Imagine a simple resource that, in the right hands, can greatly increase your class's deep understanding of multiplication. Something that will make your multiplication Number Talks even more effective. It would be worth trying out! When children are learning to use the four operations, they need concrete experiences with manipulatives. A LOT of concrete experiences with manipulatives! And this concrete experience deepens their understanding of multiplication. During whole class Number Talks, however, it often isn't possible for children to use manipulatives. So how can you, as the class teacher, best support children's understanding when they are not yet at the abstract (equation only) stage? |

To solve this problem for multiplication Number Talks, I made multiplication dot cards for each of the times tables children need to memorise (1-12). I made sets showing (for example) '2 groups of x', as well as sets showing 'x groups of 2'. Both sets are important - while these 2 equations might give the same answer, they represent very different pictures!

Arrays are also an important visual for children who are beginning to multiply. So I made dot card sets that showed both the '2 rows of x' array and the 'x rows of 2' array. My favourite visual set was the one to the right. Because both versions of the equation are on the card along with the array, you can easily turn the card on its side to illustrate how '4 rows of 2' looks different than '2 rows of 4', even though the number of 'candies/dots' stays the same. The second picture to the right shows how I put my sets together. For each times table, I had 5 sets made up. For the 2 times table, the different sets showed the following visuals and equations for all equations from 0 x 2 to 12 x 2 : |

1) 2 groups of x

2) x groups of 2

3) 2 rows of x

4) x rows of 2

5) Cards showing both 'x rows of 2' (equation at the top of the card) and '2 rows of x' (equation to the side of the card).

You can easily print and use only 3 sets (the 2 'groups of' sets, and the set showing both equations along with the correct array) if printing is an issue. I liked having all 5 sets, however, as I often had children use these as a math station. Once children are familiar with how these cards are used during Number Talks, 3 children can work together. One child can be the 'teacher', while the other 2 solve the equation and explain their mathematical thinking to the others (recording sheets for this are included in the 2 and 10 times table files you can access through this blog post). My classes always loved this!

So - how do you use these cards during Number Talks to deepen understanding?

When I put up an equation for children to solve, I also showed them the accompanying visual. This immediately supported children who were still functioning at a more concrete/ representational mathematical level.

Then as children defended their answers by explaining the strategies they used, I could use a white board pen to mark the card to show how children were thinking about the equation. If a child was using 'Partial Products' (you can get multiplication posters showing this strategy here), for example, I could put in dividing lines to show where the child was splitting the larger equation into 2 smaller (easier) equations.

There is a fuller explanation (with illustrations) in the 2 files you can download. It's always hard to add something new into your teaching routine, but this addition will pay off hugely for your class's understanding of multiplication.

Try these sets out in your classroom during multiplication Number Talks. They will make your Number Talks, and your class's mathematical reasoning, more accessible for all of the children.

To get these 2 FREE sets, click the 10 Times Table cover page at the top and the 4x2 / 5x2 ARRAY visual in the middle of the post.

And check back - I will be posting links to the visual sets for the other multiplication tables as well!

2) x groups of 2

3) 2 rows of x

4) x rows of 2

5) Cards showing both 'x rows of 2' (equation at the top of the card) and '2 rows of x' (equation to the side of the card).

You can easily print and use only 3 sets (the 2 'groups of' sets, and the set showing both equations along with the correct array) if printing is an issue. I liked having all 5 sets, however, as I often had children use these as a math station. Once children are familiar with how these cards are used during Number Talks, 3 children can work together. One child can be the 'teacher', while the other 2 solve the equation and explain their mathematical thinking to the others (recording sheets for this are included in the 2 and 10 times table files you can access through this blog post). My classes always loved this!

So - how do you use these cards during Number Talks to deepen understanding?

When I put up an equation for children to solve, I also showed them the accompanying visual. This immediately supported children who were still functioning at a more concrete/ representational mathematical level.

Then as children defended their answers by explaining the strategies they used, I could use a white board pen to mark the card to show how children were thinking about the equation. If a child was using 'Partial Products' (you can get multiplication posters showing this strategy here), for example, I could put in dividing lines to show where the child was splitting the larger equation into 2 smaller (easier) equations.

There is a fuller explanation (with illustrations) in the 2 files you can download. It's always hard to add something new into your teaching routine, but this addition will pay off hugely for your class's understanding of multiplication.

Try these sets out in your classroom during multiplication Number Talks. They will make your Number Talks, and your class's mathematical reasoning, more accessible for all of the children.

To get these 2 FREE sets, click the 10 Times Table cover page at the top and the 4x2 / 5x2 ARRAY visual in the middle of the post.

And check back - I will be posting links to the visual sets for the other multiplication tables as well!