Maths Journeys: The Super Strategies of Counting On & Counting Back!

Hello Young Mathematicians! Did you know that you can go on little number journeys in your head to solve maths problems? Today, we’re going to explore two super useful mental strategies: Counting On for addition, and Counting Back for subtraction. These are like your first steps into becoming a mental maths explorer!

What is “Counting On”? (Your Addition Helper!)

“Counting On” is a simple way to add numbers, especially when you’re adding a small number to a bigger one. You start with the bigger number and then count on the smaller number, one step at a time.

Example: 45 + 3

• Start with the bigger number in your head: 45.
• Now, we need to count on 3 more steps.
• Let’s count:
  • One step on from 45 is… 46
  • Two steps on from 45 is… 47
  • Three steps on from 45 is… 48
• So, 45 + 3 = 48! You just “counted on” to find the answer!

You can use your fingers to keep track of the small number of steps if it helps at first!

What is “Counting Back”? (Your Subtraction Helper!)

“Counting Back” is a great way to subtract, especially when you’re taking away a small number. You start with the bigger number and then count back the smaller number, one step at a time.

Example: 38 − 4

• Start with the bigger number in your head: 38.
• Now, we need to count back 4 steps.
• Let’s count:
  • One step back from 38 is… 37
  • Two steps back from 38 is… 36
  • Three steps back from 38 is… 35
  • Four steps back from 38 is… 34
• So, 38 − 4 = 34! You “counted back” to solve it!

Again, using your fingers to track the steps can be useful when you’re starting.

Practice Your Counting Strategies! (18 Questions)

Ready to go on some mental number journeys? Here are 18 questions. For the addition ones, try “Counting On.” For the subtraction ones, try “Counting Back.” Think carefully and see if you can find the answers in your head!

(Your web app with the 18 questions will go here. The questions should involve adding or subtracting small numbers where these strategies are most effective.)

Why Are These Counting Strategies So Useful?

• They’re Easy to Learn: These are often the first mental strategies we discover!
• Build a Strong Start: They give you a solid foundation for all other maths.
• Great for Small Numbers: Perfect when you’re adding or subtracting 1, 2, 3, 4, or 5.
• Boosts Your Confidence: Using them successfully makes you feel like a real maths whizz!

Tips for Grown-Ups: Encouraging Counting Strategies

“Counting On” and “Counting Back” are foundational mental calculation strategies, particularly effective when adding or subtracting small quantities (typically up to 5). They help children develop an internal number line and an understanding of the sequential nature of numbers.

• Start with Physical Actions: Encourage using fingers, or moving objects, to represent the “counts” when first learning.
• Use Number Lines: Visually demonstrate “counting on” by hopping forwards on a number line, and “counting back” by hopping backwards.
• Verbalise the Process: Ask children to say the numbers aloud as they count on or back. “I’m starting at 45, then 46 (1), 47 (2), 48 (3).”
• Keep it Fun: Use games, like board games with dice, where counting on is a natural part of play.
• Know When to Move On: As numbers get larger, these strategies become less efficient. Guide children towards more advanced strategies (like using number bonds or place value) when appropriate, but ensure these basics are solid.