Multiplication Facts
(Update 9/3/17 )
Research on Learning Facts (Crawford. D, Otter Creek Institute: Raising Classroom Achievement)
There are three stages of “learning” multiplication facts
Stage 1 – Figuring Out Facts
Students have a procedural knowledge of multiplication. They can draw an array, skip count, write a repeated addition problem, or use another strategy to
solve given plenty of time. Procedural knowledge of counting should be developed prior to memorization, rather than replace it.
Stage 2 – Strategies for remembering facts
Goal is simple accuracy rather than developing fluency or automaticity. Students use relationships to be accurate. 5 x 9 = 45, so 6 x 9 = 45 + 9 or 54 ; 3 x 8 = 24 so 6 x 8 = 24 + 24 or 48.
Stage 3 – Developing Automaticity with facts (This is where students need to be now for success in middle school math and beyond!)
Children develop the capacity to simply recall the answers to facts without resorting to anything other than direct retrieval of the answer. Once a students has moved to direct retrieval, response rates decrease from over 3 seconds down to less than a second. For practice to lead to automaticity, students must be “recalling” the facts, rather than “deriving” them from a procedure like skip counting on fingers or thinking of nearby facts to get there (stage 1 and 2).
Why is Automaticity so Important?
Although correct answers can be obtained using procedural knowledge, these procedures are effortful and slow, and they appear to interfere with learning and understanding higher-order concepts (Hasselbring, Goin and Bransford, 1988).
What Type of Practice Leads to Automaticity?
Practice is required to develop automaticity with math facts. The child who uses skip counting or repeated addition to find a product when practicing multiplication learns to use repeated addition more skillfully—but he continues to add instead of “recalling” the product of the facts. Automaticity can be attained very quickly if there is not much to be learned. Even if there is much to be learned, parts of it can be automatized quickly if they are trained in isolation.
Here is a recommended progression of sets of facts to practice. When you are automatic with one set (1 second recall), move to the next. Don’t forget to practice the previous sets as you make progress. Check below for recommended activities and strategies to practice direct retrieval.
Progression of Fact Practice / Recall (100 facts)
- 1s (81 facts left)
- 2s (64 facts left)
- 5s (49 facts left)
- 10s (38 facts left)
- 9s (27 facts left)
- Squares 4x4 , 3x3, 6x6 , 7x7 8x8 (22 facts left)
- 3s (14 facts left)
- 6s ( 6 facts left)
- 4s ( 2 facts left)
- 7 x 8 and 8 x 7 (0 facts left) - This often is the hardest fact for students to master.!
Flash Card Strategy
Everyone knows how to use flash cards to practice math facts, but use this simple strategy when practicing with your child to put more emphasis on those facts that they can not yet automatically "recall".
Use a set of multiplication flash cards bought from a store or you can make some of your own on index cards.
While practicing with your child make sure the practice is based on automaticity. This means they can't use skip counting, work it out on paper, or have more than 1-2 seconds to respond. You are not encouraging Stage 3 automaticity if you allow strategies from Stage 1 and 2 when practicing.
If your child cannot respond correctly within 1-2 seconds, read the fact and answer to them " 6 x 7 .... 42" then have them repeat it aloud. Place that card just 3-4 cards down in the pile so they will see it again quickly and have to respond. Continue placing it 3-4 cards back until the child has responded correctly 4 times in a row. If it comes around again and they can't respond automatcally the process begins again. They will be getting elicit practice on the facts they need the most help with.
Timed Math Fact Quizzes (How to practice at home)
Like it or not, teachers are going to use timed math fact quizzes to help access mastery of facts. There are sometimes exceptions made for students that have high anxiety with timed quizzes. However, this is the least time consuming strategy for teachers in order to access this life skill. Sitting down with each student and doing a verbal check of facts would take a lot of academic time away from students.
Here is a link to a resource for parents to print fact sheets for students to practice timed quizzes. A parent of a student found this!
http://www.math-aids.com/Multiplication/Multiplication_Worksheets_SDV.html
Again, it is so important to emphasize automaticity practice. If you give one of these to your child to practice and walk away, they will skip count with fingers or write them down on the side of their paper. That would not be practicing automaticity. Instead, use it as a strategy to find those facts they have not yet mastered. If you see it taking less than 1-2 seconds to respond or they are counting verbally, mentally, or physically (fingers), highlight the fact and they move to the next one. Don't encourage just "writing something" either. Then they are practicing automaticity with the wrong answer and it may be hard to transition back to the correct answer.
I recently attended a workshop led by Alex Kajitani, Rappin Mathematician and California Teacher of the Year, and his school uses
a 3 minute 50 fact timed multiplication quiz for students to become members of their school's Multiplication Nation. This allows a little more than 3 seconds per fact and students must correctly solve 45 out of 50. When your child practices facts on paper quizzes at home, strive for a similar time frame and percentage to access mastery. Challenge them by reducing it down to 2 - 3 seconds.
Multiplication Practice Resources for Home
Multiplication Table - https://www.dadsworksheets.com/worksheets/multiplication-table.html
Multiplication Chart - https://www.dadsworksheets.com/charts/multiplication-chart.html
Multiplication Worksheets - https://www.dadsworksheets.com/worksheets/multiplication.html
Multiplication Calculator - https://www.dadsworksheets.com/multiplication-calculator.html