MAE3270 Module 2 - Lecture 1: Number sense and fluency

Chapter 1: Introduction

  • Number sense and fluency

  • Proficiency strands: additive thinking, multiplicative thinking, money and financial maths

  • Number sense is about developing a useful and effective feel for numbers

    • Interpreting and using numbers for specific purposes

    • Computing efficiently and recognizing if results make sense

    • Using and understanding numbers effectively for everyday living

  • Proficiency strands are implicit in lesson planning

    • Students demonstrate evidence of understanding and fluency

  • Building knowledge and transferable skills in mathematical concepts

    • Making connections between concepts

    • Applying familiar concepts to new ideas and situations

    • Understanding the relationship between the why and how of maths

    • Connecting ideas and representing concepts in different ways

    • Identifying commonalities and differences between content

    • Describing and explaining thinking

    • Interpreting information

  • Demonstrating fluency

    • Choosing appropriate procedures

    • Carrying out procedures flexibly, accurately, efficiently, and appropriately

    • Recalling knowledge and concepts readily

    • Choosing appropriate methods and approximations

    • Recalling definitions and terminology

    • Manipulating expressions and equations

Chapter 2: Mental Math

  • Mental computation

    • Using hands-on materials, manipulatives, and diagrams

    • Visualizing calculations mentally

    • Sound mental computation skills empower students in math learning

  • Choosing to compute mentally

    • Understanding relationships and operations

    • Demanding mental thought and unthinking recall of procedures

    • Developing mental strategies suited to the numbers involved

  • Importance of understanding algorithms

    • Learning procedures without understanding can lead to shortcomings

Chapter 3: Addition And Subtraction

  • Students might forget a step in the procedure

    • Examples: not holding a 0, not holding a place, trading numbers into the wrong column or not trading at all

  • Students might not make sense of the numbers they're dealing with

    • They don't understand the place value

  • Addition and subtraction are inverse operations

    • Multiplication and division are also inverse operations

  • Multiplication is viewed as repeated addition

    • Remind students that multiplication is simply repeated addition

    • Helps students understand multiplication as a step on from addition

  • Division is viewed as repeated subtraction

    • Example: 24 divided by 6 equals 4

Chapter 4: Subtract The Numbers

  • Using a number line to subtract numbers

    • Example: Starting at 24 and subtracting 6 each time until reaching 0

    • Counting the number of jumps on the number line

  • Understanding additive thinking

    • Manipulating numbers by joining, separating, or comparing

    • Working flexibly with addition and subtraction

    • Moving beyond memorization of basic arithmetic skills

    • Demonstrating understanding through words, diagrams, algorithms, manipulatives, etc.

  • Adding and subtracting numbers to change a quantity

    • Combining parts or comparing two quantities

Chapter 5: Vertical Number Lines

  • Partitioning numbers into part part whole to relate addition and subtraction

  • Useful models for addition

    • Counters, unifix cubes, number lines, 100 square, balance

  • Introduce number line as soon as possible

    • Visualizing number line in concrete and abstract

    • Helps with subtraction, negative numbers, and fractions

  • Models for subtraction

    • Using 2 color counters for positive and negative numbers

    • Using a number line to subtract

  • Utilizing vertical number lines and other representations

    • Interchanging horizontal and vertical number lines

    • Using thermometers, scales, and syringes for different representations

Chapter 6: Thinking Addition

  • Terminology for addition:

    • How many or how much altogether

    • Add or combine

    • Increase by or go up by

    • What is the sum or total

    • Start at and count on

  • Use of number lines

  • Difference between sum and product

    • Sum is used for addition

    • Product is used for multiplication

  • Terminology for subtraction:

    • Takeaway

    • How many left

    • How many more

    • Count back by

    • What is the difference

  • Contexts for addition:

    • Money

    • Temperature

    • Age

    • Length

    • Mass

    • Time

  • Properties of addition

Chapter 7: Conclusion

  • Commutative property

    • The order of adding numbers does not affect the answer

    • Example: 5 + 2 = 2 + 5

  • Associative property

    • The grouping of numbers does not affect the sum

    • Example: (2 + 3) + 4 = 2 + (3 + 4)

  • Additive property of 0

    • Adding 0 to any number does not change the original number