Perimeters of polygons

PROCEDURAL

Mathematics›Measurement|Ages 8—9|ID: mt_WtcFrxGOgw

Solve problems involving perimeters of polygons: find perimeter from side lengths, find an unknown side length, and explore rectangles with same perimeter but different areas (or vice versa)

Mastery Evidence

Calculate the perimeter of a rectangle with sides 8 cm and 5 cm
Find the missing side of a pentagon with perimeter 30 cm and four known sides
Draw two rectangles both with perimeter 24 cm but different areas

Assessment Prompt

“If a rectangle has a perimeter of 24 cm and one side is 8 cm, can [child] work out the length of the other side — without drawing it?”

Prerequisites2

Understanding angles (age 8+)
softAges 8—9
Measuring Perimeters
hardAges 7—8

Show full prerequisite tree

Understanding angles (age 8+) soft
Area of rectangles supports exploring same-perimeter-different-area relationships
- Area by Tiling hard
  Must see tiling→multiplication connection before computing area via side lengths
  - Area (age 8+) hard
    Counting unit squares is prerequisite to connecting tiling to multiplication
    - Understanding Area hard
      Must understand unit squares and area concept before measuring by counting
      - Measuring length (age 7+) soft
        Length measurement experience supports understanding area as a 2D measurement
        
        Measuring length (age 6+) hard
        Using standard measurement tools extends measuring with non-standard units
        
        Measuring length and height (age 5+) hard
        Measuring with iterated units extends Y1 beginning to measure length
        
        Comparing Lengths & Heights hard
        Measuring length with units requires first being able to compare lengths directly
        
        Measurable Attributes of Objects hard
        Comparing lengths/heights requires first identifying length as a measurable attribute
        
        Measuring length soft
        Measuring with units benefits from ability to order and compare lengths
        
        Comparing Lengths & Heights hard
        Ordering 3 objects by length and indirect comparison extends direct length comparison
        
        Measurable Attributes of Objects hard
        Comparing lengths/heights requires first identifying length as a measurable attribute
        
        Choosing measurement units soft
        Choosing appropriate tools builds on choosing appropriate units
        
        Capacity and volume hard
        Using standard units for capacity extends from beginning to measure capacity
        
        Comparing Capacity hard
        Measuring capacity with units requires first being able to compare capacities
        
        Measurable Attributes of Objects hard
        Comparing capacity requires understanding capacity as a measurable attribute
        
        Measuring length and height (age 5+) hard
        Using standard units for length extends from beginning to measure length
        
        Comparing Lengths & Heights hard
        Measuring length with units requires first being able to compare lengths directly
        
        Measurable Attributes of Objects hard
        Comparing lengths/heights requires first identifying length as a measurable attribute
        
        Measuring mass and weight hard
        Using standard units for mass extends from beginning to measure mass
        
        Measuring mass and weight (age 4+) hard
        Measuring mass with units requires first being able to compare masses directly
        
        Measurable Attributes of Objects hard
        Comparing mass/weight requires first identifying mass as a measurable attribute
Measuring Perimeters hard
Measuring perimeter of simple shapes is prerequisite to perimeter problem solving
- Calculating with measurements hard
  Measuring perimeter requires measuring lengths and adding them
  - Comparing and ordering measurements hard
    Extends comparing/ordering measures to adding/subtracting them
    - Choosing measurement units hard
      Comparing and ordering measurements with symbols requires being able to measure in standard units
      - Capacity and volume hard
        Using standard units for capacity extends from beginning to measure capacity
        
        Comparing Capacity hard
        Measuring capacity with units requires first being able to compare capacities
        
        Measurable Attributes of Objects hard
        Comparing capacity requires understanding capacity as a measurable attribute
      - Measuring length and height (age 5+) hard
        Using standard units for length extends from beginning to measure length
        
        Comparing Lengths & Heights hard
        Measuring length with units requires first being able to compare lengths directly
        
