3rd Grade Math
Number and Operations
The student will develop number and operation sense needed to represent numbers and number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable estimates in problem solving.
Understanding numbers, ways of representing numbers, relationships among numbers, and number systems
⎯count by 10’s, 100’s, or 1,000’s from any whole number (3-M[HM/Ch 2]A/IT)
⎯skip count by 10’s from any whole number less than 1,000 (3-M[HM/Ch 2]D/B)
⎯read and write whole numbers to 9,999. (3-M[HM/Ch2]D/B)
⎯represent numbers to 9999 in flexible ways using a variety of materials 3-M[HM/Ch2]D/B)
⎯name the place value of a given digit in whole numbers to 10,000’s 3-M[HM/Ch 2]D/B)
⎯represent whole numbers up to 10,000 in expanded form (e.g., 1,000’s + 100’s + 10’s + 1’s) (3-M[HM/Ch 2]A/IT)
⎯connect written and pictorial representations of fractions with denominators up to ten (3-M[HM/Ch 2]A/IT)
⎯compare fractions with numerators of 1 and denominators up to 10 (3-M[HM/Ch 2]A/IT)
⎯compare and order decimal amounts in the context of money 3-M[HM/Ch 3]D/B)
⎯count the value of a combinations of coins and bills up to $5 3-M[HM/CH 3]A/IT)
⎯make change from a transaction that is less than a dollar 3-M[HM/CH 3]A/M)
⎯order and sequence whole numbers up to 10,000 (3-M[HM/Ch 1& 2]A/B)
⎯compare and order whole numbers up to 9,999 using the appropriate symbol (i.e., <, >, and =) (3-M[HM/Ch 28]A/IT)
⎯represent whole numbers to 9,999 with models (3-M[HM/Ch2]A/IT)
Understand meanings of operations and how they relate to one another
⎯relate skip counting to multiplication (3-M[HM/Ch 4, 7 &9]I/B)
⎯connect division to sharing situations 3-M[HM/CH 10 &11]I/B)
⎯demonstrate multiplication using repeated addition (e.g., arrays) (3-M[HM/Ch 4, 7 &9]I/M)
⎯write and identify number sentences that describe situations involving addition, subtraction, and multiplication (3-M[HM/Ch4, 5, 8,9, 21]D/IT)
⎯write and explain related addition and subtraction sentences (3-M[HM/Ch 4 & 5]D/IT)
⎯develop a story problem that illustrates a given addition or subtraction number sentence (3-M[HM/Ch 4 & 5]D/B)
⎯use the number line to demonstrate addition and subtraction (3-M[HM/Ch 4 & 5]D/B)
⎯write and identify number sentences that describe situations involving addition and subtraction (3-M[HM/Ch 4 & 5]D/B)
⎯write and explain related addition and subtraction sentence (3-M[HM/Ch 4 & 5]D/B)
Solve problems, compute fluently, and make reasonable estimates
⎯use a variety of thinking strategies to add and subtract whole numbers and (e.g., sums of ten, doubles plus one) (3-M[HM/Ch 4 & 5]D/IT)
⎯explain the reasonableness of a solution (3-M[HM/Ch 4, 5, 7, 8-11]D/IT)
⎯relate adding doubles to multiplying by two (3-M[HM/Ch 4, 8 & 9]I/M)
⎯use known multiplication facts to determine a related product (e.g., 9 x 7 is 7 less than 10 x 7) (3-M[HM/Ch 8 &9]D/IT)
⎯use multiplication facts 0, 1, 2, 5, and 10 as a factor (3-M[HM/Ch 8 & 9]AIT)
⎯explain and justify solution strategies used in problem solving (3-M[HM/ALL]D/IT)
⎯select and apply an appropriate problem-solving strategy (e.g., organized list, guess and check, diagram, table) (3-M[HM/ALL]D/IT)
⎯mentally calculate the sum or difference of any two numbers up to 100 (3-M[HM/Ch 4 & 5]D/IT)
⎯use strategies to estimate in problem-solving situations (3-M[HM/ALL]D/IT)
⎯identify whole numbers as odd or even (3-M[HM/Ch1, 2, 9, & 11]A/IT)
⎯identify the place value of a given digit up to thousands (3-M[HM/Ch1, 2, 3]A/IT)
⎯use estimation to select a reasonable solution in problem solving (addition and subtraction only) (3-M[HM/Ch 4&5]A/IT)
⎯demonstrate knowledge and understanding of grade level mathematical terms (3-M[HM/ALL]D/IT)
⎯identify the position of 1/2, 1/3, or 1/4 on the number line (3-M[HM/Ch 18 & 19D/M)
⎯use math journals as a means of understanding math concepts and terms (3-M[HM/ALL]I/B)
⎯add, subtract, and compare decimals (3-M[HM/Ch 20]I/M)
⎯represent numbers as both improper fractions and mixed numbers (3-M[HM/Ch18]I/E)
⎯recognize the relationship between addition and subtraction, multiplication and division (3-M[HM/Ch 4, 5, & 8-11, 21,22]I/IT)
Algebra
The student will understand and generalize patterns as they represent and analyze quantitative relationships and change in a variety of contexts and problems using graphs, tables, and equations.
