- 1. Place Value — From Hundreds to Billions
State the place value and face value of any digit in integers up to 12 digits; group digits correctly in the billions, millions, thousands, and ones framework.
- 2. Words, Numerals and Expanded Form
Convert fluently between words and numerals for integers up to 12 digits; write any integer in expanded form using standard and index notation.
- 3. Digit Arrangements, Ordering Integers and Comparison Symbols
Form largest/smallest/odd/even integers from a given set of digits; use comparison symbols correctly; order sets of integers in ascending and descending order.
- 4. The Number Line — Integers and Introduction to Decimals
Place integers accurately on number lines of varied scales; read marked values; calculate step size from endpoints and interval count; apply the same skill to decimal number lines.
- 5. Decimal Place Value, Expanded Form and Ordering Decimals
State the value of any digit in a decimal number to 4 decimal places; write decimals in expanded form (standard and index notation); compare and order decimal numbers using column-by-column comparison.
- 6. Number Line Deep Dive — Endpoints, Unknowns and Mixed Scales
Determine an unknown endpoint given a known endpoint and a marked value; handle number lines that mix integer and decimal scales; place negative numbers approximately.
- 7. Positive and Negative Numbers — Sign, Direction and Ordering
Represent signed integers and decimals using the vector model; compare and order any set of positive and negative numbers; use the number line as the primary ordering tool.
- 8. Negative Numbers on the Number Line — Crossing Zero
Read and place signed numbers on number lines; find unknown endpoints on segments that cross zero; solve number-line problems involving positive and negative values.
- 9. Multiplying by 10, 100, 1000 and Larger Powers
Multiply any integer or decimal by any positive power of 10 using column-shift reasoning; apply the Gattegno chart; avoid the 'add zeros' misconception.
- 10. Multiplying by 0.1, 0.01, 0.001 — The Gattegno Chart Reversed
Multiply any number by any negative power of 10; recognize x 0.1 = / 10; interpret the Gattegno chart in the downward direction.
- 11. Dividing by Powers of Ten — Including Division by Decimals
Divide any number by any power of 10 (including 0.1, 0.01, 0.001); explain why / 0.1 makes a number bigger; identify the column-shift direction for division.
- 12. Mixed Powers of Ten — Chains, Equivalence and Word Problems
Simplify chains of multiplications and divisions by powers of 10 into a single equivalent operation; apply powers-of-10 reasoning to practical contexts like money and sharing.
- 13. Rounding to the Nearest 10, 100, 1,000 and 10,000
Round any integer to the nearest 10, 100, 1,000 or 10,000 using number line reasoning; describe up/down rounding patterns across multiple levels of accuracy; apply the midpoint convention.
- 14. Rounding to the Nearest 10, 100, 1000 and 10,000
Round any integer to the nearest 10, 100, 1000 or 10,000 using number line reasoning; describe up/down rounding patterns across multiple levels of accuracy; apply the midpoint convention.
- 15. Rounding to Significant Figures
Identify the first significant figure of any integer or decimal; round to 1, 2 and 3 significant figures; connect s.f. rounding to the place-value column language already established.
- 16. Mixed Rounding and Inverse Rounding
Apply any rounding method to any number in a mixed set; find numbers that satisfy given rounding conditions; evaluate common misconceptions about rounding.
- 17. Common Metric Conversions
Use the metric prefix table to convert between units; connect prefix scale factors to powers of 10; choose the correct direction (multiply or divide) for any conversion.
- 18. Finding the Midpoint of Two Numbers
Find the midpoint of any pair of numbers — integers, decimals, negatives — using the average formula (a+b)÷2; represent midpoints on a number line diagram; use inverse reasoning to find a missing endpoint.
- 19. The Median of Discrete Data
Find the median of odd-length and even-length ordered lists including lists with negatives and decimals; identify the missing value in a list with a known median.
- 20. What Is a Base? — Generalising the Place Value System
Explain what defines a place-value base system; identify column values for any base; count in base 3 and base 5; connect base-2 structure to the binary lessons that follow.
- 21. Binary — Counting and Reading (Base 2 to Base 10)
Count in binary from 0 to at least 20; convert any binary number up to 7 digits to its base-10 value using the column-multiplication method.
- 22. Binary — Converting Base 10 to Binary
Convert any base-10 integer up to 127 to binary using the column-subtraction (greedy) method; verify conversions; recognize the left-shift doubling pattern.
