Banana Bread Bake Off
Through this task, students will explore the inverse operations of multiplication and division by comparing the result of multiplying by a unit fraction and dividing by the inverse whole number.
Students use paper folding to partition a pan of brownies (a sheet of rectangular paper) into equal portions (first four, then eight, then ten) through a simple storyline told by the teacher.
Building a Stage
Students will determine an unknown measure by using a tape measure as a number line. Within the context of building a stage using layers of different types of wood, students will find the sum of friendly but unlike denominators. This will help them to understand the need for common units (denominators) when adding fractions.
Students use their spatial reasoning and creative thinking to design a flag given a variety of pre-cut and coloured shapes. Students investigate and determine what fraction of the whole flag the coloured shapes represent.
Building to Operations with Relational Rods
This bundle uses the foundational concept of unit fractions to help students compare fractions and build understanding of adding and subtracting fractions with friendly or unlike denominators using models and symbols. Students with fragile understanding of unit fractions often have difficulty transitioning to adding and subtracting fractions. The tasks in this lesson bundle encourage students to be flexible in recognizing that a whole can be any length.
Changing Wholes with Pattern Blocks
Students use pattern blocks as area models to compare fractional regions and explore how the regions change in relation to the whole.
Chris' Ice Cream Carton
Students are asked to create visual representations of thier thinking using number lines and arrays to perform multiplication of fractions with unlike denominators. Students may use a variety of multiplication strategies, focusing on the part-whole meaning of fractions.
Comparing and Ordering Fractions Lesson (Gr 6)
This lesson engages students in ordering fractions on a number line.
Comparing Fractions Task
This is a set of prompts consisting of purposefully paired fractions to elicit the use of various strategies. The prompts may be used on different occasions for either Minds-On activities or for Action tasks depending on student readiness.
Comparing Fractions with Like Numerators or Like Denominators
This is a set of prompts consisting of purposely paired fractions to elicit the use of various strategies. The prompts may be used on different occasions for either Minds-On activities or for Action tasks depending on student readiness.
Composing and Decomposing 1 7⁄8
In this hands-on task, each student independently represents 17⁄8 by creating either a physical model (e.g., using tiles, folded paper, relational rods, or other items with which students are comfortable working) or a two-dimensional model (e.g., a drawing or a number line) of their choice. Students are then challenged to create as many addition and subtraction number sentences as possible to represent 17⁄8.
Creating Sums Close to One
Students will explore sums of fractions to determine two fractions with unlike denominators that, when added, will be close to but not equal to one. This task encourages the student to develop the sense of fractions as quantities (fundamental to fractions understanding) and also to justify their thinking by representing their mathematics in a variety of ways.
Students will estimate and mark fractional amounts using the edge of their desks as a linear measure and the top surface as an area measure. This task is best used after a solid understanding of number line has been established.
This is a series of games to be played in pairs, which will take students from building and naming equivalent fractions, through to building and naming addition and subtraction equations. Students compose and decompose fractions in order to add and subtract using cards (fractions, equals sign and operation cards) and relational rods.
This is a set of prompts consisting of purposely paired fractions to elicit the use of various strategies. The prompts may be used on different occasions for either Minds-On activities or for Action tasks depending on student readiness. Repeated practice and exploration in making comparisons between fractions will deepen student understanding. Encourage students to build models/representations and create contexts to support visualization of fractions, which in turn supports meaning-making.
Equivalence of Fractions Lesson Bundle (Jr - Int)
This set of four lessons provides multiple learning opportunities for students to develop an understanding of equivalence through a variety of manipulatives and the number line.
Familiar Fractions and Benchmarks Comparisons
This is a set of prompts consisting of purposefully paired fractions to elicit the use of various strategies. The prompts may be used on different occasions for either Minds-On activities or for Action tasks depending on student readiness. Repeated practice and exploration in making comparisons between fractions will deepen student understanding.
Students will explore equivalent fractions and sums of fractions as they flick an eraser along game boards that are divided into thirds, sixths, ninths and eighteenths. The process of recording the scores on a number line – and determining the sum of their personal score, as well as their team score – reinforces the need for a common unit for addition of fractions.
Fraction Shape Sets
In this task, students will work with a discrete (set) model of shapes with various characteristics. Students will demonstrate their understanding of fractions of a set by using different attributes to compose or identify fractions.
Fractions Representation Lesson
This lesson allows students to share what they understand about fractions by representing 2⁄5 or 4⁄10.
Fractions Representations with Set Area Models Lesson (Gr 6)
In this lesson, students use a set of pattern blocks to generate fractions. This allows for discussion of the similarities and differences between set models and area models for part-whole relationships.