Sort and classify objects by size, number, and other properties
⎯sort objects by three attributes (3-M[HM/Ch 15,16,&17]A/IT)
⎯identify the rules by which objects or numbers have been sorted (3-M[HM/ Ch 15,16,&17]A/IT)
⎯devise, carry out, and explain how a group of objects has been sorted (3-M[HM/ Ch 15,16,&17]M/IT)
Represent and analyze patterns and functions
⎯extend repeating and growing numerical or geometric patterns (3-M[HM/ALL]A/IT)
⎯identify the unit of a three-part repeating pattern (3-M[HM/-]M/IT)
⎯describe a growing pattern, involving objects, shapes, or numbers (3-M[HM/ALL]D/IT)
⎯create patterns of figures or numbers (3-M[HM/ALL]D/IT)
⎯determine the output number for a particular input number given a one-operation function rule involving addition or subtraction (3-M[HM/Ch4, 5, 8- 11, 13, 20-22]A/IT)
Use concrete, pictorial, and verbal representations to develop an understanding of the language and symbols of mathematics
⎯solve open sentences that involve addition and subtraction of whole numbers zero to twenty (3-M[HM/ALL]A/IT)
⎯demonstrate understanding that an equation is a number sentence stating two quantities are equal (3-M[HM/ALL]I/IT)
⎯demonstrate knowledge (with words or symbols) of the commutative properties of addition and multiplication (3-M[HM/ALL]D/IT)
⎯use the language and symbols of mathematics appropriately to communicate mathematical thinking (3-M[HM/ALL]M/B)
⎯use manipulatives to demonstrate addition and subtraction sentences written symbolically involving numbers 0-20 (3-M[HM/Ch 4 & 5]M/B)
Illustrate general properties of operations
⎯use the commutative property of addition and multiplication (3-M[HM/Ch 4 & 8]D/IT)
⎯show that subtraction is not commutative (3-M[HM/Ch 5]D/IT)
⎯apply the addition and subtraction properties of 0 (adding or subtracting 0 doesn’t change a number) (3-M[HM/Ch 4 &5]M/B)
⎯apply the zero and identity properties of multiplication (adding 0 or multiplying by 1 doesn’t change a number) (3-M[HM/Ch 8&9]I/M)
⎯use arrays to represent the commutative property of multiplication (3-M[HM/Ch 8&9]I/M)
Analyze Change in Various Contexts
⎯describe qualitative change (e.g., a student growing taller) (3-M[HM/-]D/IT)
⎯describe quantitative change (e.g., a student growing two inches in one year) (3-M[HM/-]D/M)
⎯represent repeating geometric patterns as repeating numerical patterns (3-M[HM/Ch15-17]A/IT)
⎯connect open sentences to real-world situations (3-M[HM/ALL]A/IT)
⎯use appropriate mathematical language to find a point on a grid using whole number coordinates (3-M[HM/Ch 6]A/IT)
⎯show or represent and solve open sentences, involving addition, subtraction, and multiplication, with concrete objects or pictures (3-M[HM/Ch 4, 5, 8-11]D/M)
Geometry
The student will develop an understanding of geometric concepts and relationships as the basis for geometric modeling and reasoning to solve problems involving one-, two-, and three-dimensional figures.
