New Zealand

Number

• Number structure

  • skip count from any multiple of 100, forwards or backwards in 25s and 50s

  • identify, read, write, compare, and order whole numbers up to 10,000, and represent them using base 10 structure

    • Write numbers in words (4-A.1)
    • Comparing numbers (4-B.1)
    • Which number is greatest/least? (4-B.2)
    • Put numbers in order (4-B.3)
    • Place value models up to thousands (4-C.1)
    • Place value names up to hundreds (4-C.2)
    • Place value names up to thousands (4-C.3)
    • Place value word problems (4-C.9)

• Operations

  • use rounding, estimation, and inverse operations to predict results and to check the reasonableness of calculations

    • Estimate sums (4-O.8)
    • Estimate differences (4-O.10)
    • Estimate products (4-O.12)
    • Estimate quotients (4-O.14)
    • Estimate sums, differences, products and quotients: word problems (4-O.16)

  • round whole numbers to the nearest thousand, hundred, or ten

    • Rounding (4-O.1)
    • Round decimals to the nearest whole number (4-O.2)

  • add and subtract two- and three-digit numbers

    • Add two numbers up to three digits (4-E.1)
    • Addition input/output tables - up to three digits (4-E.2)
    • Add two numbers up to three digits - word problems (4-E.3)
    • Complete the addition sentence - up to three digits (4-E.4)
    • Subtract numbers up to three digits (4-F.1)
    • Subtraction input/output tables - up to three digits (4-F.2)
    • Subtract numbers up to three digits - word problems (4-F.3)
    • Complete the subtraction sentence - up to three digits (4-F.4)

  • recall multiplication and corresponding division facts for 4s and 6s

    • Multiply by 4 (4-H.5)
    • Multiply by 6 (4-H.7)
    • Divide by 4 (4-L.4)
    • Divide by 6 (4-L.6)

  • multiply a two-digit by one-digit number and two one-digit whole numbers (e.g., 23 × 5; 7 × 8)

    • Multiplication sentences (4-G.1)
    • Multiply by 0 (4-H.1)
    • Multiply by 1 (4-H.2)
    • Multiply by 2 (4-H.3)
    • Multiply by 3 (4-H.4)
    • Multiply by 4 (4-H.5)
    • Multiply by 5 (4-H.6)
    • Multiply by 6 (4-H.7)
    • Multiply by 7 (4-H.8)
    • Multiply by 8 (4-H.9)
    • Multiply by 9 (4-H.10)
    • Multiplication facts for 6, 7, 8, 9: sorting (4-I.6)
    • Multiply one-digit numbers by teen numbers using grids (4-J.3)
    • Multiply one-digit numbers by two-digit numbers using area models I (4-J.4)
    • Multiply one-digit numbers by two-digit numbers using area models II (4-J.5)
    • Multiply one-digit numbers by two-digit numbers (4-J.6)
    • Multiply one-digit numbers by two-digit numbers: word problems (4-J.7)

  • divide up to three-digit whole number by a one-digit divisor, with no remainder (e.g., 65 ÷ 5)

    • Divide by 1 (4-L.1)
    • Divide by 2 (4-L.2)
    • Divide by 3 (4-L.3)
    • Divide by 4 (4-L.4)
    • Divide by 5 (4-L.5)
    • Divide by 6 (4-L.6)
    • Divide by 7 (4-L.7)
    • Divide by 8 (4-L.8)
    • Divide by 9 (4-L.9)
    • Division facts for 6, 7, 8, 9: sorting (4-M.5)
    • Divide two-digit numbers by one-digit numbers using area models (4-N.4)
    • Divide two-digit numbers by one-digit numbers (4-N.5)
    • Divide three-digit numbers by one-digit numbers using area models (4-N.6)
    • Divide three-digit numbers by one-digit numbers (4-N.7)

• Rational numbers

  • identify, read, write, and represent tenths as fractions and decimals

    • Graph decimals on number lines (4-BB.2)
    • Identify decimals on number lines (4-BB.3)
    • Model decimals and fractions (4-BB.4)
    • Graph fractions and mixed numbers as decimals on number lines (4-BB.5)
    • Understanding decimals expressed in words (4-BB.8)

