Topic 1 - Whole Numbers
Big idea
Arithmetic skills, including order of operations, estimation, technology, and symbolic expressions, are essential tools for problem-solving and building a strong foundation for advanced mathematical concepts.
(1.01) Basic arithmetic operations such as addition and subtraction are essential to understanding more advanced mathematical concepts and can be visualised on a number line.
(1.02) Visualising multiplication can be accomplished through the use of rectangular grids and the area model, while the vertical algorithm is a way to multiply larger numbers efficiently by keeping place values aligned.
(1.03) Division is the inverse operation of multiplication and can be approached through strategies such as visual models and short division.
(1.04) It is essential to use the order of operations when evaluating expressions with multiple operations in order to perform accurate mathematical calculations.
(1.05) Estimation is a useful tool for checking the accuracy and reasonableness of calculations and involves rounding numbers.
(INVESTIGATION: How long does it take to count to a million?) Use estimation and rounding as a method to perform large calculations with more ease.
(1.06) Mastering the use of a hand-held calculator for whole number operations is a fundamental skill to efficiently solve problems, minimise errors, and verify the reasonableness of answers.
(1.07) Learning to express mathematical ideas using symbols and operations allows for clear communication and effective problem-solving in various math situations.
Syllabus Outcomes
Background
Topic Expected Timing: ~1 week
Key Vocabulary and Student supports included for each lesson outlined in detail below.
1.01 Addition and subtraction
Essential understanding
Basic arithmetic operations such as addition and subtraction are essential to understanding more advanced mathematical concepts and can be visualised on a number line.
Students will be able to:
● add multi-digit numbers.
● subtract multi-digit numbers.
Estimated Time: 1 lesson
Lesson narrative
In this lesson, students will review addition and subtraction, the fundamental skills that help them combine and separate quantities. The lesson will cover the use of the + and − symbols and the strategy of adding or subtracting numbers using a place value table. Students will practice single-digit and multi-digit addition and subtraction using both methods. They will also learn how to use regrouping, where they split each number up into convenient pieces such as thousands, hundreds, tens, and ones, to add or subtract large numbers. By the end of the lesson, students will be able to add and subtract numbers using a place value table and regrouping strategy, and have the confidence to tackle more complex problems.
Syllabus Outcomes:
Background
Key vocabulary
Regrouping
Tools
Place value chart
Enlarged number lines
1.02 Multiplication
Essential understanding
Visualising multiplication can be accomplished through the use of rectangular grids and the area model, while the vertical algorithm is a way to multiply larger numbers efficiently by keeping place values aligned.
Students will be able to:
● multiply multi-digit numbers.
● use different methods to multiply small and large numbers.
Estimated Time: 1 Lesson
Lesson narrative:
In this lesson, students will review the concepts of multiplication and learn how to use both the area model and vertical algorithm to multiply larger numbers efficiently. The lesson will begin with exploring multiplication through visualising it with a rectangular grid of squares, and connecting it with place value. Students will also practice using an applet to model multiplication of single-digit numbers and answer questions based on it. Then, they will move on to using the area model to visualise multiplying larger numbers and see how a large rectangle can be divided into smaller rectangles based on place value to represent the multiplication. Finally, students will learn to use the vertical algorithm to multiply larger numbers in a more efficient way by keeping the place values aligned. They will practice solving multiplication problems using both the area model and vertical algorithm. By the end of the lesson, students will be able to explain the reasoning behind each method and choose the most appropriate method for a given problem.
Syllabus Outcomes:
Background
Key vocabulary:
Commutative law
Area model
Vertical algorithm
Tools
Grid Paper
Base ten blocks
Student Exploration (linked to student lesson)
Exploration Support (Linked to teacher guide)
1.03 Division
Essential understanding
Division is the inverse operation of multiplication and can be approached through strategies such as visual models and short division.
Students will be able to:
● divide multi-digit numbers.
● use different methods to divide small and large numbers.
