 # 100 things to do with a hundreds chart

Ok, not quite 100. Yet. But this is a work in progress.

The idea is this: all math students see a hundreds chart and write out the numbers 1 to 100 in a grid format innumerable times in their childhood. While this rote exercise is all pervasive, there are so many more mathventures to be had with this easy to use, cheap to source material. So here are a list of teaching ideas based on the hundreds chart ranging from addition patterns to GCD, multiplication to modular arithmetic.

Some of these ideas are common knowledge, some are original but many are sourced from elsewhere in the web and I have tried to link to the source in such cases.

#### 1-10: Pre-Primary: Learning the Numbers, Place Value

1. Number Writing: The ever popular – write out all the numbers from 1 to 100 (or, I recommend 0 to 99) in an empty 10×10 grid.
2. Fill in the blanks: A close second – Fill in the missing numbers in the 1 to 100 (or, I recommend 0 to 99) number chart.
3. Mystery picture colouring: Colour in different cells with different colours based on the number to create a pixelated picture of a mystery object.
4. Make a Number Line: Cut the 1-100 (or, I recommend 0 to 99) chart into rows and stick them together to make one long number line, helping kids to visualize how 34 is more than 18 for example.
5. Number Line with a Twist: Wrap the number chart to make a cylinder and then give a slight twist making the end of one row coincide with the start of the next and tape it in place. Trace the number line around this cylinder starting from 1 (or 0) all the way to 100 (or 99). (Src: whatihavelearnedteaching.com)
6. Jigsaw puzzle: Cut up the 100’s chart into uneven pieces (but always along grid boundaries) and the challenge is to reassemble the chart.
7. Find my Number: Teacher chooses a secret number between 1 and 100, kids ask questions to try and figure out what it is. Kids use the number chart to mark out responses like too high / too low to narrow down the search and find the secret number.
8. 1 More 1 Less: Students use a small square of paper with arrows and put it over the number the teacher calls out. Then figure out 1 less and 1 more than that number. It might help to do this on a number line first and then the grid.
9. 1 More 1 Less, 10 More 10 Less: Students use a small square of paper with arrows and put it over the number the teacher calls out. Then figure out 1 less and 1 more than that number.
10. Race to a 100: All players start by placing their counters at 1 (or 0). Players then take turns throwing a die or spinning a needle and moving forward that many places. The dice / spinner should be able to give a score of 10 so that the pattern of moving down a row for 10 becomes discoverable. The first player to reach exactly 100 is the winner.

#### 11-25: Primary - Understanding Numbers, Place Value, Addition, Subtraction

1. The Arrow Game: The teacher calls out a number that marks the starting number in the hundreds chart. Then writes down a sequence of Up / Down / Left / Right arrows to traverse the chart from that starting point. The challenge is to find the final square. Or given a starting number and ending number, students are to come up with a sequence of arrows for it. (Src: mathwire.com) Once students gain confidence, can be extended with arrows along the left and right diagonal as well.
2. Four in a Row on a Hundred Chart: Two or more students (more the better) start with an empty hundreds chart (10×10 grid) and different coloured pencils. Each one takes turn writing a number in a cell – it must be the correct number for that place in the hundreds chart. Getting 4 numbers in a row or column in your colour gets you one point. This again requires children to think about place value and the relationship among the numbers on the chart to score points and more importantly to block their opponents. (Src: k-5math)
3. Jigsaw puzzle pieces: Given a 3×3 grid that is part of the number chart, fill in the missing numbers. Or fill in the missing numbers in puzzle pieces of various shapes. Or a puzzle piece can be left empty challenging the student to find all the possible values that can work for it. Students can also design their own puzzle pieces and challenge their friends.
4. Addition Paths: Use the hundreds chart to demonstrate patterns in addition by drawing paths. For example: 13 + 9, 33 + 9, 43 + 9 have similar paths – the 10 more and 1 less path. Will adding 9 always give this kind of path? Can you describe the path? (Src: NCERT Grade 3 textbook)
5. Subtraction Paths: Use the hundreds chart to demonstrate patterns in subtraction by drawing paths. For example: 13 – 9, 33 – 9, 43 – 9 have similar paths – the 10 less and 1 more path. Will subtracting 9 always give this kind of path? Can you describe the path?(Src: NCERT Grade 3 textbook). This is one activity where having a 0-99 chart rather than a 1-100 chart makes a lot more sense.
6. Ways of Counting: How many numbers between 8 and 23? Do you count 8? Do you count 23? Both? Neither? These exercises can be used to illustrate inclusive / exclusive counting and demonstrate the difference between counting objects and counting intervals.
7. Race to 100 revisited: All players start by placing their counters at 1 (or 0). Players then take turns throwing two dice of different colours and moving forward that many places. One is the 10’s die and the other is the 1’s die. The first player to reach exactly 100 is the winner.
8. Skip Counting: Start at a random place in the hundreds chart, skip count by 2’s / 3’s / 5’s etc colouring in the squares you land on. Observe and describe the patterns.
9. Odd / Even colouring: Colour all the odd numbers one colour, all the even numbers another colour. What do you notice? Describe the pattern. Are there more of one than the other?
10. Hundreds Chart Bingo: Each students selects a portion of the number chart – a 5×5 grid anywhere on the chart – that they want to play with. Teacher will call out number characteristics. Students mark off those numbers on their Bingo “ticket”. The student who gets a row or column or diagonal crossed out first is the winner. There will be lot of heartache and “not fairs” but the payback comes in discussing at the end of the game which part of the 100’s chart would have been a best pick for this specific set of number characteristics.
11. Rounding: Demonstrate and allow kids to visualise rounding off to the nearest 10 by drawing a line just before and after the 5’s column. Show how 5 could go either way and everyone just decided to go higher. Erase the line after the 5’s column to show 5’s round up rather than down. On a 0-99 chart this line coincides nicely with the middle of the chart whereas it looks lopsided in the 1-100 chart.
12. Poke a Hole: Print the 1-100 (or, I recommend 0-99) chart on both sides of a paper (make sure the margins are the same on top, left and right). Now, a student holds the sheet with one side facing him and pokes a hole in a number of his choice. The challenge is to predict what number is on the hundreds chart on the other side of the paper. While initially baffling, kids will slowly figure out the pattern and start guessing right.
13. Mystery picture colouring revisited: Colour in different cells with different colours based on a set of number riddles / addition or subtraction problems to create a pixelated picture of a mystery object.
14. x and + addition: Choose any 3 by 3 grid on the hundreds chart. Draw a + and a x in it. Add the numbers along each arm of the + and each arm of the x. They add up to the same total. Does this happen for any 3×3 square on the hundreds chart? Why does this work this way?
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#### 26-35: Primary - Number Sense, Multiplication, Division