Analyze characteristics and properties of geometric shapes
⎯name, identify, build, draw, and compare two- and three-dimensional geometric figures (e.g. rectangle, square, triangle, circle, cube, cylinder, sphere, and cone) (3-M[HM/CH 15-17]D/M)
⎯draw lines of symmetry in two-dimensional designs and shape (3-M[HM/CH 15-17]D/M)
⎯describe attributes and parts of two- and three-dimensional geometric figures (3-M[HM/CH 15-17]D/M)
⎯name two and three-dimensional geometric figures (e.g., rectangle, square, triangle, circle, cube, cylinder, sphere, and cone) (3-M[HM/CH 15-17]A/IT))
⎯investigate and predict the results of putting together and taking apart two- and three-dimensional geometric figures (3-M[HM/CH 15-17]I/IT)
⎯recognize geometric figures that are congruent (the same size and shape) (3-M[HM/CH 15-17]A/IT)
⎯identify the line of symmetry in a two-dimensional design or shape (3-M[HM/CH 15-17]I/IT)
⎯identify and draw horizontal and vertical lines (3-M[HM/CH 15-17]I/IT)
⎯identify and draw diagonals of polygons (3-M[HM/CH 15-17]I/IT)
⎯predict and identify the results of sliding, flipping, or turning two-dimensional shapes (3-M[HM/CH 15-17]D/M)
Specify locations and describe spatial relationships
⎯identify the position of whole numbers on the number line (3-M[HM/CH 1]M/B)
⎯identify the position of 1/2, 1/3, or 1/4 on the number line (3-M[HM/Ch 18]D/M)
⎯identify a location on a grid using whole number coordinates (3-M[HM/Ch 6]I/M)
Recognize and apply flips, slides, and turns
⎯identify the result of a transformation that has been applied to a simple two-dimensional geometric shape (i.e., flips or slides) (3-M[HM/CH 15-17]AIT)
⎯illustrate flips, slides, and turns using concrete and pictorial materials (3-M[HM/CH 15-17]D/M)
⎯predict and describe the results of sliding, flipping, and turning in two-dimensional shapes (3-M[HM/CH 15-17]D/M)
Measurement
The student will become familiar with the units and processes of measurement in order to use a variety of tools, techniques, and formulas to determine and to estimate measurements in mathematical and real-world problems.
Demonstrate understanding of units of measure and measurable attributes of objects
⎯determine when an estimate of a measurement is sufficient. (3-M[HM/Ch 13 & 14]D/M)
⎯demonstrate understanding of the concepts of perimeter, area, and capacity (3-M[HM/Ch 17]D/M)
Apply appropriate techniques and tools to determine measurements
⎯solve real-world problems using a calendar (3-M[HM/Ch 12]A/IT)
⎯use strategies to estimate or determine length, perimeter, area, capacity, weight, time, and temperature (3-M[HM/Ch 12-17]D/M)
⎯explain the relationships among inches, feet, and yards (3-M[HM/Ch 13]D/M)
⎯measure to the nearest centimeter, foot, half-inch, and inch. (3-M[HM/Ch 13]D/M)
⎯measure the capacity of a container in liters, cups, pints, quarts, and gallons (3-M[HM/Ch 13 & 14]D/M)
⎯measure to the nearest ounce, pound, kilogram, and gram (3-M[HM/Ch 13 & 14]D/M)
⎯find the perimeter of polygons (3-M[HM/Ch 17]A)
⎯find the perimeter of a rectangle on a grid (3-M[HM/Ch 17]A/IT)
⎯select and apply the most appropriate standard units of length, area, capacity, weight, time, and temperature (3-M[HM/Ch 12-17]D/M)
⎯solve real-world problems involving addition and subtraction of one- or two-digit measurements (3-M[HM/Ch 13-14]A/IT)
⎯solve real-world problems involving elapsed time to the half-hour (3-M[HM/Ch 12]A/IT)
⎯read thermometers with Fahrenheit and Celsius scales (positive whole number temperatures) (3-M[HM/Ch 12]A/IT)
⎯read and write time at five-minute intervals (3-M[HM/Ch 12]A/IT)
⎯use estimation to determine if a length measurement is reasonable (3-M[HM/CH 13 & 14]A/IT)
⎯measure length to the nearest centimeter and inch (3-M[HM/Ch 13 & 14]A/IT)
⎯measure to the nearest liter, milliliter, cup, pint, quart, and gallon (3-M[HM/Ch 13&14]D/M)
⎯select an appropriate standard unit to measure length (3-M[HM/CH 13&14]A/IT)
⎯read and write time to the nearest hour, half-hour, and quarter-hour (3-M[HM/Ch 12]A/IT)
Data Analysis and Probability
The student will understand and apply basic statistical and probability concepts in order to organize and analyze data and to make predictions and conjectures.
