models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Which is bigger? Have students focus on the size of the unit fraction. Which is bigger 1/5 or 1/6? The standards give good examples of fraction operations. Module 4: Multiplying and Dividing of Fractions and Decimal Fractions (14 days—including 2 days for benchmark assessment) Do not forget the following Common Core Lessons from Chapter 4: Lesson 4.0 Pg. Apply and extend previous understandings of multiplication and division. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional Product, Common factor, Proper fraction, Improper fraction, Mixed Number, Reciprocal Building understanding of multiplying a fraction by a whole number that results in a smaller number than the whole number will be important. You can build some understanding through using a semantic map to compare multiplying and dividing whole numbers and fractions. Estimation will be a key to build number sense of working with decimals. Remember to use distributive property for multiplication. Continue to use the visuals of
fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1 Module 11: Graphs and Probability (13 days) Add Common Core Lesson 11.1a on Page 304B M.P. 2 M.P. 4 M.P. 6 Convert like measurement units within a given measurement system. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Represent and interpret data. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Graph points on the coordinate plane to solve real-world and mathematical problems. Double bar graph, Key, Coordinate grid, x-axis, y-axis, Coordinate plane, Coordinates, Ordered pair, x-coordinate, y-coordinate, Origin, Straight line graph, Equation, Combinations, Organized list, Tree diagram Favorable outcome, Theoretical probability, Experimental probability Probability is not a topic in K-5. However, probability is used as a real life example to meet the measurement and data standards. Continue to use the strategies in computation with this unit.
Module 13: Properties of Triangles and Four-Sided Figures (15 days—including one day for benchmark assessment) M.P. 1 M.P. 2 M.P. 4 M.P. 6 Classify two-dimensional figures into categories based on their properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Equilateral triangle, Isosceles triangle, Scalene triangle, Right triangle, Obtuse triangle, Acute triangle, Parallelogram, Rhombus, Trapezoid Chapter 12 was Angles. Angles were taught in previous grades. So use the concepts of angles in classifying the shapes. Embed understanding not just angles, but sides to classify tow dimensional figures. Module 14: Shapes (7 days) M.P. 1 M.P. 2 M.P. 4 M.P. 6 Not specifically in CCSSM but leads to Surface Area and Volume in Module 15 Face, Base, Edge, Vertex, Prism, Sphere, Rectangular prism, Pyramid, Triangular prism, Square pyramid, Net, Triangular pyramid, Cylinder, Cone Again, the concept so fangles and the previous module will be used to solve problems with 3 dimensional shapes. Continue to use the strategies with number operations. Module 15 Surface Area and Volume: (16 days—including Convert like measurement units within a given measurement system. Convert among different-sized standard measurement units within a given measurement Surface area, Right triangle, Unit cube Students should master the formulas for area of rectangles and use that concept to build to compound shapes as in the surface area. Volume formulas
multiplication. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. Perform operations with multi-digit whole numbers and with decimals to hundredths. Fluently multiply multi-digit whole numbers using the standard algorithm. Module 5: Algebra (10 days) M.P. 1 M.P. 2 M.P. 4 M.P. 7 Write and interpret numerical expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as Numerical expression, Variable, Algebraic expression, Evaluate, Simplify, Like terms, Inequality, Equation, True, Equality Properties, Solve This unit is not a major focus of 5th grade so was put at the end of the year. However, the concepts should have been embedded with all the computation in previous chapters.
18932 + 921, without having to calculate the indicated sum or product. Module 6: Area of a Triangle (8 days—including 2 days for benchmark assessment) Add Common Core Lesson 6.0 from Pg. 318G M.P. 3 M.P. 4 M.P. 7 M.P. 8 Apply and extend previous understandings of multiplication and division. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Classify two-dimensional figures into categories based on their properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Vertex, Side, Angle, Base, Height, Perpendicular, Area, Right triangle, Acute triangle, Obtuse triangle Area of a triangle is not a topic in 5th grade. However, connecting the triangle to rectangles builds a better understanding of rectangles and area.