You need to have JavaScript enabled in order to access this site.

Balancing Rigor Holding Tank

Balancing the Rigor of Mathematics (3.NBT.1)
Conceptual Understanding Understand place value concepts Understand that “rounding” means to identify the multiple of 10, 100, etc. that is closest to a given number Understand that numbers exactly between two multiples of 10, 100, etc. round to the larger multiple	Procedural Understanding Round whole numbers to the nearest 10, 100, etc. Represent rounding using tools such as a number line, base ten blocks, or hundreds charts	Application Accurately explain why a number rounds to another number based on the number’s relationship to the nearest multiple of 10, 100, etc. Solve real-world problems or use problem solving tasks that involve rounding to the nearest 10, 100, etc. Identify numbers that can round to a given number (multiple of 10, 100, etc.) Solve word problems or use problem solving tasks involving rounding Use and explain how rounding is helpful in computation estimation

Balancing the Rigor of Mathematics (3.NBT.2)
Conceptual Understanding Understand place value concepts Understand a variety of computation strategies for adding and subtracting within 1,000 Understand the commutative property, associative property of addition, and identity property of zero Understand the inverse relationship between addition and subtraction Understand that addition and subtraction problems can be written vertically and horizontally	Procedural Understanding Use multiple strategies to add and subtract within 1,000.	Application Solve real-world problems or use problem solving tasks that involve adding and subtracting within 1,000 Apply known strategies to solve addition and subtraction problems sums larger than 1,000 Decide if an answer is reasonable using mental math, estimation or rounding

Balancing the Rigor of Mathematics (3.OA.8)
Conceptual Understanding Understand that a symbol/letter can be used to represent an unknown number Understand mental math, rounding, and estimation Understand how to fluently add and subtract within 1,000 Understand that more than one step may be needed to solve problems	Procedural Understanding Accurately choose the correct operations to perform the first and second computations Write equations using a letter for the unknown number Decide if an answer is reasonable using mental math, estimation and/or rounding Solve two-step word problems using manipulatives, pictures or written equations	Application Represent the problem in multiple ways Use flexible strategies to solve problems Apply strategies to problems with larger quantities Make strategy adjustments based on initial estimates

Balancing the Rigor of Mathematics (3.OA.9)
Conceptual Understanding Understand that there are patterns on hundred charts, number lines and addition and multiplication tables Understand that using patterns can help to master basic facts Understand that multiplying any number by an even number results in an even product Understand that multiplying two odd numbers results in an odd product	Procedural Understanding Identify and model patterns on hundred chart, number line and addition and multiplication tables	Application Accurately explain found patterns Apply patterns to larger numbers Use patterns to solve problems

Balancing the Rigor of Mathematics (3.OA.1)
Conceptual Understanding Understand that multiplication represents and then combines equal groups of objects Understand that multiplication can be represented with arrays, repeated addition and skip counting Understand that in a multiplication equation, the first factor equals the number of groups and the second factor equals the quantity in each group	Procedural Understanding Solve multiplication equations using repeated addition, skip counting, number lines, arrays and pictures.	Application Solve real-world problems, word problems or use problem solving tasks involving multiplication Apply known strategies to a digit number multiplied by a multiple of 10 (i.e. use 8 x 7 to solve 8 x 70 and 80 x 7) Write an appropriate story problem to match a given multiplication equation

Balancing the Rigor of Mathematics (3.OA.2)
Conceptual Understanding Understand that division can be partitive - the total number of groups are known and the number of items in each group must be found Understand that division can be quotative - the number of items in each group is known and the total number of groups must be found Understand that division is sharing equally among groups	Procedural Understanding Find how many equal groups can be made out of a certain number of objects. Find how many objects can be shared equally among a certain number of groups Use pictures, manipulatives, numbers or repeated subtraction to solve division equations	Application Solve real-world problems, word problems or use problem solving tasks involving division Write an appropriate story problem to match a given division equation When given two different division scenarios (one partitive and one quotative), discuss differences and similarities

Balancing the Rigor of Mathematics (3.OA.3)
Conceptual Understanding Understand that word problems can be represented in multiple ways including equations, arrays, equal groups, repeated addition, repeated subtraction, and number lines Understand when to multiply or divide to solve problems	Procedural Understanding Write an accurate equation that matches a word problem Solve multiplication and division word problems using a variety of strategies including arrays, equal groups, number line, drawings, repeated addition, repeated subtraction.	Application Represent the problem in multiple ways Use flexible strategies to solve problems Write scenarios to match a given equation or a given product/quotient

