Five in a Row: Addition and Subtraction

I’ve been blogging recently about doing math with my daughter and trying out different centers from the newly released Illustrative Mathematics K-5 curriculum. You can read about our experiences with the two centers we’ve already tried: Can You Build It? and Number Puzzles: Addition and Subtraction.

In this post, I’m going to share our experiences with a new center, Five in a Row: Addition and Subtraction. Similar to Number Puzzles, I like the flexibility of this center because it has multiple stages giving me lots of choice about what kinds of numbers we’re going to work with:

• Stage 1: Add 1 or 2 (1st Grade)
• Stage 2: Subtract 1 or 2 (1st Grade)
• Stage 3: Add 7, 8, or 9 (1st Grade)
• Stage 4: Add or Subtract 10 (1st Grade)
• Stage 5: Add within 100 without Composing (1st Grade)
• Stage 6: Add within 100 with Composing (1st and 2nd Grade)
• Stage 7: Add within 1,000 without Composing (2nd Grade)
• Stage 8: Add within 1,000 with Composing (2nd Grade)

I decided to start with Stage 6 because my daughter already reviewed adding within 100 without composing when we played the Number Puzzles center. Now I wanted to give her a chance to review adding within 100 with composing.

Here’s what the game board for Stage 6 looks like:

Five in a Row: Addition and Subtraction, Stage 6

I’ll be honest I have some issues with this game immediately. There are 45 possible sums that can be created with all of these addends. There are 10 duplicate sums, which leaves 35 unique sums that can be created (3 of which are over 100). However, the game board only includes 25 of these possible sums. That means 10 of the possible sums are missing completely from the game board! Students could spend a lot of time adding numbers together only to get sums they can never cover.

I didn’t want to play with this game board, so I came up with two options for modifying it:

1. Increase the size of the game board to include all 35 possible sums, or
2. Decrease the number of addends so that the number of possible sums is 25, or as close to 25 as possible

I went with option 2. I decreased the number of addends from 10 to 8. I basically left off 26 and 48. This brings the number of possible sums down from 45 to 28. There are 2 duplicate sums, which leaves 26 unique sums that can be created. I opted to leave off 122 (65 + 57) because it’s not within 100 anyway.

Here’s my redesigned game board:

If you look closely, you’ll see another modification I made: the game is now Four in a Row, not Five in a Row. The game board feels too cramped to attempt five in a row, especially when you have an opponent actively trying to block you.

As the pictures below show, this game really got my daughter thinking!

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The further we got into the game, the longer each turn took. On one hand this is great practice because it means she’s doing lots and lots of adding in her head. At the same time, it got pretty exhausting. I even found myself not wanting to be too strategic on some turns because I just didn’t care to try out all the different combinations available to me to see if I could work on making my row or block her from making her row.

Dan Finkel has some great advice about what makes a good math game which he shares in this 3-minute video:

Here are his three ideas:

• Choice needs to be a part of the game
• Math should be the engine of the game
• Simple and quick to play

Choice is definitely part of this game. Students get to choose which of the two clips to move on their turn. They also get to choose to which number they move the clip. Students get to choose whether they’re going to try to place a counter such that it helps them make a row or blocks their opponent from completing a row.

Math is the engine of the game. Students aren’t just solving random addition problems. They have to look at the possible sums they might want to cover and then look at the addends to see how they can achieve their goal.

The game is simple to learn. However, where it falters is that it is not quick to play. This game took us a while, and we were only aiming for four in a row instead of five. We’ve played Stage 6 on two different days and we only played one round each day. Each round took so long, we were ready to move on after that one round.

The game does a lot right, but because of the length of time it can take to play, I don’t know that this is going to be a “go-to” game for lots of kids. Skill level probably affects playing speed quite a bit. Students who are quick and efficient at adding will have a much easier time than students who are inefficient or inaccurate. There’s also the issue of working memory. If students want to be strategic, they have to hold a lot of possible sums in their head as they plan their next move. One strategy you could try is to give students a white board so they can jot down each equation they’re considering to avoid overloading their working memories. This will also help prevent frustration that can make the game feel a lot less fun.

I asked my daughter the other day if she wanted to play Four in a Row again or go back to Number Puzzles. Considering she made comments like, “I don’t like this game,” while we were playing, I was totally surprised that she said she wanted to play Four in a Row again!

I decided to move on to Stage 7 which is about adding within 1,000 without composing. Similar to what I did with Stage 6, I redesigned the game board so that exactly 25 sums are possible.

This time there are two rows along the bottom. The way it works is that you always add one of the numbers from the top row with one of the numbers from the bottom row. On your turn, you’re still only allowed to move one of the clips, either the one on the top row or the one on the bottom row.

Since Stage 7 didn’t require composing, it was much less mentally exhausting to play, and my daughter seemed to enjoy it. She was particularly happy that she beat me. 🙂

I don’t want to dissuade anyone from trying out the Five in a Row center the way that it’s presented in the IM curriculum. However, if you’re interested in trying out the modified version I created, here’s a PDF of the modified game boards for Stages 6 and 7.