Strengthen number sense, operations, fractions, proportional reasoning, problem solving, geometry and data. This reader-friendly shelf contains 160 focused learning guides, grouped by related skills and ideas.
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Number sense (20 guides)
- Counting Objects Accurately with One-to-One Correspondence
- Understanding Place Value in Two-Digit Numbers
- Understanding Place Value in Three-Digit Numbers
- Understanding Place Value in Four-Digit Numbers
- Reading and Writing Whole Numbers
- Comparing Whole Numbers with Place Value
- Ordering Whole Numbers on a Number Line
- Recognising Odd and Even Numbers
- Identifying Number Patterns
- Understanding the Value of Zero
- Estimating Sensible Quantities
- Rounding Whole Numbers to the Nearest Ten
- Rounding Whole Numbers to the Nearest Hundred
- Rounding Whole Numbers to the Nearest Thousand
- Understanding Factors of a Number
- Understanding Multiples of a Number
- Recognising Prime and Composite Numbers
- Finding Common Factors
- Finding Common Multiples
- Using Number Sense to Check an Answer
Operations (22 guides)
- Understanding Addition as Combining Quantities
- Understanding Subtraction as Finding Difference
- Adding Two-Digit Numbers Without Regrouping
- Adding Two-Digit Numbers with Regrouping
- Subtracting Two-Digit Numbers Without Regrouping
- Subtracting Two-Digit Numbers with Regrouping
- Understanding Multiplication as Equal Groups
- Understanding Division as Equal Sharing
- Building Accurate Multiplication Facts
- Connecting Multiplication and Division Facts
- Using the Commutative Property of Addition
- Using the Commutative Property of Multiplication
- Using the Distributive Property with Friendly Numbers
- Multiplying by Ten One Hundred and One Thousand
- Dividing by Ten One Hundred and One Thousand
- Multiplying Multi-Digit Numbers
- Dividing with Remainders
- Interpreting a Remainder in Context
- Using Order of Operations in Simple Expressions
- Choosing an Efficient Calculation Strategy
- Estimating Before Performing a Calculation
- Checking an Operation with Its Inverse
Fractions (25 guides)
- Understanding a Fraction as Equal Parts
- Recognising Numerator and Denominator
- Representing Fractions with Area Models
- Representing Fractions on a Number Line
- Recognising Unit Fractions
- Comparing Fractions with the Same Denominator
- Comparing Fractions with the Same Numerator
- Finding Equivalent Fractions
- Simplifying Fractions to Lowest Terms
- Converting Improper Fractions to Mixed Numbers
- Converting Mixed Numbers to Improper Fractions
- Adding Fractions with the Same Denominator
- Subtracting Fractions with the Same Denominator
- Finding a Common Denominator
- Adding Fractions with Unlike Denominators
- Subtracting Fractions with Unlike Denominators
- Adding Mixed Numbers
- Subtracting Mixed Numbers
- Finding a Fraction of a Whole Number
- Multiplying a Fraction by a Whole Number
- Interpreting a Fraction of a Set
- Comparing Fractions with Benchmarks
- Solving Fraction Comparison Problems
- Recognising Fraction Misconceptions
- Checking Fraction Answers for Reasonableness
Decimals and percentages (20 guides)
- Understanding Tenths as Decimals
- Understanding Hundredths as Decimals
- Representing Decimals on a Number Line
- Comparing Decimal Numbers
- Ordering Decimal Numbers
- Rounding Decimals to an Appropriate Place
- Adding Decimal Numbers
- Subtracting Decimal Numbers
- Multiplying Decimals by Whole Numbers
- Dividing Decimals by Whole Numbers
- Connecting Fractions and Decimals
- Understanding Percentage as Parts per Hundred
- Converting Simple Fractions to Percentages
- Converting Decimals to Percentages
- Finding a Percentage of a Quantity
- Understanding Percentage Increase
- Understanding Percentage Decrease
- Comparing Discounts and Sale Prices
- Solving Multi-Step Percentage Problems
- Checking Percentage Answers Against the Original Whole
Ratio and rates (15 guides)
- Understanding Ratio as a Comparison
- Writing Ratios in Simplest Form
- Finding Equivalent Ratios
- Dividing a Quantity in a Given Ratio
- Comparing Part-to-Part and Part-to-Whole Ratios
- Understanding Rate in Everyday Contexts
- Finding Unit Rate
- Comparing Prices Using Unit Rates
- Understanding Speed as Distance per Unit Time
- Solving Distance Speed and Time Problems
- Understanding Average Speed Carefully
- Connecting Ratio and Fractions
- Scaling a Recipe Using Ratio
- Solving Ratio Problems with Models
- Recognising When Proportional Reasoning Applies
Problem solving (25 guides)
- Reading a Mathematics Word Problem Carefully
- Identifying the Question Before Calculating
- Separating Relevant and Irrelevant Information
- Drawing a Part-Whole Model
- Drawing a Comparison Model
- Using a Before-and-After Model
- Representing Equal Groups with a Model
- Representing Repeated Difference
- Using a Systematic Listing Strategy
- Using Guess and Check Responsibly
- Working Backwards from a Final Quantity
- Looking for a Repeating Pattern
- Solving a Two-Step Word Problem
- Solving a Three-Step Word Problem
- Tracking Units Throughout a Problem
- Choosing Between Addition and Subtraction
- Choosing Between Multiplication and Division
- Translating Words into Number Sentences
- Comparing Two Possible Problem-Solving Methods
- Explaining Mathematical Reasoning in Words
- Checking Whether an Answer Fits the Story
- Repairing a Misread Word Problem
- Avoiding Premature Calculation
- Handling Challenging Problems Without Panic
- Building Transfer Across Unfamiliar Problem Contexts
Geometry and measurement (22 guides)
- Recognising Basic Two-Dimensional Shapes
- Describing Properties of Triangles
- Describing Properties of Quadrilaterals
- Recognising Lines of Symmetry
- Understanding Right Angles
- Comparing Acute Obtuse and Right Angles
- Measuring Angles with a Protractor
- Understanding Parallel and Perpendicular Lines
- Finding the Perimeter of a Rectangle
- Finding the Area of a Rectangle
- Finding the Area of a Triangle
- Understanding Area as Covering a Surface
- Understanding Volume as Occupied Space
- Calculating Volume of a Cuboid
- Converting Units of Length
- Converting Units of Mass
- Converting Units of Capacity
- Reading Time on an Analogue Clock
- Calculating Elapsed Time
- Understanding Timetables and Schedules
- Solving Measurement Problems with Mixed Units
- Checking Geometry and Measurement Units
Data and uncertainty (11 guides)
- Reading a Simple Picture Graph
- Reading a Bar Graph Accurately
- Creating an Appropriate Data Table
- Comparing Categories in a Bar Graph
- Interpreting a Line Graph in Context
- Recognising Misleading Graph Scales
- Finding the Average of a Small Data Set
- Understanding Why an Average May Be Misleading
- Collecting Data Fairly
- Explaining What a Data Display Shows
- Checking Conclusions Against the Available Data
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