The 9 Times Table: The Finger Trick and Other Strategies

Child finger trick for math learning

Introduction to the 9 Times Table

The 9 times table holds a reputation for being challenging, yet it offers some of the most engaging strategies for mastery. Although students are introduced to this table later than others, the tricks available make it more approachable than the 7s or 8s. Understanding these strategies helps children move from reliance on tricks to automatic recall, which is the ultimate goal. Here, we delve into these strategies and explore methods to help students achieve fluency in the 9 times table.

The Finger Trick: A Hands-On Approach

How It Works

The finger trick is a classic method that transforms the 9 times table into an interactive and magic-like experience. Here's how you can guide your child through it:
  • Hold up both hands, palms facing you, with all ten fingers extended.
  • Number the fingers from left to right: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
  • To find a product like 9 x 4, fold down the fourth finger.
  • Count the fingers to the left of the folded finger for the tens digit (3 fingers = 30).
  • Count the fingers to the right for the ones digit (6 fingers = 6).
  • The answer is 36.

Why Kids Love It

Children are naturally drawn to the finger trick because it feels magical. It provides an immediate, tactile way to interact with multiplication, making it more intuitive and less abstract. This approach works seamlessly for every fact from 9 x 1 to 9 x 10, ensuring that kids can quickly verify answers.

Case Study: Emily's Journey

Emily, a fourth-grader, struggled with multiplication until she learned the finger trick. Her teacher introduced it during a math game day, and Emily was fascinated. She practiced at home, showing her parents how she could calculate the products quickly. Within weeks, Emily's confidence in math soared, and she began using the trick as a stepping stone to solve more complex multiplication problems without hesitation.

The Digit Pattern: Seeing is Believing

Understanding the Pattern

The digit pattern in the 9 times table offers a visually appealing method for understanding multiplication facts. As you list the products of the 9 times table, two patterns emerge:
  • The tens digit increases by 1 with each step.
  • The ones digit decreases by 1 with each step.
  • Each product's digits add up to 9.

Examples of the Pattern

  • 9 x 1 = 9 (or 09)
  • 9 x 2 = 18 (1 + 8 = 9)
  • 9 x 3 = 27 (2 + 7 = 9)
  • 9 x 4 = 36 (3 + 6 = 9)
  • 9 x 5 = 45 (4 + 5 = 9)
  • 9 x 6 = 54 (5 + 4 = 9)
  • 9 x 7 = 63 (6 + 3 = 9)
  • 9 x 8 = 72 (7 + 2 = 9)
  • 9 x 9 = 81 (8 + 1 = 9)
  • 9 x 10 = 90 (9 + 0 = 9)

Visual Learners and the Pattern

For children who are visual learners, recognizing this pattern can be more powerful than any mnemonic device. Visualizing the consistent increase and decrease in digits helps in committing these facts to memory, making it easier for students to recall them during tests.

The Subtraction Strategy: Simplifying the 9s

Breaking Down the Strategy

The subtraction strategy leverages what students already know about the 10 times table. It simplifies the 9 times table into a quick subtraction problem, making it less daunting for students. Here's how it works:
  • Multiply the number by 10.
  • Subtract the number from the result.
  • The difference is the product of the 9 times table.

Examples of the Subtraction Strategy

  • 9 x 7 = 70 - 7 = 63
  • 9 x 4 = 40 - 4 = 36
  • 9 x 8 = 80 - 8 = 72

Why It Works

This method is particularly effective for children who have mastered the 10 times table. By converting the problem into a subtraction task, students can rely on a familiar process, boosting their confidence in tackling the 9s. Over time, this practice leads to faster recall without needing to compute each step.

From Tricks to Automatic Recall

Building Fluency Over Time

While tricks provide an excellent foundation, the ultimate goal is automatic recall. This means students can answer multiplication facts without consciously thinking through steps. To achieve this, follow a structured progression:
  • Weeks 1-2: Introduce the trick. Encourage children to use it to answer every 9-fact correctly.
  • Weeks 3-4: Drill the facts with the trick available but not required. Aim for speed and accuracy.
  • Week 5 onward: Remove the trick. Drill in random order under time pressure. Strive for immediate recall.

Tools for Practice

Online platforms, such as TimesTablesTrainer, offer randomized quizzes that help transition from tricks to automatic recall. These short, varied practices prevent reliance on shortcuts and emphasize true mastery.

Age-Specific Tips for Teaching Multiplication

Grades K-2: Laying the Foundation

At this early stage, focus on building a solid understanding of numbers and simple addition. Introduce multiplication as repeated addition. Use physical objects like blocks or beads to demonstrate groups and quantities. Playful activities such as counting by 2s or 5s can set the stage for later learning.

Grades 3-4: Introducing the 9s

This is the critical age for introducing multiplication tables, including the 9s. Incorporate the finger trick and digit pattern methods. Engage students with math games and songs that reinforce the multiplication facts in a fun and memorable way.

