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

Sort Students into Groups Using Integers

If you want a quick activity that you can use to randomly put students into groups of two or four, look no further. This activity uses integers represented in words and with tiles to sort students into groups. This could be used with any class where students can add integers (subtraction is not needed) and represent them with tiles.
In each row is a set of integer cards that represent the same number. The next row will have a set of cards that has the opposite number. 

• Grade 7 Number Sense & Numeration 
• Grade 8 Number Sense & Numeration (review)

• Integer Cards Prep work: Cut the cards out. Note that every two rows of cards make up a set of four. Remove sets according to how many students you have.
• Bag or Bin to put cards in

1. Each person chooses a card and finds their partner. The person with a card that represents the same integer. Stop here if you only want students in pairs.
2. Next this pair of students looks for the other pair of students who has a number that will add together with theirs to equal zero

• Choosing Groups with Integer Cards (doc) (pdf)

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

Sort Students into Groups using Equivalent Fractions

If you want a quick activity that you can use to randomly put students into groups of four, look no further. This activity uses fractions with common denominators and then equivalent fractions to sort students into groups. This could be used with any class where students can add fractions and compare equivalent factions.
In each row are two sets of fractions with common denominators. When you add each pair (with the same denominator) they will simplify to the same fraction

• Grade 7 Number Sense & Numeration
• Grade 8 Number Sense & Numeration (review)
• MPM1D
• MFM1P

• Fraction Cards Prep work: Cut the cards out. Note that there are 8 rows of fractions. Remove sets according to how many students you have.
• Bag or Bin to put cards in

1. Choose a fraction and find your partner (the person who has the same common denominator). Introduce yourself. He or she is your team member. 
2. Add your fractions and simplify the answer. 
3. Find the other team with the same simplified fraction. Introduce yourselves. This is your group of four

• None yet

• Choosing Groups with Fractions Cards (doc) (pdf)

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