Here’s my latest What Do You Notice? poster. All you need is inch graph paper, a black sharpie, and small circular stickers (or two different colored sharpie pens to draw in the circles).
Title: Crossed Lines
K-2: colors, counting, even/odd numbers
3-5: multiplication, even/odd numbers, multiples of 3, square numbers
Crossed lines is an easy strategy for learning multiplication facts. The horizontal and vertical lines represent the factors in the multiplication problem. For example, in the problem 4 x 3, students would draw 4 horizontal lines and then intersect them with 3 vertical lines as is shown in the last example above. The intersection of the lines is the answer to the problem. So for 4 x 3, there would be 12 intersections.
To make the strategy more visible, I used colored dots to highlight the intersections. I was deliberate in the colors I chose. The green dots represent an even product and the pink dots represent an odd product. Notice how all the products are multiples of 3. At a higher level, older students may notice that 3 x 3 makes a square and 9 is a square number.
Here’s what it looked like at the event:
Family Math Night Collaborative Project: Number Skyline
Here’s a super simple activity that helps students to “see” multiplication facts. It’s also a great way for them to see the connection between addition and subtraction as they “use addition to find the total number of objects arranged in rectangular arrays” (CCSSM 2.OA.C.4) and to “interpret products of whole numbers” (CCSSM 3.OA.A.1).
Using inch graph paper, have students make rectangular arrays and record the rows (horizontal) and columns (vertical) as multiplication equations. This is a good time to discuss the vocabulary factor and product.
And while we’re at it, let’s throw in some geometry by showing students that a 2 by 3 array is the same as a 3 by 2 array…they are congruent.
Algebra?? Absolutely! The product of 2 x 3 is the same as the product of 3 x 2. The Commutative Property of Multiplication. Ask students how knowing this property can help them.
Here’s a video I put together a long time ago that talks about this and other concepts that can be taught by rectangular arrays:
Connections to the CCSSM: 2.OA.C.4; 3.OA.A.1; 3.OA.A.3; 3.OA.A.4; 3.OA.B.5; 3.OA.C.7
See how simple objects like tiles, stickers, rubber stamps, dice, and graph paper help teach students important concepts in number theory: factors, primes, composites, and square numbers…not to mention the great reinforcement of multiplication facts. Grades 2 – 5