Grades 5-6: Reinforcing and Mastering

By this stage, students should be moving towards automatic recall. Use timed drills and flashcards to build speed and accuracy. Encourage students to apply multiplication in real-life situations, such as calculating the cost of multiple items or planning a budget.

What to Avoid: Common Mistakes

Many parents fall into the trap of pushing for speed too early, leading to anxiety and frustration. Avoid emphasizing speed at the expense of understanding. Another common mistake is relying solely on rote memorization without context or application. Ensure that students understand the "why" behind multiplication to foster deeper learning.

Actionable Tips for Parents and Teachers

  • Incorporate daily practice into routines, such as during car rides or before dinner.
  • Use rewards and positive reinforcement to motivate practice.
  • Create a multiplication wall chart to visualize progress.
  • Introduce math apps and games to make learning interactive.
  • Regularly review older material to prevent forgetting.

For Special Situations: Tailoring Strategies

Test Anxiety

For students with test anxiety, practice under timed conditions at home to build confidence. Teach relaxation techniques, such as deep breathing, to use during tests.

ADHD

Children with ADHD benefit from short, focused sessions. Break learning into manageable chunks and incorporate movement breaks.

Gifted Students

Challenge gifted students with advanced problems or by exploring multiplication in different bases. Encourage them to teach peers, reinforcing their understanding.

Dyscalculia

For children with dyscalculia, employ multi-sensory approaches and provide extra time for practice. Use visual aids and concrete examples to reinforce learning.

Cooperating with Schools

Effective communication with your child's teacher can significantly enhance learning. Regularly check in on your child's progress and seek feedback on areas needing improvement. Attend school meetings and stay informed about the math curriculum and resources available. Collaborate with teachers to align home practice with school instruction.

Fostering a Long-Term Perspective

Developing a solid foundation in multiplication goes beyond immediate academic success. These skills are crucial for future math achievements and everyday problem-solving. Encourage a growth mindset, emphasizing effort and persistence over quick results. By nurturing a love for learning, you equip your child with the tools to tackle increasingly complex mathematical challenges.

Talking to Your Child's Teacher

Engaging with your child's teacher about their progress in math can yield valuable insights. Schedule regular check-ins or attend parent-teacher conferences to discuss your child's strengths and areas for improvement. Ask the teacher about the methods being used in class and how you can support your child’s learning at home. Offer to volunteer for math-related activities at school to stay involved.

When to Seek Outside Help

Sometimes, additional support is necessary to help a child succeed in math. If your child consistently struggles despite using various strategies, consider seeking outside help. Look for tutors who specialize in math and can provide personalized instruction. Also, educational apps and online resources can offer supplementary practice tailored to your child's needs.

A Weekly Routine for Mastering the 9 Times Table

Setting a consistent weekly routine can greatly enhance your child's ability to master the 9 times table. Here is a suggested plan:

Monday: Introduction and Practice

  • Introduce a new strategy or pattern.
  • Spend 15-20 minutes practicing using the finger trick or digit pattern.

Wednesday: Reinforcement Activities

  • Engage in math games that focus on the 9 times table.
  • Incorporate visual aids, such as charts or flashcards.

Friday: Assessment and Fun

  • Conduct a fun quiz or challenge to assess progress.
  • Reward effort and improvement with a small treat or privilege.

Weekend: Real-World Application

  • Encourage your child to apply multiplication in everyday situations, like cooking or shopping.
  • Discuss how multiplication is useful in real life.

What Research Says About Learning Multiplication

Research shows that understanding multiplication as a concept, rather than mere memorization, leads to better math fluency. Studies emphasize the importance of building a strong foundational number sense in early grades. Interactive and visual strategies, like the finger trick, are effective because they engage multiple areas of the brain. Consistent practice and immediate feedback are also critical in helping students achieve automatic recall.

Common questions parents ask

How long does it take to learn the 9 times table?

The time it takes varies by student, but with consistent practice, most children can become proficient within a few weeks. The key is regular, short practice sessions.

Should my child rely solely on tricks?

Tricks are a great starting point, but aim for fluency and understanding. Encourage your child to understand the logic behind the multiplication facts.

What if my child gets frustrated?

Keep practice sessions positive and stress-free. Use games and rewards to maintain motivation. If frustration persists, consider different strategies or professional support.

Can older students still benefit from these strategies?

Absolutely. These strategies can be useful for students of all ages, especially if they never mastered the 9 times table earlier.

How can I support my child at home?

Incorporate multiplication practice into daily routines, and use resources like charts, flashcards, and apps to make learning engaging. Keep communication open with your child and their teacher.

Last word

Mastering the 9 times table can be a rewarding journey when approached with engaging strategies and consistent practice. By leveraging techniques like the finger trick, digit patterns, and subtraction strategies, students can gain confidence and fluency in multiplication. With the right support, encouragement, and practice, every child can achieve success in math. Embrace the process, celebrate progress, and watch as your child's mathematical abilities flourish.