Mathematics 7 Fractions, Decimals and percents
Specific Curriculum Outcomes
N04 Students will be expected to demonstrate an understanding of the relationship between positive terminating decimals and positive fractions and between positive repeating decimals (with one or two repeating digits) and positive fractions.
N07 Students will be expected to compare, order, and position positive fractions, positive decimals (to thousandths), and whole numbers by using benchmarks, place value, and equivalent fractions and/or decimals.
N02 Students will be expected to demonstrate an understanding of the addition, subtraction, multiplication and division of decimals to solve problems (for more than onedigit divisors or more than twodigit multipliers, the use of technology is expected).
N03 Students will be expected to solve problems involving percents from 1% to 100% (limited to whole numbers).
N04 Students will be expected to demonstrate an understanding of the relationship between positive terminating decimals and positive fractions and between positive repeating decimals (with one or two repeating digits) and positive fractions.
N07 Students will be expected to compare, order, and position positive fractions, positive decimals (to thousandths), and whole numbers by using benchmarks, place value, and equivalent fractions and/or decimals.
N02 Students will be expected to demonstrate an understanding of the addition, subtraction, multiplication and division of decimals to solve problems (for more than onedigit divisors or more than twodigit multipliers, the use of technology is expected).
N03 Students will be expected to solve problems involving percents from 1% to 100% (limited to whole numbers).
N04 activities
 The Pattern of Ninths when Converted to Decimals from Adrianne Burns  Students investigate the pattern that ninths make when converted to decimals. This leads to a debate... is 9/9 or 1 equivalent to 0.9 repeating? Get your students to pick a side and try to convince the rest of the class with mathematical reasoning.
 Why does 1=0.999...? video from Numberphile  A common question, why does 1=0.999... If you want to know more, watch Matt Parker chat with Jordan Ellenberg.
N07 Activities
 Decimal Time from Nrich Maths  Can you convert time on a digital clock to decimal time? In decimal time, there are 10 hours in a day and 100 minutes in each hour (instead of 24 hours in a day and 60 minutes in each hour).
 Comparing Fractions Game from Illustrative Mathematics  This activity is designed for pairs of students. They will require a set of cards (which are supplied as an attached resource, after the commentary). The goal is to compare the two fractions appearing on each card, determine if they are equivalent and, if not, which is larger. You could extend these cards to include decimals.
 Too Big or Too Small? from NCTM Illuminations  A series of 3 different decimal based activities.
 Clothesline Math from The Maths Project Journal and Clothesline from Andrew Stadel  One of the greatest tools for teaching number sense is the number line. The clothesline is a dynamic manipulatible number line that makes the facilitation of class discourse on number sense efficient and effective. “Benchmark” numbers may be adjusted when needed, as well as the values that are placed on the line. These two websites give some great ideas on how you could use this to order positive fractions and decimals and record student work.
 Translating between Fractions, Decimals and Percents from Mathematics Assessment Resource Service A lesson unit intended to help students to: Compare, convert between and order fractions, decimals, and percents; Use area and linear models of fractions, decimals, and percents to understand equivalence.

 Nearest To Decimal from Don Steward  A nice warmup question for decimals and place value.
 Matching Fractions Decimals Percentages from NRich  This online game or printable cards can be played to reinforce the recognition of equivalent fractions, decimals and percentages.
N02 Activities

 Connecting Area Diagrams to Calculations with Decimals from Open Up Resources  An activity to demonstrate how to use an area diagram to model multiplication with decimals and how it connects to partial products. Also contains interactive GeoGebra material for dynamic modeling. Watch James Tanton's video Five Objections to teaching the Area Model in Schools to learn more about the power of the area model for student understanding.
 Martha's Multiplication Error from Illustrative Mathematics  Marta made an error while finding the product 84.15×10. She said the answer was 84.150 (because when you multiply by 10, you put a zero on the end of the number). Can you help explain to here why that is wrong.

 Gassed 3Act Task from Graham Fletcher  Use decimal multiplication to determine how much it will cost to fill up the gas tank of Graham's Toyota Prius.
 Which One Doesn't Belong? from wodb.ca  Find a reason why each item does not belong with the rest of the group. A great strategy for promoting classroom discussion.
 Multiplying Decimals Given One from Open Middle  X.X is multiplied by 3.2 to get X.X. What numbers could you use to create this equation?



N03 Activities

 From One Percentage to Another from Don Steward  Don presents an activity and handout in which students are given one percent of a number and asked to find another percent of the same original value. For example if 25% of a number is 17, then what is 50% of that number?