  • compare and order tenths as fractions and decimals, and convert decimal tenths to fractions (e.g., 0.3 = ³/₁₀)

    • Convert between decimals and fractions (4-BB.6)
    • Compare decimals and fractions on number lines (4-BB.7)
    • Inequalities with decimals (4-BB.10)
    • Put decimal numbers in order (4-BB.11)

  • divide whole numbers by 10 to make decimals

  • for fractions with related denominators of 2, 4, and 8, 3 and 6, or 5 and 10:

    • compare and order the fractions

      • Graph and compare fractions with like denominators on number lines (4-Z.2)
      • Put fractions in order (4-Z.5)

    • identify when two fractions are equivalent by directly comparing them, noticing the simplest form (e.g., ³/₆ = ¹/₂), which is the simplest form)

      • Find equivalent fractions (4-Y.1)
      • Select equivalent fractions (4-Y.2)
      • Write fractions in lowest terms (4-Y.3)

  • convert (using number lines) between mixed numbers and improper fractions with denominators of 2, 3, 4, 5, 6, 8, and 10

    • Convert between improper fractions and mixed numbers (4-Y.4)

  • find a unit fraction of a whole number, using multiplication or division facts and where the answer is a whole number (e.g., ¹/₅ of 40)

    • Fractions of a number - unit fractions (4-X.17)
    • Fractions of a number - unit fractions: word problems (4-X.19)

  • identify, from a unit fraction part of a set, the whole set

    • Unit fractions: modelling word problems (4-X.7)
    • Unit fractions: word problems (4-X.8)

  • add and subtract fractions with the same denominators to make up to one whole (e.g., ³/₈ + ³/₈ + ²/₈ = ⁸/₈ = 1)

    • Decompose fractions multiple ways (4-AA.1)
    • Add fractions with like denominators using strip models (4-AA.2)
    • Subtract fractions with like denominators using strip models (4-AA.3)
    • Add and subtract fractions with like denominators using number lines (4-AA.4)
    • Add and subtract fractions with like denominators (4-AA.5)

  • add and subtract decimals to one decimal place (e.g., 1.3 + 0.2 = 1.5)

    • Add and subtract decimals (4-BB.12)
    • Add and subtract decimals: word problems (4-BB.13)

  • use doubling or halving to scale a quantity (e.g., to double or half a recipe)

• Financial mathematics

  • make amounts of money using dollars and cents (e.g., to make 3 dollars and 70 cents)

    • Count coins and notes - up to $5 note (4-S.1)

  • estimate and calculate the total cost and change for items costing whole-dollar amounts

Algebra

• Equations and relationships

  • form and solve true or false number sentences and open number sentences involving multiplication and division, using an understanding of the equal sign (e.g., 5 × _ = 20; _ ÷ 3 = 6)

    • Multiplication sentences up to 10: true or false? (4-I.10)
    • Division sentences up to 10: true or false? (4-M.9)
    • Multiplication and division facts up to 12: true or false? (4-DD.5)

  • recognise and describe the rule for a growing pattern using words, tables, and diagrams, and make conjectures about further elements in the pattern

    • Growing patterns (4-D.2)
    • Find the next row in a growing pattern (4-D.6)
    • Addition input/output tables - up to three digits (4-E.2)
    • Subtraction input/output tables - up to three digits (4-F.2)
    • Multiplication input/output tables (4-I.11)
    • Division input/output tables (4-M.10)

• Algorithmic thinking

  • create and use an algorithm for generating a pattern or pathway

    • Repeating patterns (4-D.1)
    • Growing patterns (4-D.2)
    • Find the next shape in a pattern (4-D.3)
    • Complete a repeating pattern (4-D.4)
    • Make a repeating pattern (4-D.5)
    • Find the next row in a growing pattern (4-D.6)

Measurement

• Measuring

  • measure body parts (e.g., the arm) or familiar objects and use these as benchmarks to estimate and then measure length, mass (weight), capacity, and duration, using appropriate metric or time-based units

    • Measure using a centimetre ruler (4-U.3)

