**Topics:**Multiplication, area, strategy, addition.

**Materials:**Crayons, Blockout game sheet

**Recommended Grades:**3, 4

**Common Core:**3.OA.A.1, 3.OA.C.7, 3.MD.C.6, 3.MD.C.7

Roll the dice and shade in a rectangle. How can you claim the most space on the board? For 2-4 players.

#### Why We Love Blockout

This is one of those rare games that reinforces both the skill of multiplication and the visual model that makes sense of it. Blockout can be played competitively or collaboratively, and is a wonderful game to introduce or reinforce the concepts behind multiplication.

#### How to Play

- Players choose colors, then take turns rolling the dice, and shading in a rectangle given by the dice rolls. If you roll a 2 and a 5, you can shade in a 2 by 5 (or 5 by 2) rectangle. No one can shade in a square that has already been colored.
- If there is no room to fit the rectangle you rolled on the board, you pass. If all players pass in a row, the game is over.
- Players get a point for each square they have colored in at the end of the game.
- Students can play in groups of 2-4. It is also possible to play individually or collaboratively. For a collaborative or solitaire game, players roll and try to cooperatively fill up as much of the board as possible. If every player must pass in a row, the game is over. The fewer the number of leftover squares, the better the game.

#### Tips for the Classroom

- Take a volunteer and demonstrate the first several turns of a game of Blockout.
- For the first time playing, students can play as above. For subsequent games, you can show students how to track their points as they go. For example, they can write 2 x 5 = 10 inside the 2 by 5 rectangle, and know that they have 10 points for that turn. This connects the game to multiplication without making it feel to academic right away.

#### Rules

- Players take turns rolling two dice, and drawing a rectangle on the game board with side lengths given by the two numbers they rolled. For example, if you rolled a 3 and a 6, you would draw a 3 by 6 rectangle, placed horizontally or vertically on the board.
- Your rectangle cannot intersect or be contained in any previously drawn rectangles. If you cannot add a rectangle to the board on your turn, pass the dice to the next player. If all players pass in a row, the game is over.
- Players get a point for each square they’ve drawn a rectangle around. For example, a 3 by 4 rectangle is worth 12 points. Whoever boxes the most squares wins.

## About this Lesson

9 comments

## Comments 9

I really like this as a way of visualizing multiplication. I was thinking that, for younger children, you could modify it a little bit to teach and visualize addition: Use a 1×10 or 1×20 grid, then roll a D4 and shade in the blocks as per the instructions above.

Author

I like that idea a lot. You could even use a 2 x 10 grid and have a die that’s all ones and twos, so you even get a 1 by __ rectangle or a 2 by __ rectangle.

This is awesome visual learning. May be I could add on top of it. We can add 2 digits to 2 digits, by creating a grid of 20×20 and then make permutation combination of those 4 numbers (by rolled 4 dice) such that the sum fit in the grid. For Instance, they rolled 3,4,5,2 ….Possible combinations could be 34+52=86, 35+42=77 or 35+24=59 and so on …. Now there are two goals to maximize their sum and fit in grid too !!! So 59 can be drawn like 50 as 5 grids of 1×10 and 9 as 1 grid of 1×9. (horizontally or vertically too could be parameters). Rest rules follow as above.

I play a variant of this in my class that I call Gridracer on smaller (1 cm) grids. The key difference is that new arrays have to be connected to pre-existing arrays by at least one square (the inspiration was Tron’s lightcycles). The other difference is that, like Go, it’s how many squares you seal off/territory you control that counts as the winning calculation (as opposed to how many squares are in your arrays). This adds a further strategic element, and gives a reason for getting into composite area and decomposition/factorization of products so that you can make L-shaped arrays and “turn a corner” against your opponent’s array to force them off the board or seal off/penetrate their territory.

I’m a math coach, and I love your stuff so far, for real.

Author

Good idea for a variation! I think there are a lot of good ways to approach this game mechanic. I’ve also heard of people playing collaboratively, which is nice too.

Glad you like our stuff!

I love the concept and am so curious to extend on it in our Math Club. I am thinking — Roll the dice to get the area, but then let the child choose the length and width for that area for more flexibility. The dice gives them an easy option to go with, but if that length and width does not fit, what other possible rectangles might fit on the board for that area. Maybe as players become advanced, scoring could become based on perimeter to further explore the benefits of different sized rectangles that share the same area. You have me off thinking of new games for our third grade math club and I so appreciate that!

I also think it would be a great idea for them to, after they have filled in a large portion of the board, try and figure out what area, or multiplication problem they could come up with to fill in the blank spaces. This would definitely be after students have learned how to properly play the game but would be a great add on!

I am currently a Special Ed major. I was curious if there is any way that I could modify this for students who struggle with these kind of concepts?

In question to Rene Hayden’s variation, which sounds intriguing but we are clearly missing something, how do you play so that the game doesn’t seem so luck-dependent and a chase down the middle of the gameboard? I.e. once the middle is blocked off so that each player’s territory is captured, why keep playing? You mention allowing L-shaped arrays; could you include a photo of a finished game board?