        Measurable Attributes of Objects hard
        Comparing lengths/heights requires first identifying length as a measurable attribute
      - Measuring mass and weight hard
        Using standard units for mass extends from beginning to measure mass
        
        Measuring mass and weight (age 4+) hard
        Measuring mass with units requires first being able to compare masses directly
        
        Measurable Attributes of Objects hard
        Comparing mass/weight requires first identifying mass as a measurable attribute
    - Comparing and ordering numbers soft
      Using >, <, = for measurements parallels using them for numbers
      - The two digits of a two-digit number hard
        Comparing two-digit numbers using PV requires understanding tens and ones
        
        A Ten Is Ten Ones hard
        Understanding tens and ones place value requires the concept of 10 as a bundle
        
        The teen numbers hard
        Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
        
        How Many in Total? hard
        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        How Many in Total? hard
        Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Writing digits 0-9 hard
        Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
        
        Sitting and holding a pencil soft
        Same motor skills for digit formation
        
        The teen numbers hard
        General two-digit place value extends from understanding teen number composition
        
        How Many in Total? hard
        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        How Many in Total? hard
        Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Writing digits 0-9 hard
        Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
        
        Sitting and holding a pencil soft
        Same motor skills for digit formation
      - Two written numerals between 1 and 10 soft
        Comparing two-digit numbers extends from comparing single-digit written numerals
        
        Comparing groups: more or fewer soft
        Comparing written numerals is the symbolic form of comparing quantities — conceptual comparison helps but isn't strictly required
        
        Counting objects to 20 soft
        Counting a set helps when comparing groups, but younger children (GB age 4) can compare using matching without formal counting to 20
        
        How Many in Total? hard
        Answering 'how many?' requires the cardinality principle
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        One-to-one counting hard
        Counting objects to answer 'how many?' requires one-to-one correspondence
  - Choosing measurement units hard
    Extends Y2 standard unit measurement to include mm and to add/subtract measures
    - Capacity and volume hard
      Using standard units for capacity extends from beginning to measure capacity
      - Comparing Capacity hard
        Measuring capacity with units requires first being able to compare capacities
        
        Measurable Attributes of Objects hard
        Comparing capacity requires understanding capacity as a measurable attribute
    - Measuring length and height (age 5+) hard
      Using standard units for length extends from beginning to measure length
      - Comparing Lengths & Heights hard
        Measuring length with units requires first being able to compare lengths directly
        
        Measurable Attributes of Objects hard
        Comparing lengths/heights requires first identifying length as a measurable attribute
    - Measuring mass and weight hard
      Using standard units for mass extends from beginning to measure mass
      - Measuring mass and weight (age 4+) hard
        Measuring mass with units requires first being able to compare masses directly
        
        Measurable Attributes of Objects hard
        Comparing mass/weight requires first identifying mass as a measurable attribute
- 2-D shapes (age 6+) soft
  Perimeter of 2-D shapes requires knowing shape properties (number of sides)
  - Angles in triangles (age 6+) soft
    Understanding defining attributes supports describing shape properties formally
    - 2-D shapes hard
      Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
    - 3-D shapes (age 5+) hard
      Identifying defining attributes builds on informal analysis and comparison of shapes
      - 2-D shapes hard
        Analysing and comparing shapes requires being able to name them first
      - 3-D shapes hard
        Analysing 3-D shapes requires recognising and naming them
  - 2-D shapes hard
    Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first
  - 3-D shapes (age 5+) hard
    Formal property description extends informal analysis of sides and vertices
    - 2-D shapes hard
      Analysing and comparing shapes requires being able to name them first
    - 3-D shapes hard
      Analysing 3-D shapes requires recognising and naming them

Unlocks3

Estimating answers (age 9+)
hardAges 9—10
Perimeter of Compound Shapes
hardAges 9—10
Multi-Step Problem Solving
softAges 8—9