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.
July 25, 2014
2014-2015 5th Grade Math Concept Map – Unit 1
RT3: Addition and Subtraction Computation
PSa) Use models (number line, arrays, ratio table) to demonstrate an understanding of addition and subtraction of fractions and decimals
5.NBT.7
PSb) Choose, combine and apply strategies for answering addition and subtraction problems involving fractions (to include unlike denominators and mixed
numbers) & decimals, including contextual situations
5.NBT.7, 5.NF.1, 5.NF.2
PSc) Approximate sums and differences by replacing numbers with ones which are close and easy to compute, including contextual addition and subtraction
problems involving fractions and decimals
5.NBT.4
*Operations with decimals are limited to the hundredths
RT7: Algebraic Thinking
PSc) Solve missing number equations using a letter for the unknown (e.g., x+1/2=3)
PSf) Evaluate expressions with parenthesis, brackets or braces (e.g., [1/2 + (1/4 + 1/4)])
5.OA.1
RT1&2: Number Systems, Relationships & Representations
PSa) Compose and decompose numbers recognizing that in a multi-digit whole number, a digit in
one place represents ten times what it represents in the place to its right and 1/10 of what it
represents in the place to its left (e.g., 700 is 10 times 70, 40 is 1/10 of 400)
5.NBT.1
PSb) Read, write, compare and order whole numbers, fractions and decimals to the thousandths,
including use of symbols <, >, =
5.NBT.3
July 25, 2014
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.
July 25, 2014
2014 – 15 5th Grade Math Concept Map – Unit 2
RT4: Multiplication and Division Computation
PSa) Use models (number line, arrays, ratio table, area models, partial products, and standard algorithm) to find quotients of whole numbers (4 digit by 2 digit)
including contextual situations and explain the calculations
5.NBT.6
PSb) Demonstrate fluency with multiplication of multi-digit whole numbers using the standard algorithm *
5.NBT.5
PSc) Use models (number line, arrays, ratio table) to demonstrate an understanding of multiplication and division of fractions, mixed numbers and decimals
(e.g., Create a story context for (1/3) ÷ 4 or 3 ÷ (1/5), and use a visual fraction model to show the quotient)
5.NF.3, 5.NF 4, 5 NF.6, 5.NF.7, 5. NBT.7
PSd) Choose, combine and apply strategies for answering multiplication and division problems involving fractions, mixed numbers and decimals including
contextual situations (e.g., Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3 or 4 ÷ (1/5) = 20
because 20 × (1/5) = 4; how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many1/3-cup servings are in 2 cups of
raisins?)
5. NF.3, 5.NF 4, 5 NF.5, 5 NF.6, 5.NF.7, 5. NBT.7
PSe) Demonstrate number sense with fractions by estimating and comparing products of a whole numbers multiplied by fractions (e.g., 100 x ½ is larger than
100 x ¼, 400 x 1/3 is larger than 200 x 1/3, 100 x 3/2 is larger than 100)
5 NF.5
* Fluency is defined under the CCSS as “ the ability to use certain facts and procedures with enough facility that using them does not slow down or derail the problem solver as he or she works on more complex
problems and being able to use relavant ideas or procedures in a wide range of context.”
RT9: Data Collection, Representation and Analysis
PSa) Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8) and
use operations on fractions for this grade to solve problems involving information presented in line
plots ( e.g., 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)
5.MD.2
RT7: Algebraic Thinking
PSa) Recognize and describe patterns in the number of zeros in powers of 10 and use whole
number exponents to denote powers of 10
5.NBT.2
PSb) Represent contextual problems that involve computation of whole numbers as a number
equation using letters, braces and brackets (e.g., express the calculation “add 8 and 7, then multiply
by 2” as 2 × (8 + 7) and recognize that 3 × (18932 + 921) is three times as large as 18932 + 921,
without having to calculate the indicated sum or product)
5.OA.1, 5.OA.2
PSd) Generate equivalent equations (e.g., 256 ÷ 2 = 64 x 2, 3 x (2+5) = 3x7)
5.NBT.6
PSf) Evaluate expressions with parenthesis, brackets or braces (e.g., [345 +3(568 + 124)])
5.OA.1
July 25, 2014
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 twodimensional 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 handson 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.
July 25, 2014
2014 – 15 5th Grade Math Concept Map – Unit 3
RT8: Geometric Figures
PSa) Classify 2D shapes in a hierarchy based on defining attributes (e.g., a square is a rectangle and a quadrilateral because it has 4 right angles, 2 pairs of
parallel lines, and 4 sides)
5.G.3, 5.G.4
PSb) Recognize volume as an attribute of three-dimensional figures
5.MD.3
PSc) Graph points on the coordinate plane to solve real-world and mathematical problems
5.G.1, 5.G.2
RT6: Dimensional Measurement Relationships
RT5: Measurement Systems
PSa) Convert units for length, weight, and capacity within a
measurement system
5.MD.1
PSa) Use models (manipulatives, drawings, arrays) to calculate the volume of right rectangular prisms
5.MD.4, 5.MD.5
PSb) Apply the formula for volume of right rectangular prisms to solve problems, including contextual situations
5.MD.4, 5.MD.5
PSc) 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
5.NF.4
RT7: Algebraic Thinking
PSe) Generate two numerical patterns using two given rules, identify the relationship between the patterns, and plot both patterns in the first quadrant of
the coordinate plane (e.g., given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate ordered pairs
in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why
this is so)
5.OA.3
July 25, 2014