[Photo by geishaboy500.]
Are you looking for creative ways to help your children study math? Even without a workbook or teacher’s manual, your kids can learn a lot about numbers. Just spend an afternoon playing around with a hundred chart (also called a hundred board or hundred grid).
Here are a few ideas to get you started…
Addition and Subtraction
(1) Use the hundred chart as a number line to do addition and subtraction beyond what your child normally can handle. Take turns making up problems for each other to solve. Develop mental math skills by showing how to add or subtract the tens first (counting up or down) then the ones (counting left or right.)
(2) Look for addition and subtraction patterns. 3+9=? Now go to 23+9, 33+9, 63+9. What do you notice? What do 15-7, 25-7, 45-7, etc. have in common? Find other patterns.
(3) Count by whatever number you want, but start at an unusual place. Count by 5, starting at 18. Or count by 2, but start with 37. Or for a tougher challenge, practice your mental subtraction skills: count down by the number of your choice.
(4) Try some of these counting ideas with charts that start and end at other numbers. HelpingWithMath.com lets you create printable charts that start at whatever number you specify and count by whatever interval you like. You could make an even numbers chart, or a multiples of 3 chart, or . . . the possibilities are endless!
(5) How many numbers are there from 11 to 25? Are you sure? What does it mean to count from one number to another? When you count, do you include the first number, or the last one, or both, or neither? Talk about inclusive and exclusive counting, and then make up counting puzzles for each other.
Number and Pattern Activities
(6) Make picture puzzles: You give the clues — either a description of a number (“It’s two less than 26″) or an equation that equals that number — and your student colors in the appropriate square. Repeat to make a design (samples here, or try this cross-stitch heart). Now, let your student make up a puzzle for you to color.
(7) From Mathwire: Cut up a hundred board into irregular pieces to make a puzzle. For more of a challenge, cut a blank chart into puzzle pieces, writing in one or two numbers per piece. Can your student fill in the rest of the numbers? [Or use this printable puzzle worksheet. If you press the “Print” button, they will ask you for a member password (which costs money), but if you just use your browser’s print function, the page should print just fine. Refresh your screen to get a new set of numbers.]
(8) Make a hundred chart pattern (pdf) with your name.
(9) Play “Arrow Games”: Starting at the number given, each arrow means to move one square in the direction shown. What number is “45 ← ← ↑ → ↑”? How would you use arrows to say, “Start and 27 and move to 59″? Make up your own arrow code for someone to follow. Mathwire has a pdf version of this activity.
Hundred Chart Games
(11) Play “Race to 100.″ Take turns rolling one or two dice and moving that many spaces on the hundreds chart. If you correctly predict your landing place before you move (without counting squares!), then you can go one extra space as a bonus. The first person to reach or pass 100 wins the game.
(12) Play a number bonds game. Take turns pointing to any number. The other player has to say how many more it takes to make 100.
(13) Check out Hundred Chart Nim.
(14) Or try Euclid’s Game on a Hundred Chart.
Multiplication and Factors
(15) Look for counting-by (multiplication) patterns. Colored disks are nice for this, or use pinto beans. Mark the numbers you hit when you count by 2. What pattern do they make? Make the counting-by-3 pattern, or mark the 7s, etc. You may want to print several charts so you can color in the patterns and compare them. Why does the counting-by-5 pattern go down the way it does? Why do the 9’s move diagonally across the chart?
(16) Look for factors: Mark the multiplication patterns by putting colored dots along one edge or corner of each square. (That is, all the multiples of 2 get a yellow dot, for instance, and the multiples of 3 get green dots…) Which numbers have the most dots—that is, have the most factors? Which numbers have just one dot? Which don’t have any?
(17) Make the Sieve of Eratosthenes to find prime numbers. On a printed chart, blacken the box for the number 1, which is neither prime nor composite. Circle the next unmarked number (2), and then cross out all of its multiples—that is, count by 2’s and cross out every number you land on, except for 2 itself. Circle the next unmarked number (3), and then cross out all of its multiples. Keep going until every number is either circled (prime) or crossed out (composite).
(17.5) Go read the multitude of jokes about how “All odd numbers are prime.”
(18) The Factors & Multiples game: The first player marks an even number less than 50 on the hundred board. His opponent marks a factor or multiple of that number. Players alternate, each time marking a factor or multiple of the last number played. The player who marks the last number, leaving his opponent with no move, wins the game.
[Hat tip: Nrich maths.]
(18.5) Factors and Multiples Solitaire: Try to find the longest possible chain of factors and multiples. Keep track of the order in which you mark the numbers. Can you find a way to mark 50 or more without breaking the chain?
[The longest chain submitted to the Nrich website was 63 numbers.]
