Standards - Mathematics

MA19.K.16

Identify and describe measurable attributes (length, weight, height) of a single object using vocabulary such as long/short, heavy/light, or tall/short.

Unpacked Content

Knowledge

Students know:
  • how to describe similarities and differences in objects.

Skills

Students are able to:
  • Describe measurable attributes of objects using informal language.

Understanding

Students understand that:
  • objects can be described by using measurable attributes.

Vocabulary

  • Attribute

MA19.K.17

Directly compare two objects with a measurable attribute in common to see which object has more of“ or “less of” the attribute and describe the difference.“

COS Examples

Example: Directly compare the heights of two children and describe one child as taller“ or “shorter.”

Unpacked Content

Knowledge

Students know:
  • how to describe similarities and differences in objects.

Skills

Students are able to:
  • Directly compare two objects and explain which object has more of or less of the attribute.

Understanding

Students understand that:
  • objects and geometric figures have measurable attributes that allow them to be compared.

Vocabulary

  • Attribute

MA19.1.17

Order three objects by length; compare the lengths of two objects indirectly by using a third object.

Unpacked Content

Knowledge

Students know:
  • how to correctly align the objects.

Skills

Students are able to:
  • Use direct and indirect comparison to order objects by length.

Understanding

Students understand that:
  • measurable attributes of objects can be used to describe and compare the objects.

Vocabulary

  • Measurable attributes

MA19.1.18

Determine the length of an object using non-standard units with no gaps or overlaps, expressing the length of the object with a whole number.

Unpacked Content

Knowledge

Students know:
  • how to solve for addition by using strategies and understanding the relationship between addition and subtraction.

Skills

Students are able to:
  • efficiently apply strategies for solving multiple addend problems.
  • Use symbols to represent unknown quantities in equations.
  • Accurately compute sums.

Understanding

Students understand that:
  • more than two quantities can be combined in a problem.

Vocabulary

  • Concrete objects

MA19.1.19

Tell and write time to the hours and half hours using analog and digital clocks.

Unpacked Content

Knowledge

Students know:
  • addition and subtraction strategies.
  • how to form an equation.
  • li>how the commutative property works.

Skills

Students are able to:
  • Strategically apply properties of addition in order to find sums.

Understanding

Students understand that:
  • the order in which addends are joined doesn't change the sum.
  • numbers may be composed or decomposed in a variety of ways.

Vocabulary

  • Commutative property of addition
  • Associative property of addition
  • Identity property of zero for addition

MA19.1.20

Identify pennies and dimes by name and value.

Unpacked Content

Knowledge

Students know:
  • how to count on or count back from a given number within 20.

Skills

Students are able to:
  • Explain counting strategies for addition and subtraction.

Understanding

Students understand that:
  • counting patterns can be used to find solutions in addition and subtraction situations.
  • A variety of models and tools can be used to communicate justifications for mathematical ideas and solutions.

Vocabulary

  • Number paths

MA19.2.18

Measure objects with two different units, and describe how the two measurements relate to each other and the size of the unit chosen.

Unpacked Content

Knowledge

Students know:
  • standard units of length measure (inches, feet, yards, centimeters and meters) and the related tools.

Skills

Students are able to:
  • measure length in standard units.
  • choose and accurately use appropriate measurement tools and units of measure.

Understanding

Students understand that:
  • the smaller the unit of measure the more of that unit it takes to measure a length.

Vocabulary

  • Units

MA19.2.19

Estimate lengths using the following standard units of measurement: inches, feet, centimeters, and meters.

Unpacked Content

Knowledge

Students know:
  • personal benchmarks (e.g. fingernail for centimeter, door knob to floor for meter) for the length of standard units.

Skills

Students are able to:
  • use strategies for using personal benchmarks for estimating lengths in standard units.
  • explain and justify length estimates.

Understanding

Students understand that:
  • estimating before measuring helps them develop a benchmark for the length of an object.

Vocabulary

  • Estimate
  • Standards units of measurement

MA19.2.20

Measure to determine how much longer one object is than another, expressing the length difference of the two objects using standard units of length.

