2014 – 15 5th Grade Math Concept Map – Unit 1
Big Idea – RT3: Addition and Subtraction Computation
Students apply their understanding of fractions and fraction models to represent the addition and subtraction of fractions including unlike denominators and mixed numbers. They understand that the size of a fractional part is relative to the size of the whole (unitizing) and use that understanding to make sense of addition and subtraction of fractions. They apply their understandings of decimal models, place value, and properties to add and subtract decimals. They develop fluency with addition and subtraction of fractions and decimals, including problems involving measurement. They make reasonable estimates of fraction and decimal sums and differences.
Connections to the Big Idea:
RT 1 & 2: Students extend their understanding of the number system (whole numbers, decimals, and fractions) in various situations. They continue their work with place value models (e.g., base-10 blocks, grids, number line), and fractional models (number line, Cuisenaire rods, pictures) to deepen their knowledge of decimals to the thousandths and fractions. They understand that the size of a fractional part is relative to the size of the whole (unitizing) and use that understanding to make sense of addition and subtraction of fractions and decimals (e.g., ¼ of an hour is 15 minutes and/or ¼ of a dollar is $0.25).
RT 7: Students continue to develop an understanding of an unknown quantity by using a letter (variable) to represent the quantity. They solve for the unknown in computation situations, including the use of decimals and fractions in addition and subtraction contexts. They continue to develop an understanding of equality around the equal sign (=) and generate equivalent equations in computation situations involving decimals and fractions to include the use of brackets and braces.
2014-2015 5th Grade Math Concept Map – Unit 1
2014 – 15 5th Grade Math Concept Map – Unit 2
Big Idea – RT 4: Multiplication and Division Computation
Students use the meaning of fractions, of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for multiplying and dividing fractions make sense. (Note: this is limited to the case of dividing unit fractions by whole numbers and whole numbers by unit fractions.) For example, interpret 3/4 as the result of dividing 3 by 4, noting that ¾ multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size ¾. Use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Students use the relationship between decimals and fractions, as well as the relationship between finite decimals and whole numbers (e.g., a finite decimal multiplied by an appropriate power of 10 is a whole number), to understand and explain why the procedures for multiplying and dividing finite decimals make sense. They compute products and quotients of decimals to hundredths efficiently and accurately. They finalize fluency with multi-digit multiplication using the standard algorithm and find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Connections to the Big Idea
RT 7: Students continue to develop their understanding of base ten patterns by analyzing decimals and powers of ten. Students continue to develop an understanding of an unknown quantity by using a letter (variable) to represent the quantity. They solve for the unknown in computation situations involving multiplication and division contexts. They continue to develop an understanding of equality around the equal sign (=) and generate equivalent equations in computation situations involving multiplication and division whole numbers, mixed numbers and fractions (e.g., 256 ÷ a = 64 x a, 3 x (2+5)= 3 x 7).
RT9: Students continue to develop their understanding of data and data interpretation through the use of a line plot. Students gather data fractional data and display in a line plot and use the information to answer questions.
2014 – 15 5th Grade Math Concept Map – Unit 2
2014 – 15 5th Grade Math Concept Map – Unit 3
Big Idea – RT 8: Geometric Figures
Students extend their understanding of two-dimensional shapes by using defining attributes in order to classify two-dimensional figures into categories. By analyzing the properties of two-dimensional shapes, students understand that attributes belonging to one category of figures (e.g., rectangles have 4 right angles) also apply to all subcategories of that category (e.g., squares are rectangles because they have 4 right angles). In addition, through activities such as building and drawing, students recognize volume as an attribute of three-dimensional space. Students relate their understanding of 2D shapes to 3D shapes. Students analyze the properties of 2D & 3D shapes, describing them by the number of edges, vertices or faces, as well as the shape(s) of faces. In addition, students begin to work with the first quadrant of the Cartesian coordinate system by plotting points and represent real world and mathematical problems by graphing.
Connections to the Big Idea
RT 5: Students continue to develop their understanding of formal measurement systems, and performing unit conversions. Through hands-on activities, such as measuring the side lengths of rectangles in centimeters and then converting that measure to millimeters and meter equivalents, students develop a strong conceptual foundation for how units within a system compare to each other. Students measure the length, width and depth of three dimensional objects to calculate the volume as well as convert these measures into other units.
RT 6: Students apply their previous understandings of perimeter and area of two-dimensional figures to develop an understanding of volume of three-dimensional figures. Through activities such as filling boxes with cubes, students gain a conceptual understanding of volume and apply this understanding to real-world problems. In addition, students understand and use the formula for volume. Students extend their understanding of fractions and area to 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.
RT 7: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.
2014 – 15 5th Grade Math Concept Map – Unit 3
July 25, 2014