Math

## NH DOE Math 3-5 Competency :

Competency

Standard

Understandings/Skills

Students will demonstrate an understanding of adding and subtracting using various techniques to add three or more two- or three-digit numbers up to 1,000, and using various techniques to subtract two- and three-digit numbers with the whole less than 1,000.

3.NBT.A.1

•Round whole numbers to the nearest 10 or 100.

3.NBT.A.2

•Use a variety of models, representations, and strategies to fluently add and subtract within 1000.

Students will demonstrate an understanding of and fluency in facts with multiplication and division within 100 using a variety of strategies,  arithmetic properties, equal groups, arrays, and measurement quantities.

3.NBT.A.3

•Multiply multiples of ten up to 90 by a single digit whole number using strategies based on place value and properties of operations.

3.OA.A.1

•Give a situation to represent a given multiplication expression; identifying the number of groups, the number of items in each group, and then the total number of items.

3.OA.A.2

•Give a situation to represent a given division expression; identifying the total, the number of equal groups being partitioned into, and then the number of items in each group.

3.OA.A.2

•Give a situation to represent a given division expression; identifying the total, the number of items to be in each group, and then the number of groups created.

3.OA.A.3

•Solve multiplication and division (within 100) word problems involving equal groups, arrays, and measurement quantities.

3.OA.A.4

•Determine the missing value in given multiplication and division equations.

3.OA.B.5

•Can describe the Commutative Property of Multiplication, the Associative Property of Multiplication, and the Distributive Property.

3.OA.B.5

•Use properties of operations as a strategy when solving multiplication and division problems.

3.OA.B.6

•Understand the relationship between multiplication and division.

3.OA.C.7

•Multiply and divide (within 100) fluently using a variety of strategies.

3.OA.C.7

3.MD.C.7.C

•Use the area model as a strategy for the distributive property.

Students will demonstrate an understanding of the arithmetic operations by solving  one- and two-step word problems, estimating the reasonableness of answers using a variety of strategies, and in recognizing and using arithmetic patterns.

3.OA.D.8

•Solve two-step word problems that include more than one operation.

3.OA.D.8

•Create equations, using a variable, to represent two-step word problem using any of the four arithmetic operations.

3.OA.D.8

•Determine if an answer is reasonable using a variety of strategies such as mental computation and estimation.

3.OA.D.9

•Look for and find arithmetic patterns in addition and multiplication tables.

3.OA.D.9

•Look for and find arithmetic patterns.

3.OA.D.9

•Explain arithmetic patterns using the properties of operations.

3.MD.D.8

•Solve numerical and word problems involving perimeter, including finding unknown side lengths.

3.MD.D.8

•Solve numerical and word problems involving rectangles with the same area and different perimeters or with the same perimeter and different areas.

Students will demonstrate an understanding of the connection between area and multiplication and addition by using addition and multiplication to find the areas of squares and rectangles, using the distributive property to find the total areas of partitioned rectangles, and decomposing irregular shapes into rectangles to find their area.

3.MD.C.5

•Understand that area is amount of space inside a two-dimensional figure.

3.MD.C.5

•Understand that the basic unit of measure for area is the square unit.

3.MD.C.5.A

•Understand that square with a side length of one unit of measure is called a square unit.

3.MD.C.5.A

•Understand that area is measured in square units.

3.MD.C.5.B

•Find the area of a 2-dimentional figure by determining the number of square units that can cover it without gaps or overlays.

3.MD.C.6

•Determine the area of figure by counting the unit squares within the figure.

3.MD.C.7

•Connect the area of a rectangle to the area model used to represent multiplication.

3.MD.C.7.A

•Show how the multiplying the side lengths of a rectangle gives the same area of measurement as does tiling it with identical squares.

3.MD.C.7.B

•Solve numerical and word problems involving areas of rectangles, with whole number side lengths, using multiplication.

3.MD.C.7.C

•Use tiling of rectangles with the same width or length to model the distributive property; how the area model represents the distributive property.

3.MD.C.7.D

•Apply the strategy of decomposing a figure made of multiple rectangles.

3.MD.C.7.D

•Calculate the total area of a decomposed figure, using the sum of the areas of each smaller rectangle.

3.MD.C.7.D

•Solve word problems involving finding the area of composite figures made of rectangles.

