How to learn Year 0–1: Mathematics

The New Zealand Curriculum (Ministry of Education): Mathematics, Year 0–1

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1. Number · Operations

Addition as combining or putting together two: Understand addition as combining or putting together two groups to find the total
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
Counting objects to 20: Count a set of objects to answer 'how many?' for sets up to 20 (arranged in lines, arrays, circles, or scattered)
Representing Addition and Subtraction: Represent addition and subtraction using objects, drawings, and mental images
Multiplication as repeated addition: Understand multiplication as repeated addition and grouping equal sets
Division as equal sharing: Understand division as sharing equally into groups or as grouping (how many groups of a given size can be made)

Halves & Quarters of Shapes: Partition circles and rectangles into two and four equal shares and describe them using the words halves, fourths, and quarters
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

What Is a Half?: Recognise, find, and name a half as one of two equal parts of an object, shape, or quantity

Coin Values: Recognise and know the value of different coins and notes
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 number sentences
What the equals sign means: Understand the meaning of the equal sign as 'is the same as' and determine if equations are true or false

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

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
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)
Measuring mass and weight (age 4+): Compare two objects directly by mass or weight and describe the difference using language such as heavy, light, heavier than, lighter than
Capacity and volume: Measure and begin to record capacity and volume using non-standard and standard units

Measuring length (age 6+): Measure the length of an object using same-size length units laid end to end with no gaps or overlaps
Measuring Perimeters: Measure the perimeter of simple 2-D shapes

Turns & Directions: Describe movement and direction, including whole, half, quarter, and three-quarter turns
Position, direction, and movement: Use mathematical vocabulary to describe position, direction, and movement, including straight lines and distinguishing rotation as a turn in terms of right angles (quarter, half, three-quarter turns, clockwise and anti-clockwise)
Understanding angles: Recognise angles as a property of shape or a description of a turn

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
Ordering Events in Time: Sequence events in chronological order using language such as before, after, next, first, today, yesterday, tomorrow, morning, afternoon, evening
Comparing durations: Use comparative language for time: quicker, slower, earlier, later
Days, Weeks, Months & Years: Recognise and use language relating to dates, including days of the week, weeks, months, and years
Number of minutes in an hour: Know the number of minutes in an hour and the number of hours in a day

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
2-D shapes (age 6+): Identify and describe properties of 2-D shapes including the number of sides and line symmetry in a vertical line

Composing Shapes: Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, quarter-circles) to create composite shapes, and compose new shapes from the composite shape

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

Sorting into categories: Classify objects into given categories, count the number in each category, and sort the categories by count
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
Picture & Bar Graphs: Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories; solve put-together, take-apart, and compare problems using information presented in a bar graph