Balancing the Rigor of Mathematics (3.OA.4)
Conceptual Understanding Understand that both sides of an equation equal the same amount Understanding the inverse relationship between multiplication and division Understand that a symbol can be used for an unknown within an equation	Procedural Understanding Use multiplication or division to solve for an unknown in an equation Model multiplication and division using a variety of strategies including arrays, manipulatives, equal groups, repeated addition, repeated subtraction and number lines	Application When given a multiplication or division equation with a missing whole number, accurately explain how to find the missing number Solve real-world problems, word problems or use problem solving tasks involving finding a missing whole number in a multiplication/division equation

Balancing the Rigor of Mathematics (3.OA.5)
Conceptual Understanding Understand that multiplication is commutative and division is not commutative Understand that given a multiplication equation with three factors, two factors can be multiplied in either order and still result in the same product Understand that one factor can be “broken apart” and the parts can be multiplied by the other factor and still result in the same product	Procedural Understanding Model and solve multiplication problems with the commutative property, associative, and distributive property	Application Solve real-world problems, word problems or use problem solving tasks involving commutative, associative and distributive properties Given a specific multiplication equation, accurately explain what strategy is used to solve Apply the commutative, associative, and distributive property to larger numbers

Balancing the Rigor of Mathematics (3.OA.6)
Conceptual Understanding Understand that multiplication and division are inverse operations Understand both multiplication and division involve a number of groups, a number in each group and a total quantity	Procedural Understanding Represent a division problem as a multiplication problem with an unknown factor Solve for the unknown factor using a variety of strategies	Application Explain answers using the relationship between multiplication and division Solve word problems or use problem solving tasks with division as an unknown factor Apply known strategies to larger numbers

Balancing the Rigor of Mathematics (3.OA.7)
Conceptual Understanding Understand the relationship between multiplication and division Understand what it means to compose and decompose numbers Understand the commutative, associative, and distributive properties Understand how to use known facts to help learn unknown facts	Procedural Understanding Fluently multiply/divide within 100 using a variety of strategies	Application Solve word problems or use problem solving tasks that involve basic multiplication and division facts Apply known strategies to help solve multiplication and division problems with larger numbers (i.e. use the fact 8 x 5 = 40 to help solve 8 x 50 or 80 x 5) Apply known strategies to help solve unknown facts (i.e. use x10 and ÷10 to help solve x5 and ÷ 5 facts) Accurately explain the strategy used to solve a multiplication/division basic fact

Balancing the Rigor of Mathematics (3.NBT.3)

Conceptual Understanding

Understand how to multiply one-digit numbers by 10
Understand place value

Procedural Understanding

Accurately multiply one-digit whole numbers by multiples of 10 using a variety of strategies

Application

Apply knowledge of basic multiplication facts to efficiently multiply by multiples of 10
Apply understanding to division with multiples of 10 (i.e. 280 ÷ 70 = 4)
Extend understanding to larger numbers (i.e. 800 x 20)

Balancing the Rigor of Mathematics (3.NF.1)
Conceptual Understanding Understand that fractional parts are equal-sized pieces of the same whole Understand that as the number of equal parts of the whole increases, the size of those pieces decreases Understand that the numerator of a fraction tells the number of equal parts being considered Understand that the denominator of a fraction tells how many equal parts the whole is divided into Understand when dividing a region into equal parts, it is not necessary that the parts have the same shape as long as they have the same area Understand that a unit fraction is one of the equal parts that represents the whole	Procedural Understanding Identify the numerator as the number of equal parts being considered (shaded or unshaded) Identify the denominator as the number of equal parts that the whole is divided into Accurately read and write a fraction Divide a region or set of objects into fractional parts Represent fractions using a variety of models/manipulatives (circles, rectangles, fraction bars, fraction towers, Cuisenaire Rods, two-color counters, pattern blocks)	Application Apply known strategies to working with fractions that have denominators beyond those described at this grade level (2, 3, 4, 6, and 8) Solve word problems or use problem solving tasks involving fraction When given a fractional part, show what the whole could look like Explain how changing the denominator affects the value of the fraction When given a fraction, ask what fraction is needed to make one whole

Balancing the Rigor of Mathematics (3.NF.2)
Conceptual Understanding Understand that fractions can be represented as points on a number line Understand representing fractions on a number line illustrates the value of fractions; it helps students see which fractions are close to 0, 1/2, and 1	Procedural Understanding Represent a unit fraction (1/b) on a number line between 0 and 1 (denominators 2, 3, 4, 6, and 8) Represent any fraction (a/b) on a number line (denominators 2, 3, 4, 6, and 8)	Application Apply known strategies to working with fractions that have denominators beyond those described at this grade level (2, 3, 4, 6, and 8) Represent fractions greater than one on an unticked number line Place whole numbers on a number line when given one fraction Identify a given fraction on two different number lines that have different endpoints, and explain why the fraction is placed differently on each number line

