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Level Five > Number and Algebra

Body Ratios

Keywords:
Achievement Objectives:

Achievement Objective: Use rates and ratios.

Purpose: 

These exercises and activities are for students to use independently of the teacher to practice number properties.

Specific Learning Outcomes: 

write a ratio
use ratios to solve problems

Description of mathematics: 

Fractions proportions and ratios – AM to AP

Required Resource Materials: 
Practice exercises with answers (PDF or Word)
Activity: 

Background

The ideas of ratio, proportion and proportional thinking/reasoning are complex.

The “unit” (one whole) to which we are referring can change during proportional problems and often this is not obvious. This is a common feature of such problems and should always be kept in mind.

Conceptual discourse is really important to engage with in these problems. This means allowing students to discuss their ideas at length and allowing them to debate their own answers, without giving them the ‘correct’ answer. Listen and ask and listen again to see inside the mind of the student.

A fundamental concept in mathematics is that when comparing we must compare the same “size” unit. This is true with ratio, subtracting and dividing. Ratios can be operated on sensibly when the total parts involve the same “one”. Understanding this idea is a major step forward.

Related Resources: 

Book 7, Activities:

 

  • Hot Shots
  • Mixing Colours
  • Folding Fractions and Decimals
  • Comparing Apples with Apples
  • Feeding Pets

Figure It Out book references:

Proportional Reasoning, Levels 3+

  • Chocolate Choices (p4) – Using ratios to compare subsets
  • Cereal calculations (p9) – Solving problems that involve ratios and large numbers

Proportional Reasoning, Book One, Levels 3-4+

  • Magnificent Models (p11) – using ratios to scale size up and down
  • Planet Peewee(p12) – Using ratios to increase and decrease lengths
  • Smart Sizes (p21) – Exploring how scale factor for length affects area
  • The Right mix (p22) – Working with ratios

Proportional Reasoning, Book Two, Levels 3-4+

  • Flavoursome (p6/7) Comparing ratios
  • A sizeable problem (p16) – Working with inverse ratios
  • Da Vinci’s Ratio (p24) – exploring ratios and co-variation
AttachmentSize
BodyRatios.pdf355.65 KB
BodyRatios.doc722.5 KB

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