Generating Fractions between Two Numbers (Fraction Density)
This is a set of progressive prompts that will elicit the use of various strategies used to find fractions between two numbers. The prompts, when used in sequence, support students in choosing a strategy based upon the fractions being considered. Encourage students to build models/representations and create contexts to aid in visualization.
Students begin by working with pre-selected sets of rods and determine the value of the smaller rods, where the longest rod is the whole. They then add these together to determine the sum. Next, students randomly select a collection of rods from a baggie/paper bag and use the largest rod in their selection as the whole to determine the fractional value of the collection.
I Have, Who Has
This fun and addictive ‘call and response’ game can be used as a whole group minds-on activity or an exit ticket. Students love trying to be as fast as they can to recognize what unit amount they have represented on their card. They enjoy when the entire deck of cards is successfully played from start to finish. The connection between the visual representation and an oral articulation of symbolic notation is especially evident in this task.
Improper Fractions with Set Representations Lesson (Gr 6)
Based upon the Gap Closing resource, this lesson requires students to represent improper fractions using a set representation.
Living Number Line
Students place cards labelled with fractional amounts on a large number line by equi-partitioning. This physical number line, the living number line, is meant to grow throughout the year as subsequent units (i.e. fractions, percentages, decimals etc.) are placed. Students will use a variety of strategies to place cards appropriately, including relational and proportional thinking and knowledge of equivalency.
Making Mixed Numbers
This task was designed to move students from representing a mixed fraction towards using operations with fractions, and is a suitable exploration for students even prior to the formal introduction of these concepts. The task consists of a series of prompts intended to scaffold students to use multiple representations to visualize and conceptualize the problems.
Ordering on a Number Line Lesson Bundle (Gr 7)
This set of four lessons supports students in connecting fractions, decimals and percentages by ordering them on a number line. This lesson could be utilized in earlier grades with simple modifications to the numbers provided to students.
Pretty Powerful Paper Folding
Students fold colourful paper strips into equal parts that represent unit fractions and label the folded regions using symbolic notation. These strips are powerful visual tools that allow students to see the relative size of fractional regions, which allows them to compare familiar fractional quantities.
Students decompose fractional amounts in a recipe using the unit fraction 1⁄4 in order to accurately mix ingredients using only a 1⁄4 measuring cup. They compose equivalent fractions using unit fractions and represent them in a variety of ways. As an option, the recipe can be prepared and baked by the class.
Students are introduced to the concept of a relay race where participants complete various fractional distances of the total. Based on two known fractional distances of a race with unlike denominators, students will determine the distances that the other runners might complete.
Representations Lesson Bundle (Jr)
Building upon the representation lesson using 2⁄5 and 4⁄10, this bundle of five lessons supports students in connecting their knowledge of fractions to ordering on the number line and being more purposeful in the selection of representations for given contexts.
Students will determine how many decorations they can make with a given length of ribbon. Within the context of creating ribbon decorations, they will appropriately partition 3 metres of ribbon into lengths of 2⁄5 metres and calculate the number of decorations that can be made.
Set Representations Lesson Bundle (Jr)
These five lessons use a variety of materials to build student understanding of representing fractions using sets.
The Painted Door
Students will use models and representations to determine the amount of time it takes to paint a portion of a door. Within this context, they will multiply two fractions with unlike numerators and denominators using representations (e.g., number lines and grids) to build a more conceptual understanding of multiplication of fractions beyond the standard algorithm.
Students randomly grab a handful of relational rods from a paper (opaque) bag. They build a linear train with all of the rods they have selected. Keeping a denominator of 10 (the length of the orange relational rod, which is the whole), they then determine the length of the train by adding up all the fractional quantities.
Students represent the installation of turf, which is installed at different fractional rates each day, in a newly constructed field. By creating a model and determining common fractional units, they will be able to establish how much turf needs to be installed on the final two days.
Unit Fractions Counting Game
Students “count up” using unit fractions (for example, 1⁄4, 1⁄3, 1⁄2, 1⁄8, etc). The students or teacher can choose any unit fractions, and the teacher or students can set game rules such as: "When you get to one whole, stand up and state the quantity as both a fraction and as a whole". Note: this game is similar to a well-known number game called BUZZ.
Students use unit fractions to compose and decompose fractions with relational rods. Using different rods to represent the whole, students are asked to name the unit fractions they can find.
Walk the Line
Students actively equi-partition a number line using different fractional units (e.g., halves, fifths) as they place mixed and improper fractions. Students will enjoy walking, jumping or using every day classroom items as a method of kinaesthetically partitioning a number line on the floor. This task becomes increasingly complex based upon the sets of fractions used.