Estimated Time: 1 Lesson
Lesson narrative:
In this lesson, students will review the concept of division. They will learn that division is the opposite of multiplication, using the ÷ symbol, and that it involves sharing or splitting quantities into equal parts. Students will explore how to use an area model to divide numbers up to 144 and learn how division is related to multiplication. They will then learn how to use short division to divide larger numbers, by considering each place value of the dividend separately. By the end of the lesson, students will be able to use short division to evaluate division problems involving larger numbers and understand the relationship between division and multiplication.
Syllabus Outcomes:
Background
Student Exploration (Linked to student lesson)
Exploration Support (Linked to teacher guide)
1.04 Order of operations with whole numbers
Essential understanding
It is essential to use the order of operations when evaluating expressions with multiple operations in order to perform accurate mathematical calculations.
Students will be able to:
● perform arithmetic operations using the order of operations.
Estimated Time: 1 Lesson
Lesson narrative:
In this lesson, students will learn about the order of operations and how to use it to solve problems with multiple operations, like addition, subtraction, multiplication, and division. The order of operations provides a set of rules to follow that ensure we get the correct answer every time. Students will learn to evaluate expressions that contain brackets, indices, multiplication or division, and addition or subtraction. By the end of the lesson, students will have a solid understanding of the order of operations and be able to use it to solve problems accurately.
Syllabus Outcomes:
Background
Key Vocabulary
Order of Operations
Tools
Order of operations chart
1.05 Check reasonableness of calculations
Essential understanding
Estimation is a useful tool for checking the accuracy and reasonableness of calculations, and involves rounding numbers.
Students will be able to:
● estimate and check the reasonableness of an answer.
Estimated Time: 1 Lesson
Lesson narrative:
In this lesson, students will learn how to estimate and check the reasonableness of an answer. By rounding numbers to the nearest place value, students can get a rough idea of what the answer should be. They will also learn how to check the reasonableness of an answer by asking themselves if the answer makes sense in the context of the problem. This will ensure that the answer is correct and will help identify any calculation errors. By the end of the lesson, students will be able to confidently estimate and check the reasonableness of an answer.
Syllabus Outcomes:
Background
Key vocabulary
Estimate
1.06 Number calculations with technology
Essential understanding
Mastering the use of a hand-held calculator for whole number operations is a fundamental skill to efficiently solve problems, minimise errors, and verify the reasonableness of answers.
Students will be able to:
● use technology to perform operations with whole numbers and check the reasonableness of their answer.
Estimated Time: 1 Lesson
Lesson narrative:
In this lesson, students will learn how to use a hand-held calculator to perform operations with whole numbers. They will learn the basic buttons to use and how to enter numbers and operations to get an answer. Students will also learn to check the reasonableness of their answer to ensure it is correct. They will understand the common calculator errors such as missing a digit from a number, swapping digits, using the wrong operation, and adding an extra digit. By the end of the lesson, students will be able to use a calculator to perform operations with whole numbers and check the reasonableness of their answer.
Syllabus Outcomes:
Background
Key vocabulary
Order
1.07 Write mathematical statements
Essential
understanding
Learning to express mathematical ideas using symbols and operations allows for clear communication and effective problem-solving in various math situations.
Students will be able to:
● translate written text into mathematical expressions using the four operations of addition, subtraction, multiplication, and division.
● describe the relationship between numbers using symbols such as greater than, less than, greater than or equal to, less than or equal to, equal to, and not equal to.
Estimated Time: 1 Lesson
Lesson narrative:
In this lesson, students will learn about the language of mathematics and how to translate between written text and mathematical expressions. They will be introduced to the four operations: addition, subtraction, multiplication, and division, and learn different ways to refer to them. Students will also learn about the symbols used to describe the relationship between numbers, including greater than, less than, greater than or equal to, less than or equal to, equal to, and not equal to. By the end of the lesson, students will be able to write and interpret mathematical expressions using numbers and symbols.
Syllabus Outcomes:
