Math Units & Learning Expectations

20202021 Math Pacing Guide
Term 1
Unit 1: Extending Whole Numbers/Decimals & Algebraic Relationships
Guaranteed Vocabulary
 thousandthone 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
 positivegreater than zero
 rational numbersa set of numbers that can be expressed as a fraction a/b, which includes the subsets of whole numbers and counting (natural) numbers
 compositea whole number with more than two factors
 primea whole number with exactly two factors, 1 and the number itself
During this unit, students performing 'Onlevel' 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
 thousandthone of one thousand equal parts of a whole
 variablea letter, such as n, that stands for a number in an expression or an equation
During this unit, students performing 'Onlevel' for 5th Grade should be able to
 multiply a 3digit by 2digit 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
 thousandthone of one thousand equal parts of a whole
 variablea letter, such as n, that stands for a number in an expression or an equation
 gross incomethe amount of income before any deductions
 net incomethe amount of income left after deductions
During this unit, students performing 'Onlevel' 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 fractiona number in the form a/b where a and b are whole numbers and a>b where b is not equal to zero
 mixed numbera number that is composed of a whole number and a fraction
 unequal denominatortwo fractions where denominators are not identical or similar
 positivegreater than zero
 rational numbersa 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 'Onlevel' 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 patterna pattern that occurs when a constant nonzero value is added to an input value to determine the output value axesthe vertical and horizontal lines that act as a reference when plotting points on a coordinate plane
 coordinate planetwodimensional plane on which to plot points, lines, and curves
 coordinate grida grid that makes it easy to locate points in a plane by an ordered pair of numbers
 improper fractionsa number in the form a/b where a and b are whole numbers and a>b where b is not equal to zero
 mixed numbersa number that is composed of a whole number and a fraction
 multiplicative patterna pattern when a constant nonzero value is multiplied by an input value to determine the output value
 originthe starting point in locating points on a coordinate plane quadrantany of the four areas created by dividing a plane with an xaxis and yaxis
 ordered paira pair of numbers (x,y) used to locate a point on a coordinate plane
 intersectionwhere lines cross over, have a common point
 xaxisa horizontal line that includes both positive and negative numbers used to locate points in a coordinate plane
 yaxisa vertical line that includes both positive and negative numbers used to locate points in a coordinate plane
 coordinate pointa number in an ordered pair that names the location of the point on the coordinate plane
 pointan exact location in space
During this unit, students performing 'Onlevel' 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, xaxis, yaxis) & 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 yvalue first before the xvalue
 Working with fractions and decimals on the coordinate grid and tables
Unit 6: Geometry and Contextual Measurement
Guaranteed Vocabulary
 basethe surface a solid object stands on, or the bottom line of a polygon
 area of the basethe measurement attribute that describes the number of square units the base covers
 congruentof equal measure, having exactly the same size and same shape
 volumethe measurement attribute of the amount of space occupied by matter
 cubic unitsvolume of a cube 1 unit on each edge
 formulamathematical relationship or rule expressed in symbolic form
 height (layers)the vertical distance from top to bottom
 hierarchya preordered defined on a set
 geometric propertiesrelationship attributes within a geometric figure
 conversionchange from one unit to another unit
 seta collection that has common attributes or characteristic
 subseta piece from a set
 equilateral trianglea triangle in which all three sides are the same length
 isosceles trianglea triangle with two sides of the same length
 scalene trianglea triangle in which no sides have the same length
During this unit, students performing 'Onlevel' 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 datadata that represents the attributes of a group of people, events, or objects
 datainformation that is collected about people, events, or objects
 discrete paired datadata with finite and distinct values, not inclusive of inbetween values
 numerical datadata that represents values or observations that can be measured and placed in ascending and descending order
 scatterplota graphical representation used to display the relationship between discrete data pairs
 ascendingincreasing in size or value
 descendingdecreasing in size or value
During this unit, students performing 'Onlevel' for 5th Grade should be able to
 extend representing data on graphs to include stemandleaf plots & scatterplots (include decimals & fractions)
 solve one & two step problems on a frequency table, dot plot, bar graph, stemandleaf plot, & scatterplot
Some students may struggle with:
 Labeling the data in the actual graph
 Multistep 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