Fractions and Decimals
(19) What number is 1/2 of 100? How do you know? What number is 3/4 of 100? Are you sure? How can you show it is true? (What does the fraction 3/4 mean? What does any fraction mean?) What other fractions of 100 can you find? 1/10? 2/5? Can you find a number that is 1/3 of 100?
(20) The hundred chart can help you convert between fractions, decimals, and percents. Do you see how? “Percent” means “out of 100.” So 30% means “30 out of 100″—which is how much of the whole chart? If we say that the chart is one whole unit, then how much is each row (in decimal notation)? What size is each box? Can you color 0.47 of the chart? What decimal would mean the same as 1/5 of the chart? And what percent of the chart would that be?
Logic and Strategy
(21) A Cross pattern is a square plus the four squares directly up, down, left, and right from it. An X pattern is a square plus the four touching it diagonally. Choose any square that is not on an edge of the hundred board. Find its Cross and X patterns, and add up their sums. Can you explain why they add up to the same number? Can you find any other patterns that work that way? [Hint: Think symmetry.] Can you figure out how to predict the Cross or X pattern sum for any number?
(21.5) Find the Cross and X patterns for a date on this month’s calendar. How are these the same as on a hundred board? How are they different?
(23) Play Gomoku, also known as Five-in-a-Row, on a printed hundred chart. Use a wide-tip marker to make Xs and Os, or use pennies and nickels to mark the squares. On each turn, the player must make up a calculation that equals the number in the square he wants to mark.
(23.5) If you enjoy Gomoku, you can download a freeware version here. But it doesn’t come with a hundred chart.
Edited to Add
Can you think of anything else to do with a hundred chart? Add your ideas in the comments section below, and I’ll post the best ones here:
(25) Rounding to the nearest 10 — say a number and have the child put a marker on that number. Then let him decide which 10 that number is closer to and put a marker on it (or, if you’re using a paper chart, draw an arrow to the nearest 10).
[Hat tip: Tonia at The Sunny Patch.]
(26) Charlie’s Delightful Machine: Use 4 crayons or colored markers and a hundred chart to keep track of which lights glow for which numbers. Can you figure out the rules? Can you find a number that makes all the lights come on? Hit the Restart button to get a new set of rules.
[Nrich recommends this puzzle for grades 5 and up.]
(27) Factor Blaster: Player 1 marks any number and writes that down as his score, then Player 2 marks all the factors of that number which have not been previously marked and writes their sum as her score. Next turn: Player 2 marks an open number, adding that to her score, and then Player 1 marks any factors that are available and adds them to his score. Play alternates until no numbers remain. At that point, whoever has the highest score wins.
Optional: What if the player who is claiming the factors misses some? Should we allow the other player to claim those numbers as penalty points? Seems fair to me!
[Hat tip: From Mathwire.]
(28) Print out Yelena McManaman’s Hundred Chart Poster, which shows the meaning of each number. Hang it on the wall, low enough that your preschool or early-elementary student can see it easily. Talk about the patterns your child notices. (If you print and cut out the individual cards, you can arrange them so the bigger numbers are higher up, as shown in Yelena’s original blog post about her son’s reaction to the poster.)
(29) Blank 100 Grid Number Investigations: Challenge your students to deduce the secret behind each pattern of shaded squares. Then have them make up pattern puzzles of their own.
[Created by Stuart Kay. Free registration required to download pdf printable.]
(30) Can you mark ten squares Sudoku-style, so that no two squares share the same row or column? Add up the numbers to get your score. Then try to find a different set of ten Sudoku-style squares. What do you notice? What do you wonder?
[Suggested by David Radcliffe.]
(31) Have a math debate: Should the hundred chart count 1-100 or 0-99? Give evidence for your opinion and critique each other’s reasoning.
[Hat tip: Tricia Stohr-Hunt, Instructional Conundrum: 100 Board or 0-99 Chart?]
(32) Rearrange the chart (either 0-99 or 1-100) so that as you count to greater numbers, you climb higher on the board. Have another math debate: Which way makes more intuitive sense?
[Hat tip: Graham Fletcher, Bottoms Up to Conceptually Understanding Numbers.]
(33) Cut the chart into rows and paste them into a long number line. Try a counting pattern, or Race to 100 game, or the Sieve of Eratosthenes on the number line. Have a new math debate: Grid chart or number line — which do you prefer?
[Hat tip: Joe Schwartz, Number Grids and Number Lines: Can They Live Together in Peace? ]
This post is a revision and update of my original post, 7 Things to Do with a Hundred Chart, and most of these ideas are included in my book Let’s Play Math: How Homeschooling Families Can Learn Math Together, and Enjoy It!
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