Arrays of SunshineUsing materials and

arrays to solve simple ratio and proportion

problems – L3 & 4 (Stage 6 and 7)

Presented by Robyn Wilson

Objective To explore key activities,

equipment and resources that will help support the development of ratio and proportion knowledge at Level 3 and 4 of the New Zealand Curriculum.

Card Arrays

The key to

proportional

thinking is being

able to see

combinations of

factors within

numbers.

http://www.nzmaths.co.nz/resource/card-arrays

What skills do our students need to solve ratio and proportion problems?

Mathematical vocabulary (equivalent, proportion, ratio) and comprehension skills

Multiplicative thinking and strategies – multiplication and division facts

Understanding of what a ratio is and able to work one out (repeated replication)

Able to find fractions of a set Able to solve division problems with remainders

Possible student learning intentionsWALT: Demonstrate how ratios are similar to and different from fractionsWALT: Use ratios to solve problems

http://www.nzmaths.co.nz/limited-understanding-arrays

Resource:New Zealand Curriculum Maths – Connecting all strands – Book Level 4A (Early level 4)A Fraction tells you the proportion of the whole or the number of parts out of the total number of parts that are red or blue.

A Ratio compares the red parts to the blue parts.

RATIOKNOWLEDGE

Resource:NZ Curriculum Mathematics, Stage 7, Advanced Multiplicative Book, Ratio and Proportions and Algebra. (Orange Book)

RATIO and PROPORTION GAME

Strawberries and BlackberriesUsing Cards and a die-red number cards from 1 to 10-black numbered cards from 1-10-A die

Notes*red card represents strawberries,Black card = blackberries

Stage 6 (Level 3) Activities to develop strategy: proportions and ratios At this stage students are learning to solve problems using known

multiplication and division facts to find fractions of a set, solve division problems with remainders and work out simple ratios

Finding fractions of a set Draw a circle to represent a birthday cake. Tell the students that

there will be 5 people sharing the cake. If there are 30 lollies evenly spread over the cake, how many lollies will each person get? Record this question as 1/5 of 30. Vary the number of people sharing the cake and the number of lollies decorating it.

Using the fraction of a set to find the whole The Mystery Stars equipment animation shows how to find the

total in the whole set if you know part of it. For example, if a third of the circle has 6 stars on it then by multiplication the whole circle will have 18 stars on it. Therefore 1/3 of 18 is 6.

Stage 6http://www2.nzmaths.co.nz/frames/ONPD/M10/26.aspx

Ratios – Stage 6RatiosAt this stage students are learning to use repeated replication to solve simple ratio problems. Show the students a clear bag with 12 objects in it, 8 red ones and 4 yellow ones. Ask the students questions about what happens if the number of bags or objects changes. For example, how many red objects there would be in 2 bags? If there are 24 red objects how many bags are there? If there are 12 yellow objects how many red objects are there? Students can use the materials to answer the questions or to check their answers.

Stage 7 (Level 4)Strategy being developedStudents at this stage are learning to use a range of strategies including multiplication and division to solve number problems.Students at this stage need to solve problems in each of the operational domains of the Number Framework.Addition and Subtraction

involving decimals, related fractions, and integers. For example, 3.2 + 1.9 = 3.2 + 2 – 0.1 = 5.1 (using compensation).using multiplication and division. For example, 81 – 36 = (9 x 9) – (4 x 9) = 5 x 9 = 45.

Multiplication and division problems:using a range of multiplication and division partitioning strategies. For example,72 ÷ 3 = 72 ÷ 9 x 3 = 24

Proportions and Ratios problems:using multiplication and division strategies to solve problems with fractions and ratios. For example 2/3 of 36 = (36 ÷ 3) x 2 = 24

Stage 7http://www2.nzmaths.co.nz/frames/ONPD/M11/20.aspx

Pinned ideas

Ratio and Proportion Scavenger Hunt

Foldable study guide:http://www.aldenschools.org/webpages/hstotz/resources.cfm

RICH TASKSOther ideas:• Painting on a marae • Comparing rainfall• Comparing resources

for a camp or trip• • •

ResourcesFoldableshttp://www.aldenschools.org/webpages/hstotz/files/6thgrade,ratio%20vocab,%20foldable.pdfFoldables websitehttp://www.aldenschools.org/webpages/hstotz/resources.cfmNZ Mathshttp://www.nzmaths.co.nz/resource/card-arrays

Discussion/ Sharing Ideas

What have you found to work well when teaching your students concepts around ratio and proportion?

What resources do you use to help your learners?

What follow-up games and activities have you find to work well?