Balancing the Rigor of Mathematics (3.NF.3)
Conceptual Understanding Understand two fractions are equivalent (equal) if they are the same size, or the same point on a number line Understand when fractions are equivalent there is an underlying assumption that the wholes are the same size Understand benchmark fractions of 0, ½, and 1 and how to use them when comparing fractions Understand that as the number of equal parts of the whole increases, the size of those pieces decreases	Procedural Understanding Use models to show and explain equivalent fractions Generate simple equivalent fractions on a number line Express and recognize fractions that are equivalent to whole numbers Compare two fractions with the same numerator Compare two fractions with the same denominator Compare two fractions using benchmark fractions Explain and justify fraction comparisons	Application Solve word problems or engage in problem solving tasks that involve equivalent fractions and/or comparing fractions Apply known strategies to working with fractions that have denominators beyond those described at this grade level (2, 3, 4, 6, and 8) Order three or more fractions and explain reasoning for the correct order

Balancing the Rigor of Mathematics (3.MD.1)
Conceptual Understanding Understand that time can be measured in standard units such as seconds, minutes, hours, and days Understand the relationship between these units Understand that time is also categorized by a.m. and p.m. Understand that both an analog and digital clocks are instruments to tell time Understand ime is the duration of an event from beginning to end Understand elapsed time can be found by finding the total amount of time that passes between a starting time and an ending time Understand the concept of elapsed time, including between a.m. and p.m. Understand concepts of whole, half and quarter on a number line	Procedural Understanding When shown the time (to the 1 minute interval) on an analog clock, correctly state and write the time When given the time on a digital display or written (to the 1 minute interval), show or draw the time accurately Measure the duration of time in minutes Solve addition and subtraction word problems involving durations of time measured in minutes Demonstrate elapsed time on a number line	Application Identify a connection between fractions and expressions such as quarter after, half past and quarter till Demonstrates an understanding of the 24 hour day and a.m./p.m. through discussions Engage in real-world problems and tasks involving telling time to the minute

Balancing the Rigor of Mathematics (3.MD.2)
Conceptual Understanding Understand liquid measurement or capacity is used to refer to the amount that a container will hold Understand liquid is measured in liters, ounces, gallons, quarts, and cups Understand mass is a measure of the amount of how heavy an object is and is measured using grams or kilograms Understand and work with customary measurement of length including inches, feet, yards and miles Understand measuring tools for capacity, mass, and length and their application to real life (e.g., two liters of soda)	Procedural Understanding Estimate liquid volumes and masses of objects using standard units of measure (grams, kilograms, and liters) Measure liquid volumes and masses of objects using standard units of measure (grams, kilograms, and liters) Estimate and measure length using customary units of measure including inches, feet and yards Use a drawing to represent one-step word problems involving masses, volumes, and length Solve one-step word problems involving masses, volumes, and length using addition, subtraction, multiplication, and division	Application Choose appropriate units of measure for real-world items Solve two-step word problems for measurement situations Discover relationships between units of measurement (i.e. recognizing 3 feet= 1 yard)

Balancing the Rigor of Mathematics (3.MD.3)
Conceptual Understanding Understand that a scaled picture graph contains a key that indicates what each symbol stands for Understand how to use the key and appropriate multiplication to accurately to interpret picture graphs Understand how to use the scale to accurately read a bar graph Understand the bars in a bar graph do not need to be represented in numerical order	Procedural Understanding Create a scaled picture graph or bar graph with several categories to represent data Read and interpret scaled bar graphs in order to solve one- and two-step problems	Application Interpret picture and/or bar graphs to answer questions accurately about the data shown Explain why a picture graph or bar graph is or is not the best choice for a given set of data Write questions about the data for a picture graph or bar graph

Balancing the Rigor of Mathematics (3.MD.4)
Conceptual Understanding Understand that a line plot is a visual representation of data Understand that a line plot is used to display numeric data Understand how a line plot and a number line are related Understand that a line plot must show continuous points of data (similar to a number line) even if not shown by the data (i.e. objects are measured at 2 ½, 3, 3 ¼ , and 3 ½ , however the line plot must still include 2 ¾ ) Understand the concept of fractional parts of an inch, including halves and quarters	Procedural Understanding Students can find accurate length measurements (to the nearest quarter inch) and show the data using a line plot Use a ruler to measure lengths in whole, half, and quarter inches Gather and record measurement data (to the nearest quarter inch) and display the data in a line plot	Application Understand and interpret data on a line plot Explain why a line plot is or is not the best choice for a given set of data Write questions about the data for a line plot