Develop, select, and use appropriate methods to collect, organize, display, and analyze data
⎯interpret and construct tables using tally marks (3-M[HM/Ch 6 & 7]D/M)
⎯construct pictographs and bar graphs (3-M[HM/Ch 6 & 7]D/M)
⎯interpret pictographs (3-M[HM/Ch 6 & 7]A/IT)
⎯interpret bar graphs (3-M[HM/Ch 6 & 7]A/IT)
⎯read and interpret tables, bar graphs, and pictographs (3-M[HM/Ch 6 & 7]D/M)
Apply basic concepts of probability
⎯make and justify predictions based on data gathered and displayed (3-M[HM/6 & 7]D/M)
⎯explain whether an event is certain, possible, or impossible (3-M[HM/6 & 7]M/M)
⎯determine whether an event is certain, possible, or impossible (3-M[HM/Ch 6&7]A/IT)
⎯determine the most likely, least likely, or equally likely outcomes in simple experiments (i.e., spinner, number or color cube) (3-M[HM/Ch 6&7]A/IT)
⎯write questions and gather data to answer questions (3-M[HM/6 & 7]D/M)
⎯select all possible outcomes of a simple experiment (i.e., spinner, coin toss, number or color cube) (3-M[HM/Ch 6&7]A/IT)
⎯solve real-world problems in which data is represented in tables (3-M[HM/Ch 6&7]A/IT)
⎯determine the median of a data set (3-M[HM/6 & 7]I/E)
Graphs and Graphing
The student will make simple graphs using concrete objects and pictures.
Graphing
⎯interpret and construct tables using tally marks (3-M[HM/Ch 6]D/M)
⎯construct pictographs and bar graphs ((3-M[HM/Ch 6]D/M)
⎯interpret pictographs (3-M[HM/Ch 6]A/IT)
⎯interpret bar graphs (3-M[HM/CH 6]A/IT)
⎯read and interpret tables, bar graphs, and pictographs (3-M[HM/Ch 6]D/M)
Real World Problem Solving
The student will gather information to compute and solve real world problems.
Story Problems
⎯develop a story problem that illustrates a given addition or subtraction number sentence (3-M[HM/Ch 4 & 5]I/B)
⎯compare and order decimal amounts written as money (3-M[HM/Ch 20]I/M)
⎯connect division to sharing situations (3-M[HM/Ch 10, 11, 22]I/E)
⎯explain the reasonableness of a solution to a computation or to a word problem (3-M[HM/ALL]D/IT)
⎯explain and justify solution strategies used in problem solving (3-M[HM/ALL]D/IT)
⎯select and use an appropriate strategy to solve word problems (e.g., organized list, guess and check, diagram, and table) (3-M[HM/ALL]D/IT)
⎯use strategies, including rounding, to estimate in story problems (3-M[HM/ALL]D/IT)
⎯solve real-world problems involving measurement (3-M[HM/Ch 12-14]D/IT)
⎯solve real-world problems in which data is represented in tables (3-M[HM/Ch 6]A/IT)
⎯solve real-world problems using a calendar (3-M[HM/Ch 12]A/IT)
⎯solve real-world problems involving addition and subtraction of one- or two-digit measurements (3-M[HM/Ch 4, 5, 12, 13, 14]A/IT)
⎯solve real-world problems involving elapsed time to the half-hour (3-M[HM/Ch 12]A/IT)
Computation
The student will learn to compute using concrete objects.
Counting/Identifying/Matching/Ordering Numbers
⎯count by 10’s, 100’s, or 1,000’s from any whole number (3-M[HM/Ch 1 & 8]A/IT)
⎯skip count by 10’s from any whole number less than 1,000 (3-M[HM/Ch 1 & 8]D)
⎯add and subtract efficiently and accurately with single-digit whole numbers (3-M[HM/Ch 4 & 5]A/IT)
⎯add efficiently and accurately with two- and/or three-digit whole numbers (3-M[HM/Ch 4]A/IT)
⎯subtract efficiently and accurately with two- and/or three-digit whole numbers (3-M[HM/Ch 5]A/IT)
⎯use the multiplication facts 0, 1, 2, 5, and 10 efficiently and accurately (3-M[HM/Ch 8, 9, 21]A/IT)
⎯use a variety of thinking strategies to add and subtract whole numbers (e.g., sums of ten, doubles plus one) (3-M[HM/Ch 4&5]D/IT)
⎯use known multiplication facts to determine a related product (e.g., 9 x 7 is 7 less than 10 x 7) (3-M[HM/Ch 8,9, 21]I/IT)
⎯mentally calculate the sum or difference of any two numbers up to 100 (3-M[HM/Ch 4&5]A/IT)
⎯count the value of a combinations of coins and bills up to $5 (3-M[HM/Ch 3]D/M)
⎯make change from a transaction that is less than a dollar(3-M[HM/Ch 3]D/M)