1. Multiplication Paths: Use addition paths to demonstrate multiplication as repeated addition on the hundreds chart thus creating new multiplication paths. Observe and describe the patterns.
2. Multiplication table colouring: Colour in the multiples of 2 in a hundreds chart. Observe the pattern. What would you call this pattern? Similarly colour in the multiples of 3 in another chart. Observe. Repeat for all the tables, observing the patterns and describing them.
3. Multiplication table family colouring: Colour in the multiples of 3, 6, 9 using different colours in a single hundreds chart and observe the patterns. Why is it this way? Repeat for tables of 2, 4, 8. Does this pattern seem similar to the 3/6/9 in any way?
4. Name Pattern: Write your first name over and over in an empty hundreds chart (10×10 grid) – one letter in each square. Colour in each square where the first letter of your name appears. Observe the pattern. Does this seem familiar? Why? (Src: mathwire.com)
5. Race to 100 revisited: All players start by placing their counters at 1 (or 0). Players then take turns throwing two dice and moving forward by as many places as the product of the numbers on the two dice. The first player to cross 100 is the winner.
6. Division as repeated subtraction: This would be ideal with a 0-99 chart. To make it work on a 1-100 chart, you could add a 0 just before the 1. Starting at the square of the dividend, use subtraction paths of the divisor till you reach 0 to demonstrate division as repeated subtraction.
7. Division as inverse of multiplication: Use the coloured in multiplication tables sheets to answer division questions.
8. Hundreds chart patterns: Colour in the appropriate squares of a blank hundreds chart (a 10×10 grid) given a rule in words like “every third square”. Then try the inverse. Show a blank hundreds chart with some pattern of coloured in squares. The challenge for the students is to observe the pattern, identify the rule and write it in words. (Src: tes.com)
9. Tiling the grid:
10. Choose a number, eliminate its row and column, choose the next. Repeat until you can choose no more. Add the selected numbers – always add up to the same sum.

#### 36-40: Upper Primary / Middle - Factors, Multiples, Primes

1. Finding Factors:
2. Factors and Multiples game:
3. Factors and Multiples solitaire:
4. Factor Blaster:
5. Prime Sieve: In a hundreds chart, divide each square into eight sections. (You can use this 1-100 chart or this 0-99 chart) Students colour in multiples of 2, 3, 4, 5, 6, 7, 8, 9 in different colours. Observe the patterns, the numbers that have escaped colouring. Is there anyway to get these numbers coloured in?

#### 40-45: Upper Primary / Middle - Fractions, Percentages, Decimals

1. Marking fractions
2. Marking decimals
3. Marking percentages
4. Converting between fractions, decimals and percentages
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#### 46-50: Middle - Integers, HCF, LCM, Modular math

1. Mark positive and negative integers on an empty 100s chart (10×10 grid) and perform arithmetic.
2. The Flip Game: Arrange 30 coins on the numbers 1-30 in a hundreds chart – one in each cell, all with heads facing up. Now starting at 3, flip the coin in each cell that has a multiple of 2. Then start at 4 and flip the coin in each cell that has a multiple of 3. So on till 10. Now observe which of the coins are heads and which are tails. Can you reason why this is so? Can you predict what numbers would be tails if you repeated this for numbers upto 50? Test your hypothesis. Now can you predict for numbers upto 100?
3. Finding LCM by drawing paths
4. Euclid’s game: Two players play against each other taking turns choosing numbers. Each player can choose any number they want for their first move. But from then on a player can only choose a number that is the difference of any two numbers already chosen. The player who finds himself unable to make a move loses. In trying to develop strategies to win at this game players will make many key observations and discoveries. (Src: cut-the-knot.org)
5. Rainbow colouring: