What Is An Array

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SWBAT create arrays up to 5x5 and use them to solve repeated addition problems.

Big Idea

Repeated addition lays the foundation for multiplication.

Warm Up

10 minutes

Students begin today by reviewing doubles and doubles plus one using the "mystery number" format that they have used in the past. The reasons for reviewing doubles is because in creating arrays and adding up the total, students use their knowledge of doubles to make the process of repeated addition simpler to grasp.  This addition/subtraction situation is a put together/take apart addend unknown problem type that is supposed to be mastered by first grade.

I put 8 + ? = 16 on the board. I ask students to copy and complete the equation. I write ? + 7 = 15. I ask students to copy and complete the equation. I ask for a student to share how they solved the first equation. We check to see if the answer is correct, and students correct their own work. Next I ask for a volunteer to show how they solved the second equation. 

I tell students I am going to put 3 more on the board and I would like them to solve them in their math journals. I tell them to watch the street signs that tell us what to do with the equations. 

I write 17 - ? = 9,  16 - 8 = ?  and ? - 6 = 7. I give students time to solve the problems while I circulate around to see what they are doing. When they are done we correct these as we did the first two. 

If I feel that students are still struggling with these, I may carry out 2 more problems on the board where I model my own thinking as I work. If students are showing that they are competent with the mystery number, I will ask students to put away their journals and look at me.

Exploring Arrays

20 minutes

I write the word array on the board. I draw a 3 row by 4 in a row array and ask students why an array might be helpful in math. I tell students that an array is a way of way of organizing a set of objects into rows (across) and columns (holding it up). In an array there has to be the same number of objects in each row and column. (I ended up making a power point for this. You can use the power point for the beginnings of this lesson.)

I draw an array on a piece of grid paper on the smart board. I put 3 rows of circles and I put 2 in each row. I ask students how many rows do I have? (3). How many columns holding up the rows? (2). I ask do I have the same number of objects in each row? How about in each column? Can anyone tell me how many circles I have in all with 3 rows and 2 in each row? (6). 

Could anyone give me an addition sentence for the array on the board? I ask for a volunteer. I am looking for 3 + 3 = 6 or 2 + 2 + 2 = 6. If a child gives me 5 + 1 = 6 I say, this is a true sentence, but it doesn't match the way the array is organized. Arrays are a way for students to model with mathematics (MP4).

I clear my array and create a new array of 4 rows and 5 columns. I repeat my questions for this display. 

If children are still unsure, I will repeat the process 1 - 3 more times, (keeping the numbers to a maximum of 6 x 6 (Common Core only requires 5 x 5). Each time we ask the same questions about the display.

I hand out a piece of graph paper and ask students to draw an array that has 2 rows with 6 dots in each row. I ask them if they have an even number of dots? How can they tell? (the objects all have a partner, they can pair up the numbers, they know that 12 is an even number) (2OA.3). 

I draw the same array on my board and we once more answer the questions. 

To check for understanding I draw six dots in no particular pattern (no columns or rows) on the board and ask if that is an array? I ask students to give a thumbs up if they say yes and a thumbs down if they say no it is not. 

At this point I review that an array has to have things arranged in rows and columns with an equal number of objects in each row and column.  I repeat my question about the random dots to make sure everyone has a clear picture of what an array really is.

I tell students that they will be building arrays in a game.

Playing the Game

20 minutes

I tell students that they will be playing an array game with a partner. Each group will get a white board, 2 different colored dice and some colored chips. The first person will roll a number and lay out the first chip for that number of rows (essentially what will become the first column in our array). I demonstrate on the board. The second person will roll the dice and put that many chips in each row BUT.. they must remember that the chips laid out by their partner already counts as their first one in each row. They will then write the total number of chips on their white board. 

They will play the game this way for 4 rounds and then stop (or I will call stop in 5 minutes).

At the end of 4 minutes I ring the bell and ask for attention. I ask students to give me a thumbs up if they feel they are good at making arrays. 

Next I explain to the students that arrays are fun and they can also help us solve addition problems. I display a 3 x 4 array on the board. I ask how many dots in each of my rows? (4). How many rows do I have? (3) Can anyone think of a way to make an addition  number sentence for my picture/model? 

If someone says 8 + 4, I would say to them "Great, how did you see the 8?" (4+4). So then what would my number sentence be? (4+ 4+ 4= 12). 

I show a different array of 3 x 2 and ask if anyone can write that number sentence? I have a volunteer come up and write 2 + 2 + 2  or 3 + 3. When a student writes one of the sentences, I show them that they can also add column + column and get the 3 + 3. We talk about how both of these add up to the same number and both match my picture.

Now I explain that they will add the equation piece to the game. Each time they roll the dice and build the array, they need to write down the addition sentence. I demonstrate and then let students resume the game for another 5 minutes. 

At the end of the 5 minutes I ring the bell and ask students to share some of the equations they found. I ask for a volunteer to try to draw 2 of the equations on the board. 

I ask students if they think they can use the array to solve a word problem.

The Array Word Problem

10 minutes

I tell students that I am going to hand them a paper with 2 word problems on it. I would like them to use the idea of the array that they had just explored to represent and solve the problem. They will need to show me how they found the answer to the problem with a number sentence.

I tell them that on the back they may make up their own problems for us to share tomorrow.

I give students 10 minutes to work on their own. If students are all finished, we will share our solutions.

If students finish earlier than their classmates, there is a place on their paper for them to try to draw and write their own array problems.