New Zealand

Number

• Number structure

  • identify, read, write, compare, and order whole numbers up to 100,000, and represent them using base 10 structure

    • Place values (5-A.1)
    • Convert between place values (5-A.2)
    • Word names for numbers (5-A.3)
    • Compare numbers up to five digits (5-A.8)
    • Put numbers in order: up to five digits (5-A.9)

  • identify factors of numbers up to 100

    • Identify factors (5-G.1)

• Operations

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

    • Estimate sums (5-B.11)
    • Estimate differences (5-C.9)
    • Estimate products (5-D.11)
    • Estimate quotients (5-H.13)
    • Estimate sums, differences, products and quotients: word problems (5-I.3)

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

    • Rounding (5-A.5)
    • Round to the nearest dollar or more (5-T.5)

  • add and subtract whole numbers up to 10,000

    • Add numbers up to four digits (5-B.1)
    • Add numbers up to four digits: word problems (5-B.2)
    • Subtract numbers up to four digits (5-C.1)
    • Subtract across zeros: four-digit numbers (5-C.5)

  • recall multiplication facts for 7s, 8s, and 9s and corresponding division facts

    • Multiplication facts for 7, 8 and 9 (5-D.1)
    • Division facts for 7, 8 and 9 (5-H.1)

  • multiply a three-digit by one-digit number and two two-digit whole numbers (e.g., 245 × 6; 34 × 83)

    • Multiply one-digit numbers by two-digit or three-digit numbers using area models (5-E.2)
    • Multiply one-digit numbers by three-digit numbers (5-E.3)
    • Multiply a two-digit number by a two-digit number: complete the missing steps (5-F.3)
    • Multiply a two-digit number by a two-digit number (5-F.4)
    • Multiply a two-digit number by a two-digit number: word problems (5-F.5)

  • divide up to three-digit whole number by a one-digit divisor, with a remainder (e.g., 83 ÷ 5 = 16, remainder 3)

    • Divide larger numbers (5-H.6)
    • Divide larger numbers: word problems (5-H.7)
    • Complete the division table (5-H.8)

• Rational numbers

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

    • Model decimals and fractions (5-M.2)
    • Understanding decimals expressed in words (5-M.3)
    • Graph decimals on number lines (5-M.6)
    • Decimal number lines (5-M.7)
    • Graph fractions as decimals on number lines (5-O.1)

  • compare and order tenths and hundredths as fractions and decimals, and convert decimal tenths and hundredths to fractions

    • Compare decimals on number lines (5-N.1)
    • Compare decimal numbers (5-N.2)
    • Put decimal numbers in order I (5-N.3)
    • Put decimal numbers in order II (5-N.4)
    • Convert decimals to fractions and mixed numbers (5-O.3)
    • Compare decimals and fractions on number lines (5-P.1)
    • Compare decimals and fractions (5-P.2)

  • divide whole numbers by 10 and 100 to make decimals

  • for fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, or 100:

    • compare and order the fractions

      • Graph and compare fractions on number lines (5-K.1)
      • Compare fractions (5-K.2)
      • Order fractions with like numerators or denominators (5-K.3)
      • Order fractions (5-K.4)

    • identify when two fractions are equivalent

      • Find equivalent fractions using area models (5-J.4)
      • Graph equivalent fractions on number lines (5-J.5)
      • Equivalent fractions (5-J.6)
      • Patterns of equivalent fractions (5-J.7)
      • Write fractions in lowest terms (5-J.8)

  • convert between mixed numbers and improper fractions with denominators of up to 10

    • Convert between improper fractions and mixed numbers (5-J.13)

  • find a fraction of a whole number, using multiplication and division facts and where the answer is a whole number (e.g., ²/₃ of 24)

    • Fractions of a number (5-J.9)

  • identify, from a fractional part of a set, the whole set

    • Fractions of a whole: word problems (5-J.2)

  • add and subtract fractions with the same denominators, including to make more than one whole

    • Add fractions with like denominators using area models (5-L.1)
    • Add fractions with like denominators using strip models (5-L.2)
    • Subtract fractions with like denominators using area models (5-L.3)
    • Subtract fractions with like denominators using strip models (5-L.4)
    • Add and subtract fractions with like denominators (5-L.5)
    • Add and subtract fractions with like denominators: word problems (5-L.6)

  • add and subtract whole numbers and decimals to two decimal places (e.g., 32.55 – 21.21 = 11.34)

    • Add decimals using blocks (5-Q.1)
    • Add decimal numbers (5-Q.2)
    • Subtract decimals using blocks (5-Q.3)
    • Subtract decimal numbers (5-Q.4)
    • Add and subtract decimals: word problems (5-Q.5)
    • Choose decimals with a particular sum or difference (5-Q.6)

  • use known multiplication facts to scale a quantity

• Financial mathematics

  • represent money values in multiple ways using notes and coins

    • Count coins and notes - up to $5 note (5-T.1)
    • Compare money amounts (5-T.2)

  • estimate to the nearest dollar and calculate the total cost of items costing dollars and cents, and the change from the nearest ten dollars

    • Round to the nearest ten cents (5-T.3)
    • Round to the nearest ten cents: word problems (5-T.4)
    • Round to the nearest dollar or more (5-T.5)
    • Making change (5-T.7)

Algebra

• Equations and relationships

  • form and solve true or false number sentences and open number sentences involving all four operations (e.g., 674 + 56 – _ = 671)

    • Multiplication sentences up to 10: true or false? (5-D.4)
    • Division sentences up to 10: true or false? (5-H.4)
    • Mixed operation sentences: true or false? (5-I.4)
    • Solve equations (5-I.5)
    • Write equations to represent word problems (5-I.6)
    • Use equations to solve addition and subtraction word problems (5-I.7)

