 # Math Units & Learning Expectations

• 2020-2021 Math Pacing Guide

Term 1

Unit 1: Extending Whole Numbers/Decimals & Algebraic Relationships

Guaranteed Vocabulary

• thousandth-one of one thousand equal parts of a whole
• order of operations- the rules of which calculations are performed first when simplifying an expression
• parentheses and brackets (levels of grouping)-symbols to show an group of terms and/or expressions within a mathematical expression
• positive-greater than zero
• rational numbers-a set of numbers that can be expressed as a fraction a/b, which includes the subsets of whole numbers and counting (natural) numbers
• composite-a whole number with more than two factors
• prime-a whole number with exactly two factors, 1 and the number itself

During this unit, students performing 'On-level' for 5th Grade should be able to:

• represent decimals to the thousandths place using expanded notation & numerals
• compare & order decimals to the thousandths
• identify prime & composite numbers
• round decimals to the tenths and hundredths (introduced in 5th grade)
• simplify expressions without exponents using up to two levels of grouping symbols (show multiple representations of multiplication & division)
• solve one & two step problems on a frequency table, dot plot, & bar graph

After this unit, students performing on the 'Compacted' level (6th grade) should be able to:

• compare and order whole numbers, decimals, & fractions within the same problem
• simplify expressions with exponents & prime factorization
• extend all operations to include integers

Some students may struggle with:

• Making the decimals that they are working with all go to the same place value
• Their basic multiplication facts and then relating them to division
• The process of division, including zeros in the quotients
• The process of regrouping in subtraction, including all zeros
• Understanding that multiplication can be represented as 2•3 or 2(3 + 4)
• Understanding that a fraction bar serves as a grouping symbol dividing the numerator by the denominator
• Lining up place values when adding or subtracting decimals with the standard algorithms
• Understanding that 0 & 1 are neither prime nor composite
• Using the correct order of operations
• Keeping organized within their work to track the steps in order of operations
• Rounding, understanding that if it says round to the nearest 10th, the answer will be a 10th and the same with 100th

Unit 2: Multiplication Operations with Decimals

Guaranteed Vocabulary

• order of operations- the rules of which calculations are performed first when simplifying an expression
• parentheses and brackets (levels of grouping)-symbols to show an group of terms and/or expressions within a mathematical expression
• thousandth-one of one thousand equal parts of a whole
• variable-a letter, such as n, that stands for a number in an expression or an equation

During this unit, students performing 'On-level' for 5th Grade should be able to

• multiply a 3-digit by 2-digit number using the standard algorithm
• use pictorial models to represent multiplication of decimals to the hundredths
• multiply decimals with products up to the hundredths
• simplify expressions to include multiplying decimals (no exponents)
• represent and solve equations using the four operations with an unknown
• solve one & two step problems on a frequency table, dot plot, & bar graph (include decimals)

Some students may struggle with:

• Understanding the multiplication decimal/area models
• Connecting the multiplication models to the actual equations
• Placement of the decimal when multiplying
• Thinking that the 2 factors have to go to the same place value like in addition and subtraction
• Understanding the meaning of a decimal times a decimal
• Estimating the reasonableness of decimal products
• Forgetting to place the zero when multiplying with the standard algorithm

Unit 3: Division Operations with Decimals

Guaranteed Vocabulary

• order of operations- the rules of which calculations are performed first when simplifying an expression
• parentheses and brackets (levels of grouping)-symbols to show an group of terms and/or expressions within a mathematical expression
• thousandth-one of one thousand equal parts of a whole
• variable-a letter, such as n, that stands for a number in an expression or an equation
• gross income-the amount of income before any deductions
• net income-the amount of income left after deductions

During this unit, students performing 'On-level' for 5th Grade should be able to

• represent and solve quotients of decimals to the hundredths using pictorial models & standard algorithm
• simplify expressions to include dividing decimals (no exponents)
• represent and solve equations using the four operations with an unknown
• solve one & two step problems on a frequency table & dot plot(include decimals)
• define gross and net income
• represent and solve equations using the four operations with an unknown
• solve one & two step problems on a frequency table, dot plot, & bar graph (include decimals)

Some students may struggle with:

• The process of whole number division
• Interpreting the remainder in a real world situation
• Understanding division models of decimals

Unit 4: Operations with Fractions (comparing, improper, mixed, equivalent, & simplifying fractions)

Guaranteed Vocabulary

• improper fraction-a number in the form a/b where a and b are whole numbers and a>b where b is not equal to zero
• mixed number-a number that is composed of a whole number and a fraction
• unequal denominator-two fractions where denominators are not identical or similar
• positive-greater than zero
• rational numbers-a set of numbers that can be expressed as a fraction a/b, which includes the subsets of whole numbers and counting (natural) numbers
• order of operations- the rules of which calculations are performed first when simplifying an expression
• parentheses and brackets (levels of grouping)-symbols to show an group of terms and/or expressions within a mathematical expression

During this unit, students performing 'On-level' for 5th Grade should be able to

• understand how to simplify a fraction
• understand the process of changing mixed numbers & improper fractions
• represent & solve addition & subtraction of fractions with unequal denominators using models & other strategies (Number Talks & common denominators)
• add & subtract benchmark fractions and their related decimals (include thousandths, hundredths, tenths, fifths, fourths, & halves)
• represent & solve multiplication of a whole number & fraction using models
• represent & solve division of a unit fraction by a whole number & a whole number by a unit fraction with models & other strategies (relating to multiplication of the reciprocal, standard algorithm)
• simplify expressions to include all operations with fractions (no exponents)
• solve one & two step problems on a frequency table, dot plot, & bar graph (include fractions)

