How to learn Year 1: Mathematics

The New Zealand Curriculum (Ministry of Education): Mathematics, Year 1

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1. Number · Operations

Addition in any order: Understand and apply the commutative property of addition: addends can be added in any order
Subtraction as taking away or separating: Understand subtraction as taking away or separating from a group to find how many remain
Adding and subtracting: Add and subtract one-digit and two-digit numbers to 20, including zero
Addition and subtraction word problems: Solve addition and subtraction word problems within 10 using objects or drawings
Addition and subtraction within 20: Add and subtract within 20 using strategies such as making ten, decomposing a number leading to ten, and using known facts
Adding Three Small Numbers: Add three one-digit numbers using strategies including looking for pairs that make 10
Division as equal sharing: Understand division as sharing equally into groups or as grouping (how many groups of a given size can be made)
Multiplication as repeated addition: Understand multiplication as repeated addition and grouping equal sets
Arrays for multiplication: Use arrays to represent multiplication and division situations

What Is a Half?: Recognise, find, and name a half as one of two equal parts of an object, shape, or quantity
Fractions of amounts: Recognise, find, name, and write fractions 1/3, 1/4, 2/4, and 3/4 of a length, shape, set of objects, or quantity
Simple Fraction Sums: Add and subtract fractions with the same denominator within one whole (e.g. 5/7 + 1/7 = 6/7)
Understanding fractions: Write simple fractions (e.g. 1/2 of 6 = 3) and recognise the equivalence of 2/4 and 1/2

Adding money and giving change: Find different combinations of coins that equal the same amount of money
Money Addition & Subtraction: Solve simple money problems involving addition and subtraction, including giving change

Reading ×, ÷, and = Symbols: Read, write, and interpret the symbols ×, ÷, and = in multiplication and division number sentences
Comparing groups: more or fewer: Compare two groups of objects to determine which has more, fewer, or whether they are equal, using matching and counting strategies
Inverse: addition undoes subtraction: Recognise and use the inverse relationship between addition and subtraction to check calculations and solve missing-number problems

Patterns & Sequences: Order and arrange combinations of mathematical objects in patterns and sequences

Choosing measurement units: Choose and use appropriate standard units to measure length (m/cm), mass (kg/g), temperature (°C), and capacity (litres/ml) to the nearest appropriate unit
Measurable Attributes of Objects: Describe and identify measurable attributes of objects such as length, height, weight, and capacity; use comparative language (longer, shorter, heavier, lighter, more, less)
Comparing lengths by measuring: Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit
Comparing and ordering measurements: Compare and order lengths, mass, and capacity and record results using >, <, and =

Measuring Perimeters: Measure the perimeter of simple 2-D shapes
Measuring length (age 6+): Measure the length of an object using same-size length units laid end to end with no gaps or overlaps
Area by Tiling: Find the area of a rectangle by tiling it with unit squares and show that the result equals the product of the side lengths

Telling time to the minute: Measure and begin to record time in hours, minutes, and seconds
Number of minutes in an hour: Know the number of minutes in an hour and the number of hours in a day
Time Units and Calendar Facts: Know the number of seconds in a minute and the number of days in each month, year, and leap year
Ordering Events in Time: Sequence events in chronological order using language such as before, after, next, first, today, yesterday, tomorrow, morning, afternoon, evening
Days, Weeks, Months & Years: Recognise and use language relating to dates, including days of the week, weeks, months, and years
Telling Time: Hours and Half Hours: Tell the time to the hour and half past the hour, and draw clock hands to show these times

Turns & Directions: Describe movement and direction, including whole, half, quarter, and three-quarter turns

3-D shapes: Recognise and name common 3-D shapes (cubes, cuboids, pyramids, spheres, cylinders, cones)
2-D shapes: Recognise and name common 2-D shapes (circles, triangles, rectangles including squares)
3-D shapes (age 5+): Analyse and compare 2-D and 3-D shapes using informal language to describe sides, vertices, and other attributes
Edges, vertices, and faces: Identify and describe properties of 3-D shapes including the number of edges, vertices, and faces

Shape patterns: Look for and use mathematical structure: apply properties of operations, place-value patterns, and relationships between shapes to solve problems efficiently

Positional Language: Describe the position of objects using terms such as above, below, beside, in front of, behind, next to

Sorting into categories (age 6+): Interpret categorical data by asking and answering questions about totals, how many in each category, and how many more or less one category has than another
Pictograms and tally charts (age 6+): Read, write, and use the vocabulary of data collection and display — data, tally, tally chart, frequency, frequency table, survey, pictogram, bar chart, axis/axes, scale, label, category, discrete data, continuous data, line graph, pie chart — and apply these terms when collecting, organising, and presenting data

Pictograms and tally charts: Interpret and construct simple pictograms, tally charts, block diagrams, and simple tables