  • use tables to recognise the relationship between the ordinal position and its corresponding element in a growing pattern, develop a rule for the pattern in words, and make conjectures about further elements or terms in the pattern

    • Input/output tables with addition (5-B.7)
    • Input/output tables with subtraction (5-C.7)
    • Input/output tables with multiplication (5-D.7)
    • Input/output tables with division (5-H.10)
    • Input/output tables with addition, subtraction, multiplication and division (5-I.15)

• Algorithmic thinking

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

    • Find the next shape in a repeating pattern (5-S.1)
    • Complete a repeating pattern (5-S.2)
    • Make a repeating pattern (5-S.3)
    • Find the next row in a growing pattern of shapes (5-S.4)
    • Complete an increasing number pattern (5-S.5)
    • Complete a geometric number pattern (5-S.6)
    • Number patterns: word problems (5-S.8)
    • Number patterns: mixed review (5-S.9)

Measurement

• Measuring

  • estimate and then accurately measure length, mass (weight), capacity, temperature, and duration, using appropriate metric or time-based units or a combination of units

    • Read a thermometer (5-U.1)
    • Reasonable temperature (5-U.2)
    • Which metric unit of length is appropriate? (5-U.4)
    • Which metric unit of mass is appropriate? (5-U.6)
    • Which metric unit of volume is appropriate? (5-U.8)

  • use the appropriate tool for a measurement and the appropriate unit for the attribute being measured

    • Choose the appropriate metric unit of measure (5-U.3)

  • use the metric measurement system to explore relationships between units, including relationships represented by benchmark fractions and decimals

    • Compare and convert metric units of length (5-U.5)
    • Compare and convert metric units of mass (5-U.7)
    • Compare and convert metric units of volume (5-U.9)
    • Metric mixed units (5-U.10)

  • describe angles using the terms acute, right, obtuse, straight, and reflex, comparing them with benchmarks of 90, 180, and 360 degrees

    • Angles greater than, less than or equal to a right angle (5-W.6)
    • Acute, right, obtuse and straight angles (5-W.7)

  • describe the differences in duration between units of time (e.g., days and weeks, months, and years), and solve duration-of-time problems involving 'am' and 'pm' notation

    • Convert time units (5-V.1)
    • Add and subtract mixed time units (5-V.2)
    • Fractions of time units (5-V.3)
    • Elapsed time (5-V.4)
    • Find start and end times: multi-step word problems (5-V.5)
    • Transportation schedules (5-V.6)

• Perimeter, area, and volume

  • visualise, estimate, and calculate:

    • the perimeter of regular polygons (in m, cm, and mm)

      • Perimeter (5-Z.1)

    • the area of shapes covered with squares or partial squares

      • Find the area of figures made of unit squares (5-Z.3)

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

      • Volume (5-Z.9)

Geometry

• Shapes

  • identify, classify, and describe the attributes of:

    • regular and irregular polygons, using edges, vertices, and angles

      • Is it a polygon? (5-W.1)
      • Number of sides in polygons (5-W.2)
      • Which two-dimensional figure is being described? (5-W.3)

    • prisms, using cross sections, faces, edges, and vertices

      • Identify three-dimensional figures (5-Y.1)
      • Count vertices, edges and faces (5-Y.2)
      • Identify faces of three-dimensional figures (5-Y.3)
      • Which three-dimensional figure is being described? (5-Y.4)

  • identify and describe parallel and perpendicular lines, including those forming the sides of polygons

    • Parallel, perpendicular and intersecting lines (5-W.5)

• Spatial reasoning

  • visualise 3D shapes and connect them with nets, 2D diagrams, verbal descriptions, and the same shapes drawn from different perspectives

    • Nets of three-dimensional figures (5-Y.6)
    • Front, side and top view (5-Y.7)

  • resize (enlarge or reduce) a 2D shape

• Pathways

  • interpret and create grid maps to plot positions and pathways, using grid references and directional language, including the four main compass points

    • Objects on a coordinate plane (5-BB.1)
    • Coordinate planes as maps (5-BB.2)
    • Follow directions on a coordinate plane (5-BB.3)

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 the 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, check for errors in it, and correct them by re-collecting the data, if possible

    • Interpret frequency tables (5-AA.8)
    • Create frequency tables (5-AA.9)

• Analysis

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

    • Read a table (5-AA.1)
    • Interpret line graphs (5-AA.2)
    • Create line graphs (5-AA.3)
    • Interpret bar graphs (5-AA.4)
    • Create bar graphs (5-AA.5)
    • Interpret line plots (5-AA.6)
    • Create line plots (5-AA.7)
    • Circle graphs (5-AA.12)
    • Choose the best type of graph (5-AA.13)
    • Mean and mode (5-CC.6)
    • Interpret charts to find mean and mode (5-CC.7)

• Conclusion

  • answer the investigative question, comparing findings with initial conjectures or assertions and their existing knowledge of the world

• Statistical literacy

  • check and, if necessary, improve the statements others make about data, including data from two or more sources

    • Read a table (5-AA.1)
    • Interpret line graphs (5-AA.2)
    • Interpret bar graphs (5-AA.4)

Probability

• Probability investigations

  • engage in chance-based investigations, including those with not equally likely outcomes, by:

    • posing an investigative question

      • More, less and equally likely (5-CC.1)
      • Certain, probable, unlikely and impossible (5-CC.2)

    • anticipating and then identifying possible outcomes for the investigative question

      • Combinations (5-CC.5)

    • 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 (5-CC.3)

    • answering the investigative question

    • reflecting on anticipated outcomes

      • Make predictions (5-CC.4)

• Critical thinking in probability

  • evaluate others' statements about chance-based investigations, with justification