Students will demonstrate an understanding of fractions as numbers by reading, writing, and comparing fractions, identifying how fractions relate to the whole, representing fractions of a whole and greater than one on a number line, partitioning shapes into equal parts and naming them using a unit fraction of the whole.

3.NF.A.1

•Understand that a unit fraction is one part out of all the equal parts of a whole.

3.NF.A.1

•Understands that a fraction is made up of that number (the numerator) of unit parts.

3.NF.A.2

•Understand that a fraction is a number representing one point on a number line.

3.NF.A.2

•Recognize that a point on a number line represents the distance between zero and itself.

3.NF.A.2

•Place a fraction appropriately on a number line.

3.NF.A.2.A

•Understand that the distance between one and zero on a number line can be partitioned into equal parts.

3.NF.A.2.A

• Recognize that one of the equal parts of the whole is a unit fraction and is written as 1/b.

3.NF.A.2.A

•Understand that a unit fraction represents its distance from zero on the number line.

3.NF.A.2.B

•Place a fraction appropriately on a number line using its unit fraction as a strategy.

3.NF.A.2.B

•Understand that a fraction represents its distance from zero on the number line.

3.NF.A.3

•Explain why fractions are equal using models, representations, or strategies.

3.NF.A.3

•Compare fractions by reasoning about their size using models, representations, or strategies.

3.NF.A.3.A

•Understand that two fractions are equal if they name the same quantity or point on a number line.

3.NF.A.3.B

•Recognize and create simple equivalent fractions.

3.NF.A.3.B

•Explain why fractions are equal using visual models or other representations or strategies.

3.NF.A.3.C

•Represent whole numbers in fraction form by placing it over 1.

3.NF.A.3.C

•Understand that when the numerator and the denominator are the same, the value of the number is one whole.

3.NF.A.3.D

•Compare two fractions with either the same numerator or the same denominator by reasoning about their size using models, representations, or strategies.

3.NF.A.3.D

•Understand that fraction comparisons need to refer to the same whole.

3.NF.A.3.D

•Write fraction comparisons using the symbols <, =, > , and support answer using visual models.

3.G.A.2

•Partition a given shape into parts with equal areas.

3.G.A.2

•Describe the fractional area of each part as a unit fraction of the whole shape.

Students will demonstrate an understanding of time, capacity, and mass by writing time to the nearest minute and identifying how much time has passed, estimating and measuring the liquid volume of a container, and estimating and measuring the mass of any object.

3.MD.A.1

•Tell and write time to the nearest minute using digital and analogue clocks.

3.MD.A.1

•Measure periods of time in minutes.

3.MD.A.1

•Use number lines or other strategies to solve word problems involving  adding and subtracting time in minutes.

3.MD.A.2

•Estimate and measure the mass of objects using grams and kilograms.

3.MD.A.2

•Estimate and measure liquids using liters.

3.MD.A.2

•Solve one-step word problems involving mass or volume given in the same units using a variety of strategies.

Students will demonstrate an understanding of representing and interpreting data drawing scaled pictographs and bar graphs, solving one- and two-step word problems using information represented in a bar graph, and gathering measurement data using whole numbers, quarters  and halves, and recording on line plots.

3.MD.B.3

•Draw a scaled picture graph to represent a data set with different categories.

3.MD.B.3

•Draw a scaled bar graph to represent a data set with different categories.

3.MD.B.3

•Solve one- and two-step " how many more or less"  problems using information from scaled bar graphs.

3.MD.B.4

•Gather data by measuring objects to the nearest half and quarter-inch using a ruler.

3.MD.B.4

•Make a line plot, using whole numbers, quarters, or halves, to display the data of the objects measured.

Students will demonstrate an understanding of quadrilaterals by identifying and defining the attributes of quadrilaterals , and  classifying a quadrilateral as square, rectangle, rhombus, or parallelogram.

3.G.A.1

•Describe, analyze, and compare properties of two-dimensional shapes.

3.G.A.1

•Recognize a quadrilateral as rhombus, rectangle, square, or none of those.

3.G.A.1

•Draw a quadrilateral that is not a rhombus, square, or rectangle.

## NH DOE Math 6-8 Competency :

Competency

Standard

Understandings/Skills

Students will demonstrate an understanding of fractions by performing operations of addition, subtraction, multiplication and division with fractions and in simplifying fractions with LCM and GCF.

