Mathematics Unit 7: Fractions and Their Uses; Chance and Probability
April 8–23, 2014
Inquiry Questions:
- What would the world be like without fractions?
- Why are fractions useful?
Essential Learning Goals:
- Explain why fraction a/b is equivalent to fraction (n x a)/(n x b) using visual fraction models. Decompose fractions into sums of fractions with the same denominators in more than one way, recording each decomposition by an equation. Express fractions with denominator 10 as equivalent fractions with denominator 100. Use decimal notation for fractions with denominators 10 or 100. (ELG.MA.4.NN5)
- Compare two fractions with different numerators and different denominators by creating common denominators or numerators or comparing to benchmark fractions, such as 1/2. Record results of comparisons with symbols >, <, = and justify conclusions using visual fraction models. Compare two decimals to hundredths by reasoning about their sizes. Record results of comparisons with symbols >, <, = and justify conclusions using visual models. (ELG.MA.4.NN6)
- Understand fraction a/b with a > 1 as sum of fractions 1/b. (ELG.MA.4.NN2)
- Add and subtract mixed numbers with like denominators. Solve word problems involving addition and subtraction of fractions. (ELG.MA.4.OC4)
Concepts:
Equivalence, joining and separating fractions, fractions as numbers, comparison of fractions, reference unit for fractions, benchmark fractions
Academic Vocabulary: Right-click on vocabulary to look it up in the dictionary.
Apply, explain, generate, compare, express, understand, increasing, decreasing, estimation, visual, model
Technical Vocabulary: Right-click on vocabulary to look it up in the dictionary.
Solve, equivalent, mixed numbers, numerator, denominator, unit fraction, benchmark fraction, whole, part, multiple, equivalent fractions, common numerator, common denominator, decompose, sum, addition, subtraction
Technology:
- Fractions — Comparing: http://nlvm.usu.edu/en/nav/frames_asid_159_g_2_t_1.html?from=search.html?qt=Fractions (compare different fractions that are equal)
- Fractions — Parts of a Whole: http://nlvm.usu.edu/en/nav/frames_asid_102_g_1_t_1.html?from=search.html?qt=circle+21 (relates parts of a whole to written descriptions and fractions)
- Number Line Bars — Fractions: http://nlvm.usu.edu/en/nav/frames_asid_265_g_2_t_1.html?open=activities&from=search.html?qt=line%20segments (divide fractions using number line bar)
- Fraction Game: http://illuminations.nctm.org/ActivityDetail.aspx?ID=18 (explore relationships among fractions)
- Fraction Pieces: http://nlvm.usu.edu/en/nav/frames_asid_274_g_2_t_1.html?open=activities&from=search.html?qt=line%20segments (work with parts and wholes of shapes)
- Fractions — Equivalent: http://nlvm.usu.edu/en/nav/frames_asid_105_g_2_t_1.html?from=search.html?qt=line%20segments (illustrates relationships between equivalent fractions)
- Equivalent Fractions: http://illuminations.nctm.org/ActivityDetail.aspx?ID=80 (create equivalent fractions by dividing and shading squares or circles and match each fraction to its location on the number line)
Common Misconceptions:
- Students do not understand the need to use models that represent the same whole to find sums or differences of fractions. The same whole is also important when comparing fractions.
- Students think the smaller the numbers in the fraction, the larger the fraction. When comparing two fractions, students need to reason about the size of two fractions. Also students need to reason about what fraction of the whole is left when comparing the size of two fractions.