I wanted to pass along something that I love using in grades 2, 3 and 4 classrooms when talking about place value and number patterns. series of hundreds charts – that don’t just stop at 100 !
I recall John Van de Walle speaking about the importance of examining number patterns beyond 100, that it was a good idea to expose kids to hundreds charts that bridge the centuries — that is, that extended from one hundred to the next. He used to like to tape all the charts together in a long strip to highlight just how big 1000 is…
I like to play games with these hundreds charts, using a die with the +10, +10, -10, +1, +1, -1 marked on its faces. Have students start on the square with a 1 in it (101, 201, 301, etc) and roll the die, following the instructions. Students should read their die and describe the new sum aloud: “301 and 10 is 311” as they move their counter. The first one to reach the next hundred (400 in this game) is the winner.
In playing the game, there are important patterns to be noticed. Adding one on a hundred chart means moving one space to the right, while subtracting one means moving to the left one space. Adding ten means moving down one line, and subtracting ten means moving upwards one line. In this game, these are the only possible moves! In this way we also highlight the patterns in place value addition – that is, when we add or subtract ones, we affect only the ones; that when we add or subtract tens, we affect only the tens digit. Most importantly, though, that these patterns continue over decades and centuries. Like Van de Walle suggests, tape two of these charts together and have students begin a game at the _50 mark on the first board (say 350) – with the winner being the first to reach 500. Observe as students play and see who struggles with the transition from 300 to 400…
Likewise, consider using these charts as addition and subtraction tools. Once they have played the dice game above, have students place a counter on a number (say 324) and ask them to add 31 more, by moving their counter to show the addition. In this case, it’ll move down 3 rows and then one to the right, landing on 355. Challenge students to add larger numbers, like 29 to their new sum. Do they move down 2 rows and over 9? (20+9) Or do they move down 3 rows and subtract one? (30-1) The latter is more efficient — making fewer moves and resulting in fewer errors – and is also an excellent use of algebraic thinking. Since, in the end, 29 is the same as 30-1.
Subtraction can be modelled in much the same way. Find 2 numbers on the hundreds chart – say 367 and 428 – and mark them with 2 different coloured counters. Ask students to find the difference between the two numbers. It is worth observing to see how many students add up to find the difference — since ultimately it results in the same amount!
Remember to record number sentences to match students’ moving around the board… Otherwise the richness of the mathematics can become lost in a game of “snakes and ladders”!