Twelfths are needed to find the difference between 2/3 and 3/4.Three quarters is more than two thirds (Why?).Expect them to record how they solved the problem using drawing, symbols, or a combination. Let students collaborate (mahi tahi) to solve the problem in pairs.
How much more cake does she eat than her sister? Nia eats two thirds of her cake and Ashanti eats three quarters of her cake. Use Slide One of PowerPoint 1 to introduce this problem:Įach birthday they each get identical birthday cakes.squares or circles), lengths, sets, and a variety of other ways. Both fractions can be represented as areas (e.g.The denominators give the size of parts, three in 2/3 indicates that the part is one of three equal parts that form one, and four in 3/4 indicates that the part is one of four equal parts that form one.The numerators (top numbers) are counters of the number of parts, two and three, respectively.Two thirds consist of two copies of one third and three quarters is made of three copies of one quarter.Invite individual students to draw representations of the fractions. What picture do you see when you think …about two-thirds?. How do we read these fractions? (two thirds and three quarters) Begin by writing the fractions 2/3 and 3/4 on the whiteboard.Te reo Māori vocabulary terms such as hautau (fraction), hautau ōrite (equivalent fraction), rārangi tau (number line), and haurua, hautoru, hauwhā, haurima… (half, third, quarter, fifth…) could be introduced in this unit and used throughout other mathematical learning. Linear models are easily applied to journeys that students make, or physical objects such as tape and rope. Orcas and dolphins might be replaced by other animals that need conservation. Birthday cakes might be replaced by areas of land, dart boards, or gold coins. Where contexts such as food and ratios of orcas and dolphins may not be appropriate for your students, find other situations likely to engage them. encouraging mahi tahi (collaboration) among students.Īdaptation involves changing the contexts used for problems to meet the interests and cultural backgrounds of your students.using collaborative grouping so students can support each other and experience both tuakana and teina roles.encouraging sharing and discussion of students’ thinking.allowing use of scientific calculators that can process fractions.altering the complexity of the numbers involved, or the relationships between numerators and denominators.The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to support students include: If each quarter is equally partitioned into 25 parts, those parts are called hundredths since 4 x 25 of those parts fit into one. Both 0.75 and 75% represent 75/100 which is an equivalent fraction to 3/4.
Understanding equivalent fractions is critical to making sense of decimals and percentages. Therefore, each third can be divided into four twelfths. The relationship between two thirds and eight twelfths can be represented in this equality.įour times as many twelfths comprise one as thirds. Twelfths are quarter the size of thirds so four times as many twelfths fit into the same length as thirds. Sixths are half the size of thirds so twice as many sixths fit into the same length as thirds. A fraction strip (length) model of the relationships looks like this: Consider these equivalent fractions: 2/3 = 4/6 = 8/12. The symbolic expression does not explain why equivalent fractions represent the same amount. Any fraction can be expressed as an infinite number of equivalent fractions that represent the same quantity and occupy the same position on the number line.įractions are important to measurement, especially where whole units are not precise enough for the purpose. Four tenths are the same quantity of chocolate as two fifths. If the bar was made up of ten pieces then each person might be given two tenths from each bar, giving them four tenths in total. In practical terms the equal share can occur by dividing each of the two bars into fifths, then giving each person one fifth from each bar. Note that the number two fifths, is composed of two units of one fifth. The operation might be recorded as 2 ÷ 5 = 2/5. Sharing two chocolate bars equally among five people requires that the bars be cut into smaller equal parts. Division often requires equal partitioning of ones. Fractions are needed when wholes (ones) are not adequate for a task. Fractions are an extension of whole numbers and integers.
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