Part 1 of the “Effective Math Skills” series, I discussed the top 5 most problematic areas in math for students according to a local research study¹. This article, we will look at applying effective strategies to tackle these areas to improve numeracy achievement.

1. Multiplication

In a controlled study group of 51 students in Grades 6-8, only 3 students achieved at their grade level. Taking a closer look, most of the students did not advance beyond Grade 4 level questions — the year we introduce multiplication in their curriculum. Coincidence? I think not. Here are some math hacks to help students build stronger skills.

Strategy 1: Memorize the Times-Table

You frowned at the word, didn’t you? Our advances in education have been moving towards stimulating creativity and abandoning traditional classroom approaches, and definitely moving away from memorization. Then, why am I recommending this strategy?

When we learn and retain information, we are able to reproduce basic knowledge from memory. We don’t really need to think anymore when asked “1 + 1” or “the alphabet”. The times-table is the alphabet in math. It is the building block of equations; it fuses coefficients and variables, and helps us “find x”. It is also the foundation for a vast number of concepts (namely, the next 4 areas we will discuss). If a student cannot recall 6 x 2, it should be as much of a red flag as knowing only 25 letters.

We are not afraid to ask our children to memorize the alphabet, in fact, we find it essential to their learning. Then why do we feel wrong to ask our students to memorize the times-table? In my opinion, the times-table is the only thing you will ever need to memorize in math.

Most of the students did not advance beyond Grade 4 level questions — the year we introduce multiplication in their curriculum.

How to…

  • Take small bites: Throughout the school term/year, pace your students through (for example, 2 rows at a time). You can create an engaging lesson plan by incorporating games, flashcards, prizes, etc.
  • No age limit: Don’t be afraid to do this at any grade level. I worked with many high school students who still use their calculator or worse, Google, when executing simple multiplication.
  • Reduce vocabulary: Chinese and Indian languages are proven to be the most effective in math learning, while English is linked to weaker math skills². The reason being, number words in English are much longer and contain irregular forms. Consider 10 (ten) and 3 (three). When we add the two numbers together, it becomes “thirteen”. In Chinese, it literally becomes “ten three”. The shorter, more straightforward numbering system in Asian languages allow the brain to switch between words and numbers much more quickly. In turn, this allows the brain to hold and process more information at one time. Speed is not the goal, but rather, a simple process helps eliminate possible confusion for learners. To emulate the benefits of Asian languages, I recommend cutting out unnecessary words. For example, instead of saying “six times six equals thirty-six”, you can say “six six thirty-six”. This is a strategy that Chinese students use to memorize the times-table.

Strategy 2: Find Patterns

There are many fun patterns in the times-table that make memorization shockingly easy. I would like to share 3 patterns that manage to surprise my students every time.

The multiples of 9… 

  • Reversed mirror effect: Imagine a yellow line between the multiples of 5 x 9 and 6 x 9. The first group of answers above the line are reflected in the second group below the line, with the digits flipped backwards. For example, 2 x 9 = 18, which is the 4th multiple above the line. Counting 4 multiples below the line, we find 9 x 9 = 81, which is “1-8” written backwards! 4 x 9=36, the 2nd multiple above the line. Counting 2 multiples below the line, 7 x 9=63. If a student memorizes the first 5 multiples of 9, they would know the rest.

9xtable

  • Logical sequence: Sometimes, a picture is worth 1,000 words. We don’t want to be the teacher who doesn’t teach our students this ↓Sequence of 9


The times-table mirrors itself diagonally… 
along the square numbers!

Times Table 12x12

Strategy 3: Think Actively

Memorization is the first step. To build a stronger foundation, students must apply their knowledge actively. They need to make connections between the multiples and their answer. One way to think actively is to practice remembering the pairs of multiples that would yield the same answer, like 12.

There are 3 pairs: 12 x 1, 6 x 2, 3 x 4.

This exercise can be presented as a fun game in class, such as Jeopardy! It is important for students to go back and forth fluidly from multiples to their answers, because it will build a strong foundation for division.

2.  Division

Strategy 4: Rephrase the Question

To help students understand division, state the question, and then rephrase it by using the multiplication concept. For example, “What is 35 divided by 7?” If the student looks confused, follow up by rephrasing, “What number multiplied by 7 equals 35?” This way, students trigger their prior knowledge and start to see how the concepts of multiplication and division connect.

This is the reason that Strategy 3: Think Actively is so important. If a student is fluent in making connections between the numbers on the times-table, then division becomes a game of finding the missing number that forms the relationship.

Strategy 5: Stay Organized

Disorganized writing is a sign of a disorganized mind. Math is highly about organization, and the most frustrating would be finding out that our own messy writing was the cause of mistakes. A trick to help sort out the confusion is to practice our organizational skills.

When doing long divisions, it is essential to remain organized by writing in columns, using arrows, and drawing horizontal lines. Long DivisionThe columns help students focus on dividing into the right numbers, the arrows help carry down the right numbers (if they missed one, it will be easy to spot out!), and the horizontal lines help organize the numbers they should be subtracting.

It seems very simple and intuitive, yet many students fail to do this. If we can help encourage good habits, students could eliminate unnecessary mistakes that can frustrate them in the learning process.

3+4.  Fractions & Decimals

Strategy 6: Part Of A Whole

Once the concept of fractions is introduced and the good ol’ pizza pie is dissected into slices, it is important to help students understand that fractions represent a part out of a whole. A trick is to emphasize “out of”:

Fraction

= 3 out of 7 “pieces”

Strategy 7: Do the Math

The relationship between fractions and decimals is by doing the math. Many students don’t understand that fractions are basically division, that when you divide the numerator by the denominator, you will arrive with the decimal answer!

5.  Money Problems

The 4 most common word problems that students got wrong on the research assessment were all money-related. Beyond the challenges that come with word problems, students can strengthen their computational skills by employing all the strategies that we explored above.

Strategy 5: Stay Organized

When solving money problems, it is helpful to set up the question vertically by using columns and aligning the decimal points. The tenth and hundredth decimal places would be aligned automatically, as color-coded below.

Money

It seems very simple and intuitive, yet many students fail to do this. If we can help encourage good habits, students could eliminate unnecessary mistakes that can frustrate them in the learning process.

Strategy 6: Part Of A Whole + Strategy 7: Do the Math

Some students have trouble understanding dollars and cents in math terms. They cannot see why 75 cents become $0.75. Fractions can be used to shed some light.

How many cents are in 75 cents? 75

How many cents are in one dollar? 100 (now, translate this to “part of a whole”)

75 cents out of a dollar is 75 out of 100, or 75/100 (here, do the math)

= $0.75

Or…

How many quarters make 75 cents? 3

How many quarters make a dollar? 4 (now, translate this to “part of a whole”)

3 quarters out of a dollar is 3 out of 4, or 3/4 (here, do the math)

= $0.75


1. Frontier College’s annual national research in low-income areas measuring community impact on academic achievements. Students in Grades 1-8 participate across Canada. Refer to Part 1: Common Mistakes for more info.
2. Shellenbarger, Sue. “The Best Language for Math: Confusing English Number Words Are Linked to Weaker Skills.” The Wall Street Journal. WSJ.com, 15 Sep. 2014. Web. 15 Mar. 2016. <http://www.wsj.com/articles/the-best-language-for-math-1410304008>.