If you remember, the last two math quilts I made were about multiplication concepts. Needless to say, I had lots of little square inches left over.
Since basic multiplication facts are always at the focus of attention in elementary school, I decided to use those scraps and make some multiplication mug rugs! A 'mug rug' is a bigger than a coaster and smaller than a place mat, so it makes the perfect size 'rug' to have at your desk or table. I use them all of the time for my drink and a snack. Everyone needs one or three.
These mug rugs are extra special because they also show how the distributive property works with basic facts. There are certain facts that are harder than others. When you talk to a student, they might say, "oh yeah, the fives are easy, so are the tens, twos are doubles." It is facts like 8 x 6, 8 x 7, 7 x 6, 7 x 7, 8 x 8, 8 x 9 etc. that are the hardest ones. WHY? Well, because generally we combine other facts and patterns to help solve these. Yes, my friends, there is so much to learn beyond memorizing them. If your teacher only told you to memorize them and not conceptually understand them...I am so sorry! Don't worry, you can still learn them in a different way! Here's an example:
Fact: 6 x 9 = 54The front of the mug rug is an area model showing 6 rows of 9 inches in each row.
If you didn't know 6 x 9, you could break up the area model and use a fact you do know to help.
Do you know your 5s? Look at the colors on this mug rug.
Green: 6 rows of 5 (6 x 5 = 30) Orange: 6 rows of 4 (6 x 4 = 24) So, 30 + 24 = 54.
(The bottom photo is the backside...another enjoyable place to put your mug!)
Can you figure out how I broke this fact up differently? I split up the rows instead of the columns this time. Try to write the number sentences!
Okay, check yourself:
(4 x 9) + (2 x 9)
36 + 18 = 54
Fact: 6 x 9 = 54
Similar to the first rug mug, yet different. Why is that?
Also, this one has a really scrappy backside! I tried to use every leftover piece!
Fact: 6 x 10 = 60
I started running out of square inches, so I partitioned this one into 4 different parts. Can you figure them out?
This mug rug is for Annie Kitty's food and water bowl. She needed a little extra room so I added a column. How many square inches did the rug increase?
Fact: 6 x 9 = 54
Yet another way to partition this fact! How many more ways can you do this same fact?
If you know a student who has trouble memorizing their facts...Get some grid paper and have them draw an area model for the one they are having trouble on! Tell them to split it in as many ways as they can do it.
One thing I know for sure, they will be doing more math this way than they would have done with flashcard drills.
All in all, my main point is that there are lots of different ways to use smaller facts to help you solve larger problems. Find what works for you! Over time, you will begin to automatize your facts and become fluent. The best part of truly understanding facts in this way is that pretty soon you will begin to multiply 2 x 2 digit numbers mentally!
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