Applies place value understanding and properties of operations to perform multi-digit arithmetic

• demonstrates an understanding of place value and number relationships in base ten system (identify values of digits and read and write numbers to 999 and using expanded form)

• uses place value understanding to sequence, compare and round 2-and 3-digit numbers

• add and subtract multiples of 10 or 100 to 2- and 3-digit numbers

• adds and subtracts 2-digit numbers

 

Represents and solves problems involving multiplication and division

• draws/creates models to represent a multiplication or division situation

• interprets and describes products and quotients of whole numbers

• solves mathematical and real-world word problems using multiplication and division in situations

Demonstrates an understanding of the properties of multiplication and the relationship between multiplication and division

• uses properties to simplify and solve multiplication problems (not naming properties)

  • commutative property of multiplication  (if 6 x 4= 24;  then 4 x 6 = 24)

  • associative property of multiplication  (2x5x5 can be found by 2 x 5 = 10, then 10 x 3 = 30)

  • distributive property:   8 x 7 can be found by 8 x (5+2) = (8 x 5) = (8 x 2)

• interprets and models division as a multiplication equation with an unknown factor

  • finds  32÷8 by solving  8 x ? = 32

Demonstrates fluency with multiplication and division combinations

• fluently multiplies (x1, x2, x5, x10 facts) using strategies which will lead to memorization

Solves problems involving the four operations, and identifies and explains patterns in arithmetic

• solves one-step word problems (+, -, x, ÷)

• represents word problems using equations with a symbol standing for the unknown quantity

• generates equivalent expression using operations for a given 2- or 3-digit number

 

Solves problems involving measurement and estimation of liquid volume, mass and length

• uses a ruler to measure lengths to the nearest inch and half-inch

• knows and uses the relationship between linear units when determining measurements, and chooses best tool and unit for the task

Tells and writes time to the nearest minute, and solves problems by calculating time intervals

• tells, shows and writes time (analog and digital) to 5 minute increments

• connects the various ways to state the time

o    2:45 “45 minutes past 2 o’clock” “quarter of/to 2” “15 minutes before 3 o’clock”

Solves problems involving money and makes change using a combination of coins and bills

• compares total values of two or more sets of coins and bills

• makes change from an amount up to $1.00

Represents and interprets data using tally charts, tables, pictographs, line plots and bar graphs

• collects, organizes and displays data in various formats

• solves one-and two-step problems using information to interpret categorical data presented in scaled pictographs and bar graphs

• organizes numerical data into a line plot

o    creates a line plot using whole number increments

o    organizes measurement data and create a line plot using fractional increments to the 1/2 inch

• interprets /describes the data shown on a line plot

 

Strategically applies concepts and processes to make sense of problems and solve them

• makes sense of and models mathematical problems appropriately and perseveres in solving them

• uses math vocabulary to clearly explain and justify reasoning

• approaches problems confidently and independently

Applies place value understanding and properties of operations to perform multi-digit arithmetic

• demonstrates an understanding of place value and number relationships in base ten system (identify values of digits, write numbers to 10,000 and write using expanded form, make representations)

• uses place value understanding to order, compare and round three-digit numbers to nearest 10 or 100

• adds and subtracts two- and three-digit numbers using appropriate, efficient strategies

• multiplies one-digit numbers by 2-digit multiples of 10

Represents and solves problems involving multiplication and division

• draws/creates models to represent a multiplication or division situation

• interprets and describes products and quotients of whole numbers

• solves mathematical and real-world word problems using multiplication and division in situations

Demonstrates an understanding of the properties of multiplication and the relationship between multiplication and division

• uses properties to simplify and solve multiplication problems (not naming properties)

  • commutative property of multiplication  (if 6 x 4= 24;  then 4 x 6 = 24)

  • associative property of multiplication  (2x5x5 can be found by 2 x 5 = 10, then 10 x 3 = 30)