After this unit, students performing on the 'Compacted' level (6th grade) should be able to:

• extend multiplying and dividing fractions to include all fractions and mixed numbers
• simplify expressions with exponents & prime factorization
• extend all operations to include integers
• extend graphs to include histograms and box plots

Some students may struggle with:

• Relating a fraction to ½ or a whole
• Estimating the solution to any operation with fractions
• Checking to see if the solution is reasonable
• Process of simplifying fractions
• Simplifying the final answer of a problem without prompting
• Keeping the processes of the fraction operations straight
• Understanding and a making a connection to the real world applications with all fraction operations
• Relating multiplication and division of fractions
• Setting up the division problem with the correct fraction being first
• Relating fractions and decimals

Term 2

Unit 5: Patterns on a Coordinate Plane & Algebraic Relationships

Guaranteed Vocabulary

• additive pattern-a pattern that occurs when a constant non-zero value is added to an input value to determine the output value axes-the vertical and horizontal lines that act as a reference when plotting points on a coordinate plane
• coordinate plane-two-dimensional plane on which to plot points, lines, and curves
• coordinate grid-a grid that makes it easy to locate points in a plane by an ordered pair of numbers
• improper fractions-a number in the form a/b where a and b are whole numbers and a>b where b is not equal to zero
• mixed numbers-a number that is composed of a whole number and a fraction
• multiplicative pattern-a pattern when a constant non-zero value is multiplied by an input value to determine the output value
• origin-the starting point in locating points on a coordinate plane quadrant-any of the four areas created by dividing a plane with an x-axis and y-axis
• ordered pair-a pair of numbers (x,y) used to locate a point on a coordinate plane
• intersection-where lines cross over, have a common point
• x-axis-a horizontal line that includes both positive and negative numbers used to locate points in a coordinate plane
• y-axis-a vertical line that includes both positive and negative numbers used to locate points in a coordinate plane
• coordinate point-a number in an ordered pair that names the location of the point on the coordinate plane
• point-an exact location in space

During this unit, students performing 'On-level' for 5th Grade should be able to

• represent and solve equations using the four operations with an unknown
• describe the parts of a coordinate plane (origin, x-axis, y-axis) & the parallel & perpendicular features of the plane
• describe how to graph an ordered pair
• graph ordered pairs including those generated by input/output tables (include fractions & decimals)
• determine if a graph or table is multiplicative or additive
• generate  & graph a pattern from y = ax or y = a + x (include fractions & decimals)

Some students may struggle with:

• Graphing the y-value first before the x-value
• Working with fractions and decimals on the coordinate grid and tables

Unit 6: Geometry and Contextual Measurement

Guaranteed Vocabulary

• base-the surface a solid object stands on, or the bottom line of a polygon
• area of the base-the measurement attribute that describes the number of square units the base covers
• congruent-of equal measure, having exactly the same size and same shape
• volume-the measurement attribute of the amount of space occupied by matter
• cubic units-volume of a cube 1 unit on each edge
• formula-mathematical relationship or rule expressed in symbolic form
• height (layers)-the vertical distance from top to bottom
• hierarchy-a preordered defined on a set
• geometric properties-relationship attributes within a geometric figure
• conversion-change from one unit to another unit
• set-a collection that has common attributes or characteristic
• subset-a piece from a set
• equilateral triangle-a triangle in which all three sides are the same length
• isosceles triangle-a triangle with two sides of the same length
• scalene triangle-a triangle in which no sides have the same length

During this unit, students performing 'On-level' for 5th Grade should be able to

• represent and solve equations using the four operations with an unknown
• classify & organize 2D figures in sets & subsets [include naming the number of sides & vertices, basic attributes including parallel & perpendicular, types of angles, congruent parts, polygons/regular polygons/irregular polygons, types of triangles (equilateral, isosceles, scalene, right, acute, obtuse), types of quadrilaterals (parallelogram, rhombus, square, rectangle, trapezoid)]
• use models to develop the formula for volume of a rectangular prism & cube
• recognize the volume is the number of cubic units it takes to fill the prism
• determine the volume of a rectangular prism by using the number of layers times the number of cubes in the base (V = Bh)
• represent & solve problems related to perimeter, area, & volume (include composite/irregular figures)
• solve problems by calculating conversions in the Customary or Metric system (reference the STAAR Grade 5 Reference Materials)

Some students may struggle with:

• Working with perimeter, area and volume at the same time
• The idea that perimeter is the straight lines going around the perimeter, area is the square units is takes to cover the figure and volume is the cubic units it takes to fill an object

Unit 7: Focus on Data Analysis

Guaranteed Vocabulary

• categorical data-data that represents the attributes of a group of people, events, or objects
• data-information that is collected about people, events, or objects
• discrete paired data-data with finite and distinct values, not inclusive of in-between values
• numerical data-data that represents values or observations that can be measured and placed in ascending and descending order
• scatterplot-a graphical representation used to display the relationship between discrete data pairs
• ascending-increasing in size or value
• descending-decreasing in size or value

During this unit, students performing 'On-level' for 5th Grade should be able to

• extend representing data on graphs to include stem-and-leaf plots & scatterplots (include decimals & fractions)
• solve one & two step problems on a frequency table, dot plot,  bar graph, stem-and-leaf plot, & scatterplot

Some students may struggle with:

• Labeling the data in the actual graph
• Multi-step questions (following through until the end)
• Solving questions that involve fractions
• Solving questions that involve decimals

Unit 8: Deepening & Spiraling Readiness Standards

Unit 9: Extending Numerical Relationships

Compacted Math

Unit 9: Applications of Mathematical Concepts

On Level Math

Unit 10: Equivalent Forms of Fractions, Decimals, & Percents

Compacted Math