Unpacked Content

Knowledge

Students know:
  • strategies for comparing the length of objects.
  • standard units of length.
  • related tools.

Skills

Students are able to:
  • choose and accurately use appropriate measurement tools and units of measure.
  • explain and justify procedures for determining the difference between the lengths of two objects.

Understanding

Students understand that:
  • comparisons of objects are determined using attributes that are measurable.

Vocabulary

  • Standard units of length

MA19.2.21

Use addition and subtraction within 100 to solve word problems involving same units of length, representing the problem with drawings (such as drawings of rulers) and/or equations with a symbol for the unknown number.

Unpacked Content

Knowledge

Students know:
  • Students know strategies for solving addition and subtraction word problems involving length.

Skills

Students are able to:
  • represent quantities and operations physically, pictorially, or symbolically.
  • strategically use a variety of representations to solve problems with all addition and subtraction contexts.
  • use symbols to represent unknown quantities in equations.

Understanding

Students understand that:
  • that they can apply the concept of length to solve addition and subtraction word problems for numbers within 100.

Vocabulary

  • Units of length
  • Drawings
  • Equations
  • Symbol

MA19.2.22

Create a number line diagram using whole numbers and use it to represent whole-number sums and differences within 100.

Unpacked Content

Knowledge

Students know:
  • how to create a number line.
  • how to count forwards and backwards on a number line.
  • how to use addition and subtraction to solve equations using the number line.

Skills

Students are able to:
  • represent quantities and addition/subtraction on number line diagrams.
  • create and use number line models to represent, solve, and justify solutions to addition and subtraction problems within 100.

Understanding

Students understand that:
  • quantities can be represented as distances from zero on a number line.
  • a variety of models, including number lines, can be used to represent and solve addition and subtraction problems.

Vocabulary

  • Number line
  • Whole numbers
  • Sum
  • Difference

MA19.2.23

Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

Unpacked Content

Knowledge

Students know:
  • how tell and write time to the nearest 5 minutes using analog and digital clocks.
  • how to explain the difference between a.m. and p.m.

Skills

Students are able to:
  • accurately read and write time to the nearest five minutes from analog and digital clocks.

Understanding

Students understand that:
  • analog and digital clocks represent the time at any particular moment.
  • clocks show the passage of time with the movement of the hands or the changing of the digits.
  • time is an attribute that can be measured.

Vocabulary

  • Analog
  • Digital

MA19.2.23a

Express an understanding of common terms such as, but not limited to, quarter past, half past, and quarter to.

MA19.2.24

Solve problems with money.

Unpacked Content

Knowledge

Students know:
  • the value of pennies, nickels, dimes, and quarters.
  • ccounting sequence and skip counting by 1s, 5s, and 10s.
  • strategies for solving word problems.

Skills

Students are able to:
  • use problem solving strategies to solve word problems involving a variety of coins.

Understanding

Students understand that:
  • a variety of strategies can be used to model and solve problems involving money.
  • mathematics procedures can be used to answer questions involving daily life situations.

MA19.2.24c

Solve word problems by adding and subtracting within one dollar, using the $ and ¢ symbols appropriately (not including decimal notation).

COS Examples

Example: 24¢ + 26¢ = 50¢

MA19.3.18

Tell and write time to the nearest minute; measure time intervals in minutes (within 90 minutes.)

Unpacked Content

Knowledge

Students know:
  • Conventions for time notation.
  • Time sequence patterns.
  • Strategies to determine elapsed time.

Skills

Students are able to:
  • Accurately read and write time to the nearest minute from analog and digital clocks.
  • Measure time intervals in minutes.
  • Illustrate elapsed time using a number line.
  • Solve problems involving elapsed time in minutes (with 90 minutes) or hours.

Understanding

Students understand that:
  • An analog clock is a whole partitioned into 60 parts and each part is one minute.
  • A number line can be partitioned to show time intervals in minutes.
  • A number line can be used to solve word problems that involve time intervals.