6.NS.A.1

•Use visual models to represent the division of a fraction by a fraction.

6.NS.A.1

•Divide fractions by fractions using an algorithm or mathematical reasoning.

6.NS.B.4

•Find the greatest common factor of two whole numbers less than or equal to 100.

6.NS.B.4

•Find the least common multiple of two whole numbers less than or equal to 12.

6.NS.B.4

•Use the distributive property to rewrite a simple addition problem when the addends have a common factor.

Students will demonstrate an understanding of decimals by performing operations of addition, subtraction, multiplication, and division with decimals, rounding decimals, in computational and real world situations.

6.NS.B.2

•Fluently use the standard algorithm to divide multi-digit numbers.

6.NS.B.3

•Fluently add and subtract multi-digit decimals using the standard algorithms.

6.NS.B.3

•Fluently multiply and divide multi-digit decimals using the standard algorithms.

Students will demonstrate an understanding of extending and applying previous understandings of whole numbers to the systems of integers and rational numbers by  writing, interpreting and explaining statements of order in real world contexts.

6.NS.C.5

•Recognize that positive and negative signs represent opposite values and/or directions.

6.NS.C.5

•Use positive and negative numbers and zero to represent real-world situations.

6.NS.C.6

•Graph rational numbers on a number line.

6.NS.C.6.A

•Graph a number and its opposite on a number line and recognize that they are equidistant from 0.

6.NS.C.6.A

•Find the opposite of any number, including 0.

6.NS.C.7

•Order rational numbers and absolute values of rational numbers.

6.NS.C.7.A

•Describe the relative position of two rational numbers on a number line.

6.NS.C.7.B

•Interpret a given inequality for rational numbers in terms of a real-world situation.

6.NS.C.7.C

•Understand that the absolute value of a number is its distance from 0 on a number line.

6.NS.C.7.C

•Interpret the absolute value of a number in a real-world situation.

6.NS.C.7.D

•Explain the reason why the value of an absolute value increases when the value of its negative rational number decreases.

Students will demonstrate an understanding of the coordinate plane by identifying and positioning ordered pairs on a coordinate plane to solve real world application problems.

6.NS.C.6

•Graph ordered pairs in all four quadrants of a coordinate grid.

6.NS.C.6.B

•Use the signs of coordinates to determine the location of an ordered pair on the coordinate grid.

6.NS.C.6.B

•Reason about the location of the coordinate grid of two ordered pairs that have the same values but different signs.

6.NS.C.6.C

•Plot a point on a number line or an ordered pair on a coordinate plane.

6.NS.C.6.C

•Read a point from a number line or an ordered pair on a  coordinate grid.

6.NS.C.8

•Solve problems by graphing ordered pairs in all four quadrants of the coordinate grid.

6.NS.C.8

• Find the distance between points with the same first or the same second coordinate using absolute value.

Students will demonstrate an understanding of  algebraic expressions by writing, evaluating, and simplifying expressions in computational and real world situations.

6.EE.A.1

•Write numerical expressions involving whole-number exponents.

6.EE.A.1

•Simplify numerical expressions involving whole-number exponents.

6.EE.A.2

•Write algebraic expressions.

6.EE.A.2

6.EE.A.2

•Evaluate algebraic expressions.

6.EE.A.2.A

•Translate a verbal math expression into an algebraic expression and vice versa.

6.EE.A.2.B

•Identify the parts of an algebraic expression using correct math terminology.

6.EE.A.2.B

•View one or more parts of an expression as a single entity.

6.EE.A.2.C

•Simplify expressions for a given value.

6.EE.A.2.C

•Substitute given values into formulas in solving real-world problems.

6.EE.A.2.C

•Apply the order of operations when evaluating arithmetic and real-world expressions.

6.EE.A.3

•Apply the properties of operations to create equivalent expressions.

6.EE.A.4

•Determine whether two expressions are equivalent or not.

6.EE.B.6

•Model and solve real-world and mathematical problems using expressions with a variable for an unknown quantity.

Students will demonstrate an understanding of linear equations and inequalities by solving one and two step problems using all four operations in real world situations.

6.EE.B.5

•Evaluate an equation for a given a set of values to determine the solution set.

6.EE.B.5

•Evaluate an inequality for a given a set of values to determine the solution set.

6.EE.B.6

•Understand that a variable represents an unknown quantity.

