PLEASE NOTE: We’re so excited to be rolling out our first math solution this year! In preparation, we asked our mathematics expert, Judy Ann Brown, to address a common theme in families with school-age kids’whether the way students learn a math topic now has really changed versus how older generations learned it. Here’s what she shared, diving specifically into common core multiplication standards.
Think about any task you do on a regular basis: driving a car, cooking a meal, mowing the grass, doing the laundry, etc. Most of the time we do these tasks without much thought’until we need to teach someone else how to do them!
Do you actually remember learning to multiply? Do you remember the first time that you made the connection that 2 + 2 + 2 is the same as 3 x 2? Did you count by 2s or skip count (2, 4, 6) to arrive at the sum or product? Were you given a multiplication table to explore patterns or to memorize? No matter how the process began, you eventually learned the standard algorithm for multiplication that you still use today.
Perhaps when you were in school, no one cared if you understood multiplication, could estimate products, could relate multiplication to division, or use it for problem-solving activities. Maybe you learned one algorithm for multiplication and repeated it over and over with differing degrees of success. You could either reproduce the required products or your math grade suffered. You could only hope to move on to algebra if you were successful with arithmetic, which was the gatekeeper to college and career success.
Once in an algebra class, you were presented with more rules to memorize. For the lucky few the rules began to make sense, the connection between multiplication and division became evident as inverse operations were used to solve equations. For others, algebra class was frustrating and was more about finding a way to survive with a grade high enough to satisfy a requirement. Times are changing; we want more for today’s students than simply meeting requirements.
We live in a technological society and our children must prepare for their future, not our past. [s1] Many of the jobs modern children will hold during their lifetime do not yet exist, and certainly, none of them will require sitting for hours multiplying numbers using a standard algorithm. However, the algorithm is still an important part of a complete understanding of multiplication, but endless practice with the algorithm is less important than a full understanding of the process and its parts.
The Common Core State Standards introduce multiplication over three grades (3, 4, and 5) with the standard algorithm as the culminating activity in grade 5. To meet these common core multiplication standards, students need to “know from memory all products of two one-digit numbers,” by the end of Grade 3, (Per 3.OA.C.7). Fact fluency needs to be developed well before students work with the standard algorithm for multiplication. Developing automaticity with facts is the first step to success with not only the standard algorithms for multiplication and division but also with fractions.
Take a look at a few of the Common Core State Standards (CCSS) that deal with multiplication:
3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 x 7.
Devin has 5 sisters and he counted 35 dolls in the house. Each sister has the same number of dolls. Write and solve an equation to find the number of dolls each sister has.
Answer: 5 x ___ = 35
Each sister has 7 dolls.
This type of problem prepares students for Algebraic notation.
5x = 35
5x ÷ 5 = 35 ÷ 5
x = 7
3.OA.A.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
The plans for a new store require a parking lot for 63 cars. Draw an array diagram to show the number of rows needed if seven cars can park on each row.
63 = 7 x ___
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Answer: 9 rows
This type of problem prepares students for Algebraic notation.
63 = 7x
63 ÷ 7 = 7x ÷ 7
9 = x
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Trent is multiplying 23 x 35 using an area model to find the product of 23 and 35.
23 x 35 = 600 + 100 + 90 + 15 = 805
This type of problem prepares students for multiplying binomials in Algebra.
(2x + 3)(3x +5) = 6×2 + 10x +9x + 15
5.NBT.B.5 Fluently multiplies multi-digit whole numbers using the standard algorithm.
The round-trip distance from San Francisco to Washington, D.C. is 5636 miles. Mr. Adams lives in San Francisco and made 13 business trips to Washington, D.C. last year. How far did he fly?
Mr. Adams flew 73,268 miles.
The text above shows five CCSS for multiplication along with a problem showing how this standard helps prepare students for algebra and samples from the Achieve 3000 Math product. Rushing to memorization of the standard algorithm without an understanding of the multiplication process will hinder students’ full understanding of the process of multiplication and division as it applies to a complete mathematics curriculum.
We’re looking forward to sharing our new Achieve3000 Math practice solution! In Achieve3000 Math’s environment designed to scaffold and support student learning students in K-12 will be able to fill knowledge gaps and build confidence in ALL mathematics concepts.