Vocabulary

  • Minute
  • Time interval
  • Number line diagram
  • Analog
  • Digital
  • Elapsed time
  • Half-hour
  • Quarter-hour

MA19.3.18a

Solve real-world problems involving addition and subtraction of time intervals in minutes by representing the problem on a number line diagram.

MA19.3.19

Estimate and measure liquid volumes and masses of objects using liters (l), grams (g), and kilograms (kg).

Unpacked Content

Knowledge

Students know:
  • Personal benchmarks for metric standard units of measure, mass (gram & kilogram) and liquid volume (liter), and the use of related tools (such as balance, spring scales, graduated cylinders, beakers, measuring cups) for measurement to those units.
  • Characteristics of addition, subtraction, multiplication, and division contexts that involve measurements.
  • How to represent quantities and operations physically, pictorially, or symbolically.
  • Strategies to solve one-step word problems that involve measurement.

Skills

Students are able to:
  • Measure liquid volume and mass in metric standard units.
  • Choose appropriate measurement tools and units of measure.
  • Represent quantities and operations physically, pictorially, or symbolically,
  • Use a variety of strategies to solve one-step word problems that involve measurement.

Understanding

Students understand that:
  • Capacity indicates the measure of the volume (dry or liquid) in a container.
  • Mass indicates the amount of matter in an object and can be represented with different sized units.

Vocabulary

  • Liquid volume
  • Mass
  • Liter
  • Gram
  • Kilogram
  • Metric unit
  • Capacity
  • Matter

MA19.3.19a

Use the four operations to solve one-step word problems involving masses or volumes given in the same metric units.

MA19.3.20

Find the area of a rectangle with whole number side lengths by tiling without gaps or overlays and counting unit squares.

Unpacked Content

Knowledge

Students know:
  • area is a measurable attribute of two-dimensional figures.

Skills

Students are able to:
  • Find the area of a rectangle by tiling it without gaps or overlaps.
  • Measure the area of a rectangle by counting the number of unit squares needed to cover the shape.

Understanding

Students understand that:
  • Area is the number of unit squares needed to cover a surface.
  • Multiple unit squares can be combined to measure the area of rectangles so long as the unit squares completely cover the figure without overlapping each other or extending beyond the edge of the figure.

Vocabulary

  • Area
  • Rectangle
  • Tiling
  • Gap
  • Overlay
  • Unit square

MA19.3.21

Count unit squares (square cm, square m, square in, square ft, and improvised or non-standard units) to determine area.

Unpacked Content

Knowledge

Students know:
  • area is a measurable attribute of two-dimensional figures.

Skills

Students are able to:
  • Determine area of a rectangle by counting unit squares.

Understanding

Students understand that:
  • A unit square is a square with a side length of 1 unit, and that such a square represents a unit of measurement.
  • The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure.

Vocabulary

  • Unit square
  • Length
  • Plane figure
  • Square cm
  • Square m
  • Square in
  • Square ft
  • Improvised
  • Non-standard unit

MA19.3.22

Relate area to the operations of multiplication using real-world problems, concrete materials, mathematical reasoning, and the distributive property.

Unpacked Content

Knowledge

Students know:
  • Area is a measurable attribute of two-dimensional figures.
  • The area measurement of rectangular regions has a multiplicative relationship of the number of square units in a row and the number of rows.

Skills

Students are able to:
  • Decompose rectilinear figures as non-overlapping rectangles using concrete materials.
  • Find the area of two rectangles, and create a rectilinear figure by joining the two rectangles (without overlapping), and determine the area of the created rectilinear figure as the sum of the two rectangles.

Understanding

Students understand that:
  • rectilinear shapes can be decomposed into non overlapping rectangles, and the sum of the areas of the nonverlapping rectangles is equivalent to the area of the original rectilinear shape.

Vocabulary

  • Compose
  • Decompose
  • Area
  • Additive
  • Rectilinear figure
  • Equivalent
  • Non-overlapping
  • Overlapping

MA19.3.23

Decompose rectilinear figures into smaller rectangles to find the area, using concrete materials.