6.EE.B.7

•Model and solve real-world problems with simple equations using positive rational numbers.

6.EE.B.8

•Recognize that inequalities have infinitely many solutions.

6.EE.B.8

•Write an inequality to represent a simple constraint or condition in real-world and mathematical problems.

6.EE.B.8

•Represent solutions to simple greater than or less than inequalities on a number line.

6.EE.C.9

•Explain the difference between the independent and dependent variables.

6.EE.C.9

•Write an algebraic equation, for a given situation, that represents the relationship between two variables.

6.EE.C.9

•Examine the relationship between the dependent and independent variable using a table and graph, and explain how these relate to the equation.

Students will demonstrate an understanding of  ratios, rates, and percents by applying ratio reasoning to solve real world problems.

6.RP.A.1

•Write and use a ratio that describes a relationship between two quantities.

6.RP.A.1

•Explain the relationship that a ratio represents.

6.RP.A.1

•Understand that a ratio can be represented in multiple ways.

6.RP.A.2

•Show an understanding of unit rate through multiple examples.

6.RP.A.2

•Find the unit rate for a given ratio. Unit rates in this grade are limited to non-complex fractions.

6.RP.A.3

•Understand that a rate is a specific type of ratio.

6.RP.A.3

•Solve real-world and mathematical problems involving proportional reasoning using various strategies.

6.RP.A.3.A

•Create tables of equivalent ratios using whole number measurements.

6.RP.A.3.A

•Use proportional reasoning to find missing values in ratio tables and plot the pairs of values as ordered pairs on a coordinate grid.

6.RP.A.3.A

•Use tables to compare ratios.

6.RP.A.3.B

•Solve a variety of real-world and mathematical problems using unit rate.

6.RP.A.3.D

•Use a ratio as a conversion factor when working with measurements of different units.

6.RP.A.3.C

•Write a percent as a rate per one-hundred.

6.RP.A.3.C

•Use proportional reasoning to find the whole when given a part and the percent.

Students will demonstrate an understanding of area and surface area of geometric figures by solving problems using area of polygons and surface areas of prisms and pyramids.

6.G.A.1

•Find the area of polygons by composing or decomposing into rectangles, triangles, or other shapes.

6.G.A.1

•Compose or decompose shapes to solve mathematical and real-life problems involving area.

6.G.A.2

•Relate filling a right rectangular prism, with fractional edge lengths, with unit cubes to the volume formulas for the right rectangular prism.

6.G.A.2

•Use the volume formulas for the right rectangular prism to solve real-world and mathematical problems.

6.G.A.3

•Use the coordinates for the vertices to draw polygons on a coordinate grid.

6.G.A.3

•Find the length of a polygon whose joining points have the same first or same second coordinate.

6.G.A.3

•Plot ordered pairs, draw figures, and find side lengths on the coordinate grid to solve real-world problems.

6.G.A.4

•Understand that nets are patterns that fold to make a model of a 3-D shape.

6.G.A.4

•Understand that surface area is the total area of the surface of a 3-D object.

6.G.A.4

•Use nets to find the surface area of a 3-D Shape.

Students will demonstrate an understanding of analyzing, representing, and interpreting data by calculating measures of central tendency  and variance, and in collecting data to interpret and represent in a variety of graphs.

6.SP.A.1

•Recognize if a question is a statistical or a non-statistical question.

6.SP.A.2

•Understand that a set of data can be described in three ways: by measures of center, by its spread, and by its overall shape.

6.SP.A.3

•Understand that a measure of center summarizes the data set with a single number.

6.SP.A.3

•Understands that a measure of variance summarizes how the data set varies.

6.SP.B.4

•Display numerical data in a dot plot, histogram, and box plot.

6.SP.B.5

•Summarize the basic features a data set in relation to its context.

6.SP.B.5.A

•Provide information on the sample set in a data summary.

6.SP.B.5.B

•Describe what is being investigated, including how it was measured and what units were used.

6.SP.B.5.C

•Find the mean and/or median for a data set.

6.SP.B.5.C

•Find the interquartile range and/or mean absolute deviation for a data set.

6.SP.B.5.C

•Describe the overall shape of a data set, including outliers if any.

6.SP.B.5.D

•Describe how the chosen measures of center and variability relate to the shape of the data and to the context of the problem.