Below is a guide showing one possible way of sequencing the teaching of skills within the 2019 Mathsquad Homework Program (2018 Skill Sequence found here). It is likely that this will be a great support to teachers new to the program, though over time it is likely that teachers will want to make modifications to the sequence based on student data to ensure their teaching best meets the needs of the students in their class.

It is important to remember that learning is the priority of any teaching that takes place, consequently some skills may need to be taught over multiple lessons or revisited at a later date. The goal of the classroom teacher it is to improve students’ skills and pacing according to students’ needs is essential.

Please note that over time it is hoped that each skill listed below will be accompanied with specific examples and scripts for explicit teaching and also suggestions for how to best support and extend students. For the time being, feel free to use the examples within the skill development book (or homework helper) as your board notes, as these have been carefully chosen to highlight key points. Regarding extension and support, the skill development book contains extension questions for each skill, which will generally be sufficient for extension, and students can be supported by being directed to a prerequisite skill that they may need practice in before they can access the skill the class is focusing on.

Topic 1: Introduction to the skill development book & Base 10 blocks

Rational: It is recommended that you start with a lesson on base 10 blocks as a way to introduce the skill development book. This is suitable as many students have enough familiarity with base 10 blocks to allow them to focus on the generic skills of using the skill development book and setting up maths exercise books correctly.

  • F01 Base 10 blocks

Topic 2: Integers and Algebra

Rational: Pretest data consistently shows that these skills are (as expected) unfamiliar to students. Since the skills don’t require much more than use of the four operations this is a great way of meeting the needs of a wide variety of students. Students with low pretest marks will benefit from the opportunity to practice arithmetic and students with higher pretest marks are likely to be filling in gaps in their knowledge.

  • F13 Adding and subtracting positive integers (expected to take at least 2 lessons)
  • F23a Substitution involving adding and subtracting
  • F23b Substitution involving multiplying and dividing
  • F24a Solving involving adding and subtracting (please use strategy as outlined in skill development book – please do not use flow charts!)
  • F24b Solving involving multiplying and dividing (please use strategy as outlined in skill development book – please do not use flow charts!)

Topic 3: Primes, Factors and Multiples

Rational: This topic equips students with the knowledge required to complete questions involving fraction arithmetic. It also helps students see how important knowing their times tables is. While during this topic they can be supported with a times tables grid it is hoped that increased practice will help them develop the efficiency in which they can recall their times tables and/or motivate them to do additional work on these outside of class (a good free app is “10 minutes a day times tables”).

  • F09d Division with remainders
  • F10 The division algorithm (expected to take at least 2 lessons)
  • F15a Factors of a number
  • F15b Multiples of a number
  • F16 – Prime factorisation (expected to take at least 2 lessons)

Topic 4: Fractions

Rational: This topic bridges between foundation and core, with the bonus being that all core level fraction skills are contained in the core section within the foundation homework booklet. This topic is long so it might be worth splitting into two parts. For example, you could do all foundation skills first and then break and then do core skills.

  • Creating a Fraction Wall (not connected directly to a skill though a great introduction and tool to help students learn upcoming skills)
  • F17 Fraction models (starting with rectangles then moving to number lines)
  • F18 Adding fractions with a common denominator
  • F19 Fractions of an amount
  • F20 Equivalent fractions
  • F21 Simplifying fractions
  • F22 Mixed numbers and improper fractions
  • C04 Lowest common multiples
  • C09 Adding and subtracting fractions (expected to take at least 2 lessons, focusing on related denominators then unrelated)
  • C10 Multiplying fractions (expected to take at least 2 lessons)
  • C11 Dividing Fractions
  • C12 Fraction arithmetic with mixed numbers

Topic 5: Order of operations and Algebra

Rational: A good change of focus from the work on fractions and another good topic for bridging between foundation and core.

  • F11 Order of operations
  • F12 Square roots and powers
  • C05 Order of operations with roots, powers and fractions of numbers
  • C17 Substitution in two step expressions 
  • C18 Solving two step equations (expected to take at least 3 lessons)
  • C19a Solving equations with integers
  • C19b Solving equations with fractional solutions
  • C21″a” Completing coordinates (start with given x and find y)
  • C21″b” Completing coordinates (given y and find x)
  • C22 Finding rules
  • F25 Plotting coordinates
  • C20 Transforming coordinates (expected to take 2 lessons)

Topic 6: Decimals and Percentages

Rational: A good topic once fraction skills are established.

  • F02a Multiplying whole numbers by 10 and 100
  • Fo2b Rounding whole numbers
  • F14a Place value of decimals
  • F14b Rounding decimals
  • C06 Comparing decimals
  • C07 Multiplying and dividing by 10, 100 and 0.1
  • C08 Converting between fractions decimals and percentages
  • F04 Addition algorithm (if needed)
  • F06 Subtraction algorithm (if needed)
  • C13 Adding and subtracting decimals
  • F08 Multiplication algorithm (if needed)
  • C14 Multiplying decimals
  • F10 Division algorithm (if needed – already covered in topic 2)
  • C15 Dividing decimals
  • C16 Calculating a percentage of a number

Topic 7: Angles

  • F26 Estimating and classifying angles
  • C26 Part 1 Angles around a point
  • C26 Part 2 Angles around parallel lines
  • C27 Angles in a triangle and classifying triangles

Topic 8: Measurement

  • F27 Perimeter and area of a rectangle
  • F28 Volume of a rectangular prism
  • C23 Units of measurement and conversions
  • C24 Using formulas in measurement (expected to take 3 lessons)

Topic 9: Probability and Statistics

  • C25 Sample space and probability
  • C28 Mean, median, mode and range, and stem and leaf plots (expected to take 3 lessons)