MATH: It's No Trouble - Just Double to Multiply

Required Knowledge: 
Students should understand what the math term "double" means and know the doubles facts from 2+2 through 12+12. Students would benefit from also knowing an addend is half the sum in a doubles fact (4 + 4 = 8, so 4 is half of 8).
They should also have an understanding of multiplication as "adding equal groups" and be able to compute 2-digit addition/ doubling such at 14 + 14 or 32 + 32.

Content:
Students will be shown how to calculate their 2's, 4's and 8's times tables through the concept of doubling or halving.  They will understand when you double the number of groups, or the amount of each group, from a previous multiplication equation that you are indeed doubling the product. Students will see how knowing the 2's times tables, will help them solve the 4's and 8's times tables through doubling, repeated patterns, reasoning, and engaged practiced.
 
Students will continue the same learning with 3's, 6's and 12's times tables, as well as with 5's and 10's. 
We will also explore solving 9's times tables by tripling the factor of 3 in a multiplication equation where 3 is a factor and the other factor is 12 or less (example: If 3 x 8 = 24, then 9 x 8 = 72 because 24 + 24 + 24 = 72).

Students will learn a strategy to determine most of their multiplication facts not through memorization, but through a solid conceptual understanding based on several of the Common Core Mathematical Practices: 

CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.

Understanding why a multiplication fact has an even product, or that 5 groups of 7 must be half of 10 groups of 7, are both some examples of how using doubles and halves to multiply will help ensure students can successfully apply multiplication to other mathematical content areas.

CLASS STRUCTURE
We will begin with practicing doubles and halves. I will engage students with colorful numbers and images and ask students to practice with me. Students will have the option to use Base 10 blocks or circles to support their computations. These can be sent to students to cut out prior to the class, or students can use virtual manipulatives online. Students will be asked to record numbers, answers, and evaluate patterns with our group collaboratively. Research shows when students write and discuss their ideas they will have a stronger retention of those ideas.

Through the use of a 100 chart and pre-made activities that will be projected on the screen and/or printed at home, we will use doubles and halves to learn multiplication. Short video clips, created by the instructor, will be sent to the class page as an extra resource for students to use in between sessions. We will analyze patterns, practice through written, verbal, and kinesthetic activities (yes - students will get up and move, and tap or hop, to engage in the learning process), and participants will have the opportunity to ask questions to clarify understanding. We will end each session with a game where our goal will be to work together to complete a multiplication mission. Printouts will be sent to participants at least 24 hours before each session begins. These will be used during the sessions and can also be used as a long-term resource for students to practice at home.

Day 1:
We will practice basic doubles facts for multiples of 5, 10.  For example; 5+5, 10+10, 15+15, 20+20, and 25+25. 
We will practice calculating half of each of the even multiples of 5 and 10. For example: Half of 20 is 10, half of 50 is 25, half of 30 is 15, and half of 70 is 35.
We will use the doubles and halves of the multiples of 5 and 10 to solve multiplication facts with 5 and 10 as one of the factors. 
Participants will double one of the factors and double the product to find the answer to additional multiplication equations. For example:  5 x 5 = 25. Double the first factor and the product to show 10 x 5 = 50. Students are doubling the amount of groups, so the product will double. This concept will be presented and practiced with visual representations and student friendly charts.

Day 2:
We will review some examples from Day 1.
We will practice basic doubles facts for multiples of 2, 4 and 8.  For example; 2+2, 4+4, 8+8, 16+16, and 32 + 32. 
We will practice calculating half of each of the multiples of 2, 4, and 8. For example: Half of 32 is 16, half of 16 is 8, half of 8 is 4, and half of 4 is 2.
We will use the doubles and halves of the multiples of 2, 4, and 8 to solve multiplication facts with 2, 4, or 8 as one of the factors. 
Participants will double one of the factors and double the product to find the answer to additional multiplication equations. For example:  2 x 6 = 12. Double the first factor and the product to show 4 x 6 = 24. Students are doubling the amount of groups, so the product will double. This concept will be presented and practiced with visual representations and student-friendly charts.

Day 3:
We will review some examples from Day 2.
We will practice basic doubles facts for multiples of 3, 6 and 12.  For example; 3+3, 6+6, 12+12, 24+24, and 48 + 48. 
We will practice calculating half of each of the multiples of 3, 6, and 12. For example: Half of 48 is 24, half of 24 is 12, half of 12 is 6, and half of 6 is 3.
We will use the doubles and halves of the multiples of 3, 6, and 12 to solve multiplication facts with 3, 6, or 12 as one of the factors. 
Participants will double one of the factors and double the product to find the answer to additional multiplication equations. For example:  3 x 7 = 21. Double the first factor and the product to show 6 x 7 = 42. Students are doubling the amount of groups, so the product will double. This concept will be presented and practiced with visual representations and student-friendly charts.

Day 4:
We will review some examples from Day 3.
As a group, we will review the skills and practice multiplication using the strategies from Days 1-3

**If participants are ready, I'll introduce basic triple facts for multiples of 3.  For example; 3+3+3 = 9, 6+6+6 =18, 9+9+9= 27, and 12+12+12 = 36. 
We will practice calculating one-third of each of the multiples of 3 and 9. For example: 1/3 of 36 is 12, 1/3 of 27 is 9, 1/3 of 12 is 4, and 1/3 of 6 is 2.
We will use the triples and thirds of the multiples of 3 and 9 to solve multiplication facts with 3 or 9 as one of the factors. 
Participants will triple one of the factors and triple the product to find the answer to additional multiplication equations. For example:  3 x 4 = 12. Triple the first factor and the product to show 9 x 4 = 36. Students are tripling the amount of groups, so the product will triple. This concept will be presented and practiced with visual representations and student-friendly charts.