Balancing the Rigor of Mathematics (3.MD.5)
Conceptual Understanding Understand area as the covering of a two-dimensional space inside a region Understand that area is measured by covering a surface using tiles or square units to cover objects	Procedural Understanding Define a unit square Define area as the measure of space covering a plane figure and explain why area is measured in square units Use manipulatives (i.e. color tiles) or graph paper to show area with no gaps or overlays	Application Explain how area and perimeter are related Recognize that two objects can have the same area but different perimeters, explain why this can be true Find the area of one object to estimate the area of another object Solve word problems or engage in problem solving tasks involving area

Balancing the Rigor of Mathematics (3.MD.6)
Conceptual Understanding Understand area as the covering of a two-dimensional space inside a region Understand that area is measured by covering a surface using tiles or square units to cover objects Understand that standard measurement units can be used (square cm, square m, square in, square ft) to measure area	Procedural Understanding When given a shape with shown square units, find the area by counting unit squares (including square cm, square m, square in, square ft) Measure the area of a shape or flat surface by covering it with unit squares, with no gaps or overlaps, and counting the number of unit squares used	Application Explain how area and perimeter are related Recognize that two objects can have the same area but different perimeters, explain why this can be true Find the area of one object to estimate the area of another object When exploring area of rectangles, make connections between counting square units and repeated addition

Balancing the Rigor of Mathematics (3.MD.7)
Conceptual Understanding Understand that area is measured by covering a surface using tiles or square units to cover objects Understand the relationship of multiplication and repeated addition to area of rectangles Understand distributive property	Procedural Understanding Use tiles to find the area of rectangles Explain the relationship between tiling and multiplying side lengths to find the area of rectangles Multiply adjacent side lengths of rectangles to solve problems Use area models to explain the distributive property Decompose an irregular figure into non-overlapping rectangles to find the total area Explain area as additive and use this understanding to solve problems involving area	Application Find possible side lengths when given an area Find missing side lengths when given the area and specific other side lengths of rectangles and other rectilinear figures Solve problems and engage in problem solving tasks that involve area

Balancing the Rigor of Mathematics (3.MD.8)
Conceptual Understanding Understand that perimeter is the distance around a figure or shape Understand shapes with the same perimeter can have different areas Understand shapes with the same area can have different perimeters Understand the missing side can be found using the perimeter and the known sides	Procedural Understanding Identify polygons Define perimeter Find the perimeter of polygons when given the lengths of all sides Find the unknown side lengths of polygons when given the perimeter Demonstrate how rectangles with the same perimeter can have different areas and show rectangles with the same area can have different perimeters Solve word problems involving area and perimeter	Application Find the area or perimeter of one object and use it to estimate the area or perimeter of another object Seek and identify patterns when working with area and perimeter

Balancing the Rigor of Mathematics (3.G.1)
Conceptual Understanding Understand a polygon is a closed figure Understand a polygon is named by the number of its sides Understand that regular polygons are made up of line segments which are the same size lengths Understand irregular polygons can have sides of different lengths Understand that classification of polygons is based on attributes	Procedural Understanding Use defining attributes (number of sides, lengths of sides and angles) to identify shapes Use defining attributes to classify shapes into categories Classify quadrilaterals, recognizing when categories overlap (i.e. squares are also parallelograms) Draw quadrilaterals other than rhombuses, rectangles, and squares	Application Solve word problems or use problem solving tasks involving quadrilaterals and other polygons Participate in various shape sorts based on attributes Discover and explain relationships between categories of shapes (i.e. all squares are rhombuses)

Balancing the Rigor of Mathematics (3.G.2)
Conceptual Understanding Understand that shapes can be divided into equal parts Understand that each part is a fraction of the whole Understand the fractional concepts of halves, thirds, fourths, sixths, and eighths	Procedural Understanding Partition shapes into equal parts Identify a fractional part as a unit fraction of the whole	Application Solve word problems or use problem solving tasks involving subdivision of shapes into fractional parts When given a shape that represents a unit fraction of the whole, draw or show what the whole could look like Show different ways that a given shape can be partitioned (i.e. consider horizontal, vertical, diagonal options for dividing shape)