  • use appropriate units to describe length, mass (weight), capacity, and time

    • Which metric unit of length is appropriate? (4-U.4)
    • Which metric unit of mass is appropriate? (4-U.8)
    • Which metric unit of volume is appropriate? (4-U.10)

  • use the metric measurement system to explore relationships between units

    • Compare and convert metric units of length (4-U.5)
    • Metric mixed units (4-U.6)
    • Compare and convert metric units of mass (4-U.9)
    • Compare and convert metric units of volume (4-U.11)
    • Conversion tables (4-U.12)

  • recognise that angles can be measured in degrees, using 90, 180, and 360 degrees as benchmarks

    • Estimate angle measurements (4-V.10)

  • tell the time to the nearest 5 minutes, using the language of 'minutes past the hour' and 'to the hour'

    • Read clocks and write times (4-T.3)

• Perimeter, area, and volume

  • visualise, estimate, and measure:

    • the perimeter of polygons, using metric units (cm and m)

      • Perimeter of polygons (4-W.2)

    • the area of shapes covered with squares or half squares

      • Find the area of figures made of unit squares (4-W.5)

    • the volume of shapes filled with centicubes, taking note of layers and stacking

      • Volume (4-W.11)

Geometry

• Shapes

  • identify, classify, and describe the attributes of polygons (including triangles and quadrilaterals) using properties of shapes, including line and rotational symmetry

    • Identify two-dimensional shapes (4-V.1)
    • Is it a polygon? (4-V.7)
    • Rotational symmetry (4-V.15)
    • Lines of symmetry (4-V.16)

  • compare angles in 2D shapes, classifying them as equal to, smaller than, or larger than a right angle

    • Angles greater than, less than or equal to a right angle (4-V.9)

• Spatial reasoning

  • identify the 2D shapes that compose 3D shapes (e.g., a triangular prism is made from two triangles and three rectangles)

    • Identify faces of three-dimensional shapes (4-V.5)
    • Nets of three-dimensional figures (4-V.6)

  • visualise, predict, and identify which shape is a reflection, rotation, or translation of a given 2D shape

    • Reflection, rotation and translation (4-V.13)

• Pathways

  • use grid references to identify regions and plot positions on a grid map

    • Objects on a coordinate plane (4-Q.1)

  • interpret and describe pathways, including those involving half and quarter turns and the distance travelled

    • Coordinate planes as maps (4-Q.2)

Statistics

• Problem

  • use multivariate data to investigate summary and comparison situations with categorical and discrete numerical data, by:

    • posing an investigative question that can be answered with data

    • making conjectures or assertions about expected findings

• Plan

  • plan how to collect primary data to support answering an investigative question, including:

    • deciding on the group of interest

    • deciding on the variable or variables for which data will be collected

    • taking account of ethical practices in data collection

• Data

  • use a variety of tools to collect the data, and check for errors in it

    • Interpret frequency tables (4-P.1)
    • Create frequency tables (4-P.2)

• Analysis

  • create and describe data visualisations to make meaning from the data, with statements including the name of the variable

    • Interpret bar graphs (4-P.3)
    • Create bar graphs (4-P.4)
    • Interpret pictographs (4-P.7)
    • Create pictographs (4-P.8)
    • Interpret line graphs (4-P.9)
    • Create line graphs (4-P.10)

• Conclusion

  • choose descriptive statements that best answer the investigative question, reflecting on findings and how they compare with initial conjectures or assertions

• Statistical literacy

  • check the statements that others make about data to see if they make sense, using information to clarify or correct statements where needed

Probability

• Probability investigations

  • engage in chance-based investigations with equally likely outcomes by:

    • posing an investigative question

      • Certain, probable, unlikely and impossible (4-EE.1)

    • anticipating and then identifying possible outcomes for the investigative question

      • Combinations (4-EE.3)

    • generating all possible ways to get each outcome (a theoretical approach), or undertaking a probability experiment and recording the occurrences of each outcome

    • creating data visualisations for possible outcomes

    • describing what these visualisations show

    • finding probabilities as fractions

      • Find the probability (4-EE.2)

    • answering the investigative question

    • reflecting on anticipated outcomes

• Critical thinking in probability

  • agree or disagree with others' conclusions about chance-based investigations