once the digit is confirmed - they can copy it on their note book.
- Guess my number - A child presses any digit a few times. Ask the other to guess, "How many". The other child presses some numbers in his calculator game to show his guess. Then both compare. If both the quantity matches - they dance together :)
For Pre-Primary years (5-6-7-8 years)
- Reach Me - Each child (or team) plays on own calculator and speed is of essence. Everybody starts with same number (say 4). A target number is announced - say 71.
Level 1 - Children (or team) have to add or subtract any number(s) to starting number (4) and reach target (71) as fast as possible.
Level 2 - Children have to reach target number is exactly five steps.
Level 3 - To bring in subtraction - start number is big (eg: 198) and target number is small (eg: 13)
Level 3 - Multiplication and Division is also brought in and target numbers can be much bigger numbers.
- Got It: (Two players) After clearing the calculator's memory, two players select a target, (say 23). Each child takes turns entering a number of their choice from 1 to 5. Every time a child chooses a number, she presses the memory-plus (M+) key. This stores the cumulative total in my (calculator's) memory - while the children have to add and keep the total in their mind. When one of the players thinks she has reached the target (23) - she says "got it" and presses 'Memory Recall' button (MR) to check and, if correct, wins.
- Score Card - One simple way to use me (calculator) is to keep scores (for any other game). Children simply enter the number to be added and press the memory-plus (M+) key. Pressing Memory Recall button (MR), at any point gives the current cumulative total.
- Checker Calculator - One player rolls two dice, mentally adds them, writes down the sum. The same player rolls the dice again and adds it to the previous sum. The other player uses me (calculator) to check the sum. Switch roles. No time limit. No winner. This is just to reinforce addition skills using regrouping.
- Table Manners - Multiplication or multiples of any number is relatively easily available in me (calculator). All you have to do is
~ enter the base number
~ press the + (plus) sign
~ followed by = (equal) sign.
Now every subsequent press of = (equal) sign gives the next multiple of the base number. This simple way of getting Multiples explores tables in many ways. One way is to determine - which number (between say 1-12) has how many multiples.
- Except 1 - Any target number is taken (say 28). Using all the numbers on me (the calculator) - except 1 - find out in how many different ways can you reach that target number? The one who finds more ways is the winner. Or as a class try to find loads of ways. Variation: make different exception rules - like reach 55 -without using 5 - in minimum key presses.
- As many - Take any two (or three) numbers. Now using any mathematical operations and ONLY the chosen numbers (as many times as you want) - try to make as many different numbers - between say 1 and 50.
- Number Golf - Few target numbers (each number representing a hole on the golf course) are decided - say 52, 124 and 201. Now each player chooses any three (or two) numbers as 'my numbers' (Players can choose common numbers also). Now they add or subtract only their numbers to reach the first target number. The number of times they add or subtract is their score. They use me (calculator) to work this out (all the while) recording the number of 'shots' on paper. Whoever covered all the target numbers with minimum steps - is the winner - just like golf!
Eg: Player Mr X choose 2, 5 and 50 >> Mr X got 52 (1st hole) in 2 steps (50+2); Got 124 (2nd hole) in 8 steps (50+50+5+5+5+5+2+2); and got 201 (3rd hole) in 7 steps (50+50+50+50+5-2-2); So Mr X's total score is 17.
But Miss Y chose 1, 25, 100 >> Ms Y got 52 (1st hole) in 4 steps (25+25+1+1); Got 124 (2nd hole) in 3 steps (100+25-1); and got 201 (3rd hole) also in 3 steps (100+100+1); So Ms Y's total score is 10 (wins over Mr X). Can you beat both Mr X and Ms Y? Use me (calculator) and try.
- Finding Factors: Do individually, in pairs or as whole class. Put any number (say 42) into the memory of your calculator and find which numbers divide it exactly. How many factors 42 has? Try with other numbers up to 100. Can you find numbers with only 2 factors? (tabulate them). Can you find numbers with an odd number of factors? Is there a rule?
- Meeting all friends: Using only 2, 3, +, -, x, and = (7 keys) can you make all the numbers till 20. Show how you did it. Try with other combination and range.
- Got it: Draw a grid of day 10 x10 and fill each square with any numbers between 1-100. Each child tries to take turn and grab a square by showing on his calculator using only multiplication of two numbers. (x 1 is not allowed). (Use a specific colour token or crayon to grab a square). The player who grabs four squares in a row is the winner.
Its quite obvious - that all the above games can have many variations. Encourage children to come up with their own variations and even their own games when they work with me (calculator). I enjoy being in the hands of children and making them think, analyze, guess, predict, win and yes, enjoy numbers.