  • distributive property:   8 x 7 can be found by 8 x (5+2) = (8 x 5) = (8 x 2)

• interprets and models division as a multiplication equation with an unknown factor

  • finds  32÷8 by solving  8 x ? = 32

Demonstrates fluency with multiplication and division combinations

• fluently multiplies (to 10 x 10) using strategies

• thinks of division as a “missing factor” multiplication problem to work toward division fluency

Solves problems involving the four operations, and identifies and explains patterns in arithmetic

• solves one- and two-step word problems (+, -, x)

• estimates sums and differences using rounding and other strategies (before computing)

• represents word problems using equations with a symbol standing for the unknown quantity

• writes expressions equal to a given 3-digit number given constraints

• identifies the missing symbol (+,-,x, ÷, <,>,=) that makes a number sentence true

 

Identifies, compares and classifies 2-D shapes and their attributes

• analyzes and defines polygons and describes using mathematical vocabulary

• names and categorizes regular and irregular polygons based on their characteristics

• compares and contrasts characteristics of polygons in order to classify them into larger groups

 

Solves problems involving measurement and estimation of liquid volume, mass and length

• uses a ruler to measure lengths to the nearest half inch and centimeter

• knows and uses the relationship between linear units when determining measurements, and choose best tool and unit for the task

Tells and writes time to the nearest minute, and solves problems by calculating time intervals

• tells, shows and writes time (analog and digital) to the minute

• connects the various ways to state the time

o    2:45 “45 minutes past 2 o’clock” “quarter of/to 2” “15 minutes before 3 o’clock”

Solves problems involving money and makes change using a combination of coins and bills

• compares total values of two or more sets of coins and bills

• makes change from an amount up to $5.00

Represents and interprets data using tally charts, tables, pictographs, line plots and bar graphs

• interprets /describes the data shown on a line plot

• solves one-and two-step problems using information to interpret categorical data presented in scaled pictographs, bar graphs and line plots marked in ½ inch increments

Solves problems involving area and perimeter of polygons and distinguishes between linear and area measures

• finds the area of 2-D figures in real world and mathematical problems by:

o    counting unit squares inside the figure

o    multiplying side lengths of rectangles

• finds the perimeter of 2-D figures in real world and mathematical problems:

o    add side lengths to find the perimeter

o    find an unknown side length when perimeter and the other side lengths are known

• correctly labels area in square units (sq in, sq cm, sq ft, etc)  and perimeter in units (in., cm, ft, etc)

• identifies and creates rectangles having the same perimeter but different areas, as well as having the same areas but different perimeters

 

Strategically applies concepts and processes to make sense of problems and solve them

• makes sense of and models mathematical problems appropriately and perseveres in solving them

• uses math vocabulary to clearly explain and justify reasoning

• approaches problems confidently and independently

Applies place value understanding and properties of operations to perform multi-digit arithmetic

• demonstrates an understanding of place value and number relationships in base ten system (identify values of digits and writing numbers to 10,000 using expanded form)

• uses place value understanding to order, compare and round two-and three-digit numbers

• adds and subtracts two- and three-digit numbers using appropriate, efficient strategies

• multiplies one-digit numbers by 2-digit multiples of 10

 

Demonstrates an understanding of fractions as numbers

• uses fractions to represent equal parts of a whole or set

  • writes the fraction that corresponds to a drawing or part of a set

  • creates a model or set that represents a given fraction

• represents fractions on a number line model

• understands that two fractions are equivalent if they are the same size, or occupy the same point on a number line

• expresses whole numbers as fractions

• compares two fractions with the same numerator or same denominator by reasoning about their size; uses >,<,= to compare them and justify reasoning

 

Represents and solves problems involving multiplication and division

• draws/creates models to represent a multiplication or division situation

• interprets and describes products and quotients of whole numbers

• solves mathematical and real-world word problems using multiplication and division in situations

