Array Multiplication Cards

Even though this is a blog that dedicates most of the resources to grades 7-12, sometimes we have to have some help with the basics for those students. In Ontario we have a new initiative called Focus on the Fundamentals and even though you could argue that we haven't forgot the fundamentals, perhaps an the idea of putting a little extra attention on the fundamentals may not be a bad idea. In this case we are looking at students "knowing" their multiplication facts. Knowing is in quotations because what one person thinks of as knowing may not agree with others. For example, memorizing the multiplication tables doesn't necessarily mean that a student knows what multiplication is.

Cut to a couple of weeks ago. We was in a primary math session from @gfletchy. In that session, we used these 10 frame cards that were basically a game to help students recognize numbers. It seemed like an engaging way to do that. With a little bit of searching, we found that he also has cards for multiplication that focus on groupings and go up to 7x7. Since we thought the idea of practicing multiplication tables would be good for grade 7&8 students, we thought a more advanced representation might be as arrays. So here are cards that can be used to practice multiplication facts up to 12x12.

Right now there are two versions and two sets of each version. We have one version with just the dots and one set with the dots with rectangles around groups to highlight the arrays a bit more. Each version also has two sets, one with the answers on the back (for kids to work in pairs) and one without (for group play).

To help with the counting of the dots on each side we have put vertical and horizontal lines to mark groups of 5 dots. This way students can see, for example, there is a group of 5 and three more on one side and two groups of 5 and 2 more on the other side so this must be 8x12. The lines can also help by letting students use decomposition to break the problem up into smaller simpler problems which they can add together. This is an effective strategy to use on their way to internalizing the multiplication table. One thing you might want to do is show them one card and just ask them to Notice and Wonder about what they see and hopefully they can recognize what the lines indicate.

• All Grades - As review 

1. Print out the cards on card stock, cut and laminate them. You will probably want more than one set. We recommend printing each set out using a different colour of card stock. This way if the sets get mixed up then you just need to match the colours.
2. When you print out the cards, the first 2 pages cover 2x1 all the way to 7x7 (with a few times one cards in there to fill the page). The next page cover 8x2 all the way to 9x9. And finally the last two pages go from 10x2 all the way to 12x12. So if you have kids struggling still with multiplication, you may want to limit them to some of the first few pages.
3. If you are printing out the cards with the answers on them, the answer pages show up every second page with the intent that when you print them, you have double sided checked off on your printer/copier. If you have the option, have it "Flip on the long edge". 

1. For Game Mode: Put kids in groups of 3-6.
2. Shuffle the cards (versions without answers on the back)
3. Someone flips over a card. 
4. The first person to say the correct product gets the card (or a point). Students have to agree that that is the correct answer.  If a student says more than one answer, they are disqualified for that card. 

You might be concerned that speed of calculations may come into play here and if you play in Game Mode, you wouldn't be wrong. One way for speed to be a factor is to start out with just the easiest of cards (first two pages) and only move on when the majority of students have mastered them. Or you could have students write their answers on white boards and then not reveal the answer until everyone has completed (with not worry about points or who answered first). 

1. Conversely, you could have kids work in pairs and use the decks with the answers on the back. 
2. Shuffle the cards (version with the numbers on the back)
3. Deal out half to each person. 
4. Each student takes their deck and holds them so the other can't see either side. 
5. They take turns showing each other a dot array and listen for their partner to say the answer (visible on the back). 

• Array Multiplication Cards (Google Doc, PDF)
• Array Multiplication Cards with answers (Google Doc, PDF)
• Array Multiplication Cards (Groups) (Google Doc, PDF)
• Array Multiplication Cards (Groups) with answers (Google Doc, PDF)
• Google Drawing Templates for each card (UnGrouped, Grouped)

Did you use this activity? Do you have a way to make it better? Did you find a mistake? If so tell us in the comment section. Thanks

I Have, Who Has - Making Change in Canada

An I Have, Who Has game is not a new concept. The premiss is that each person gets a card that has two statements. One is the "I have" statement and the other is the "Who has" statement. In this case the "I have" statement is an expression dealing with making change with money in Canada. If you are not from Canada, you may not know that here we no longer use pennies. This means that when we buy things and pay cash we actually have to round to the nearest nickel to make change. The way the game works is that a person starts by reading their "Who has" statement. For example, someone might say "Who has $4.35?". Someone else will have a card where their change equals $4.35 so they would say "I have $20 and it costs $15.63. Who has change of $1.75?" That is, they read their statement that equals $4.35 and then asks their "Who has" statement. Then someone else will have an expression that matches $1.75 and the game continues. If done correctly, it should end up with the person who started giving their "I have" statement. It works really well as a warm up and one of nice things about this is that you could do it multiple days and kids will likely get different cards.

• MAT1L - DMS1.03 – round money values to stated accuracies (e.g., the nearest cent, the nearest dollar, the nearest ten dollars, the nearest hundred dollars, the nearest thousand dollars, and the nearest million dollars), in applications drawn from everyday situations; DMS2.01 – make the correct change for an offered amount with and without concrete materials (e.g., change from a $5 bill for an item costing $4.77);
• MAT2L - EMS1.01 – read and interpret money values given in words, write money values as decimals, and round money values appropriately, in solving problems found in everyday contexts;

• This is a small set that has only 9 cards in it (you can see that the card on the top left has the "I have" to match the "Who has" of the card on the bottom right). You will likely have more than 9 students in your class and so will need multiple sets (ie groups of 9). In order for the game to work, all cards need to be passed out. So some students may need to have more than one card.
• Print out the set you want (ideally on coloured card stock) and we also suggest lamination to lengthen the lifespan of the cards.
• Be sure to print out a set for yourself that you don't cut out so that it will be easier for you to check as students play the game.

1. Make sure you have gone over the rounding rules for money first. 
2. Distribute the cards one per student. All cards must be handed out so some students might need more than one card.
3. Tell each person to calculate the change for their "I have" expression and check their answer with at least one other person. 
4. Once students are confident with their answers all students should stand in their groups and then you choose one to read their "Who has" statement. The person who's answer is the same should read their "I have" statement followed by their "Who has" statement and then sit down. Eventually the last person standing should be the person who started. 
5. A variation might be to have students walk to the front and stand next to the person who they were matched with and eventually form an entire loop around the class.

• IHaveWhoHas-MakingChange (pdf) (doc)
• IHaveWhoHas-BlankTemplate (doc)

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks