NumIO math adventure

Ratio and Percent Observatory

Scale the observatory maps while keeping every ratio in balance.

Learning goal

Connect ratios, percents, and proportions to solve scale problems.

Skills you will practise

Ratios and equivalent ratios
Percent and percent change
Proportions

Worked examples

4 : 3 = 12 : 9

A drink mixes juice and soda in a 4 : 3 ratio. To keep the same taste with 12 cups of juice, write the proportion 4 : 3 = 12 : ?.
Find how many times larger the juice part became: 12 ÷ 4 = 3.
Multiply the soda part by the same number: 3 × 3 = 9. So 4 : 3 = 12 : 9, and we need 9 cups of soda.
Check with the ratio values: 4 : 3 has the value 4/3, and 12/9 = 4/3. The values are equal, so the two ratios are equivalent.

12 ÷ 40 × 100% = 30%

12 out of 40 students chose soccer. The base amount is 40, all the students, and the compared amount is 12.
Write the ratio as a fraction and simplify it: 12/40 = 3/10.
Multiply by 100% to change the fraction into a percent: 3/10 × 100% = 30%.
Check: 30% of 40 is 40 × 30/100 = 12. That is the number of students who chose soccer.

(60 − 50) ÷ 50 × 100% = 20%

A club had 50 members and now has 60 members. Percent change compares the change with the original amount.
Find the change first: 60 − 50 = 10.
Divide by the original amount 50, not the new amount: 10/50 = 1/5. Then 1/5 × 100% = 20%, so the club grew by 20%.
Check by adding the increase to the original amount: 50 + 50 × 20/100 = 50 + 10 = 60.

Common mistake

Do not add the same number to both parts of a ratio. To make an equivalent ratio, multiply or divide both parts by the same non-zero number. For percent change, divide the change by the original amount, not by the new amount.

Teach-back question

When you find a percent, which amount is the base amount? How can you check that two ratios are equivalent?

How to play

Read the short story, explore the visual model, and complete five untimed questions. Use the hint when you need a new way to think.

Classroom idea

Ask the learner to explain the model or strategy before choosing an answer, then celebrate a clear explanation as well as a correct result.

Frequently asked questions

What grade is “Ratio and Percent Observatory” for?

“Ratio and Percent Observatory” is a Grade 6 Math lesson in NumIO. It practises: ratios and equivalent ratios, percent and percent change, proportions.

How does the “Ratio and Percent Observatory” mission work?

Each mission has five untimed questions. If an answer is not right yet you can try again, and the hint button offers another way to think.

Is “Ratio and Percent Observatory” free, and do I need an account?

Yes, it is free and there is no account or sign-up. Progress is saved in this browser, so you can come back and continue the mission later.

Back to the adventure map

Elementary math curriculum

First discoveries

Counting Companions — Count objects carefully and match each object to one number.
Bigger, Smaller, In Order — Compare groups and numbers, then put them in a clear order.
Parts Make a Whole — Split numbers into parts and find the missing friend that makes ten.
Pattern Steps — Use equal jumps of two or five to continue a number pattern.
Number Board Trail — Move right, left, up, and down on a number board to find a number.
Add and Take Away — Join and separate small groups to solve addition and subtraction stories.

Level 1

Tens and Ones to 100 — Read two-digit numbers and see how tens and ones build each number.
Twenty-Step Addition — Add and subtract within twenty, including missing parts of an equation.
Compare and Complete — Compare numbers with words and signs, then complete a missing-number equation.
Shape and Place — Name familiar shapes and describe where objects are using position words.
Measure and Tell Time — Compare lengths, measure with a simple unit, and read an hour on a clock.
Patterns and Groups — Continue repeating patterns, sort objects by a feature, and read a small count.

Level 2

Hundreds, Tens, Ones — Build three-digit numbers with hundreds, tens, and ones.
Three-Digit Adding and Taking Away — Add and subtract three-digit numbers, including regrouping when needed.
Equal Groups and Times Tables — See multiplication as equal groups, arrays, and repeated addition.
Units and Time Journeys — Choose a useful unit, convert simple lengths, and find elapsed time.
Flat Shapes and Repeating Designs — Recognize plane figures by their properties and continue a repeating design.
Tables and Picture Graphs — Read a table or graph, compare categories, and find totals and trends.

Level 3

Multiply by grouping — Build several-digit multiplication with equal groups, arrays, and partial products.
Share and find remainders — Divide equal groups and explain both the quotient and the remainder.
Fractions and decimals — See fractions and decimals as parts of one whole and compare their sizes.
Measure the journey — Add and subtract lengths, capacities, masses, and durations with matching units.
Angles, triangles, and circles — Recognize angle sizes and describe triangles and circles with accurate measures.
Read data and relationships — Read tables and bar charts, then use a simple rule to find a related number.

Level 4

Large numbers and rounding — Read the place value of large numbers and round them to a requested place.
Big multiplication and division — Use place value, products, and equal groups to solve larger multiplication and division.
Add and subtract parts — Add and subtract fractions with the same denominator and decimals by place value.
Shape clues — Use angle clues to describe triangles and quadrilaterals and classify their properties.
Perimeter and unit paths — Find the perimeter of shapes and convert measurements between familiar units.
Lines and rules — Read change on line graphs and use a correspondence rule to predict a value.

Level 5

Factor and Multiple Village — Find factors, multiples, common factors, common multiples, GCF, and LCM.
Fraction Bridge — Simplify, make equivalent fractions, use common denominators, and add or subtract fractions.
Product Workshop — Multiply fractions and decimals and explain how the product changes.
Congruence and Symmetry Garden — Recognize congruent shapes, lines of symmetry, and rotational symmetry.
Perimeter and Area Camp — Find perimeters and areas of rectangles, squares, triangles, parallelograms, and trapezoids.
Mean and Chance Harbor — Find means and describe the chance of outcomes with data models.

Level 6

Fraction Division Rapids — Divide fractions by multiplying by the reciprocal.
Decimal Division Station — Divide decimals by scaling place values and checking the size of the quotient.
Ratio and Percent Observatory — Connect ratios, percents, and proportions to solve scale problems.
Circle Circuit — Find circumference and area using the explicit classroom value π = 3.14.
Solid Shape Workshop — Find volume and surface area of cubes and cuboids.
Data Chart Lookout — Read strip and pie charts to compare, total, and interpret data.