Demonstrates an understanding of the properties of multiplication and the relationship between multiplication and division

• uses properties to simplify and solve multiplication problems (not naming properties)

  • commutative property of multiplication  (if 6 x 4= 24;  then 4 x 6 = 24)

  • associative property of multiplication  (2x5x5 can be found by 2 x 5 = 10, then 10 x 3 = 30)

  • distributive property:   8 x 7 can be found by 8 x (5+2) = (8 x 5) = (8 x 2)

• interprets and models division as a multiplication equation with an unknown factor

  • finds  32÷8 by solving  8 x ? = 32

Demonstrates fluency with multiplication and division combinations

• fluently multiplies (to 10 x 10) and divides using strategies which will lead to memorization of the multiplication and division math facts

Solves problems involving the four operations, and identifies and explains patterns in arithmetic

• solves one- and two-step word problems (+, -, x, ÷)

• estimates sums and differences using rounding and other strategies (before computing)

• represents word problems using equations with a symbol standing for the unknown quantity

• identifies the symbol (+,-,x, ÷, <,>,=) that makes a number sentence true

• solves two-step equations using order of operations with no grouping symbols

 

Identifies, compares and classifies 2-D shapes and their attributes

• analyzes and defines polygons and describes using mathematical vocabulary

• names and categorizes regular and irregular polygons based on their characteristics

• compares and contrasts characteristics of polygons in order to classify them into larger groups

Partitions shapes into parts with equal areas and expresses the area of each part as a unit fraction of the whole

• divide geometric shapes into parts, all of the parts have the same area

• express the area of each of the equal parts as a fraction (example – a shape partitioned into 4 equal area parts, each part is ¼th  of the total area of the shape)

 

Solves problems involving measurement and estimation of liquid volume, mass and length

• uses a ruler to measure lengths to the nearest quarter inch and centimeter

• knows and uses the relationship between linear units when determining measurements

• measures and estimates liquid volume using standard (c, pt, qt, gal) and metric (mL, L) units

• measures and estimates weight (mass) using standard (oz, lb) and metric (g, kg) units

• uses the four operations to solve one-step word problems involving masses or liquid volumes that are given in the same units

Tells and writes time to the nearest minute, and solves problems by calculating time intervals

• tells, shows and writes time (analog and digital) to the minute

• connects the various ways to state the time

o    2:45 “45 minutes past 2 o’clock” “quarter of/to 2” “15 minutes before 3 o’clock”

• determines the amount of time elapsed between events or the start/end time of an event given the time elapsed

Solves problems involving money and makes change using a combination of coins and bills

• compares total values of two or more sets of coins and bills

• makes change from an amount up to $5.00

Represents and interprets data using tally charts, tables, pictographs, line plots and bar graphs

• collects, organizes and displays data in various formats

• translates data from one type of data display to another

• solves one-and two-step problems using information to interpret categorical data presented in scaled pictographs and bar graphs

• organizes numerical data into a line plot

  • creates a line plot using whole number increments

  • organizes measurement data and create a line plot using fractional increments to the ¼ inch

• interprets /describes the data shown on a line plot

Solves problems involving area and perimeter of polygons and distinguishes between linear and area measures

• finds the area of 2-D figures in real world and mathematical problems by:

o    counting unit squares inside the figure

o    multiplying side lengths of rectangles

• finds the perimeter of 2-D figures in real world and mathematical problems:

o    add side lengths to find the perimeter

o    find an unknown side length when perimeter and the other side lengths are known

• correctly labels area in square units (sq in, sq cm, sq ft, etc) and perimeter in units (in., cm, ft, etc)

• identifies and creates rectangles having the same perimeter but different areas, as well as having the same areas but different perimeters

 

Strategically applies concepts and processes to make sense of problems and solve them

• makes sense of and models mathematical problems appropriately and perseveres in solving them

• uses math vocabulary to clearly explain and justify reasoning

• approaches problems confidently and independently