Unpacked Content

Knowledge

Students know:
  • That a straight angle is 180 degrees
  • That a triangle has three interior angles whose sum is 180 degrees.
  • The definition of transversal.
  • How to write and solve two-step equations.

Skills

Students are able to:
  • Make conjectures about the relationships and measurements of the angles created when two parallel lines are cut by a transversal.
  • Informally prove that the sum of any triangle's interior angles will have the same measure as a straight angle.

Understanding

Students understand that:
  • Missing angle measurements can be found when given just one angle measurement along a transversal cutting through parallel lines.
  • Every exterior angle is supplementary to its adjacent interior angle.
  • Parallel lines cut by a transversal will yield specific angle relationships that are connected to the concepts of rigid transformations (i.e. vertical angles are reflections over a point. corresponding angles can be viewed as translations).
  • The sum of the interior angles of a triangle is 180 degrees.

Vocabulary

  • Transversal
  • Corresponding Angles
  • Vertical Angles
  • Alternate Interior Angles
  • Alternate Interior Angles
  • Supplementary
  • Adjacent

MA19.3.24

Construct rectangles with the same perimeter and different areas or the same area and different perimeters.

Unpacked Content

Knowledge

Students know:
  • Perimeter is a measurable attribute of rectangles.
  • Area is a measurable attribute of rectangles.

Skills

Students are able to:
  • Construct rectangles with a given perimeter.
  • Construct rectangles with a given area.
  • Construct rectangles with the same perimeters but differing areas.
  • Construct rectangles with the same areas but differing perimeters.

Understanding

Students understand that:
  • Perimeter and area are measurable attributes of rectangles.
  • Perimeter is the distance around a figure found by adding side lengths.
  • The area of a plane figure is measured by the number of square units that cover the interior space of the rectangle.

Vocabulary

  • Perimeter
  • Area
  • Side length
  • Side measure

MA19.4.21a

Within one system of units, express measurements of a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.

MA19.4.22

Use the four operations to solve measurement word problems with distance, intervals of time, liquid volume, mass of objects, and money.

Unpacked Content

Knowledge

Students know:
  • Relative sizes of units within one system of measurement.
  • Strategies to solve word problems involving the four operations.
  • Measurement units in the same system are multiplicatively related.

Skills

Students are able to:
  • Solve measurement word problems
  • Involving distance, intervals of time, liquid volume, mass, and money.
  • Involving measurement conversion of larger units to a smaller unit.
  • Involving simple fractions or decimals.
  • Using diagrams to represent measurement quantities and solutions.

Note: Quantities and operations are limited to grade 4 standard expectations.

Understanding

Students understand that:
  • Relationships among units within a system of measurement are multiplicative comparisons.
  • The size of the unit of measurement and the number of units are inversely related.
  • Addition and subtraction of measurements require measurements in the same unit and that the common unit is maintained in the answer.

Vocabulary

  • Operations
  • Distance
  • Intervals of time
  • Liquid volume
  • Mass
  • Number line diagram
  • Measurement scale

MA19.4.22b

Solve measurement problems that require expressing measurements given in a larger unit in terms of a smaller unit.

MA19.4.22c

Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

MA19.4.23

Apply area and perimeter formulas for rectangles in real-world and mathematical situations.

Unpacked Content

Knowledge

Students know:
  • The relationship of area to the operations of multiplication and addition.
  • The relationship of three whole numbers in a multiplication or division equation.
  • How to distinguish between linear and area measures.

Skills

Students are able to:
  • Apply area formula for rectangles given real-world situations.
  • Apply perimeter formula for rectangles given real-world situations.

Understanding

Students understand that:
Given real-world situations involving rectangles,
  • Area formula represents the region inside a rectangle and is used to calculate area, or calculate one missing dimension if one side length is known.
  • Perimeter formula represents the distance around the rectangle and is used to calculate the perimeter, or calculate one missing dimension if one side length is known.

Vocabulary

  • Area
  • Perimeter
  • Formula
  • Equation
  • Dimension
  • Length
  • Width

MA19.4.24

Identify an angle as a geometric shape formed wherever two rays share a common endpoint.

Unpacked Content

Knowledge

Students know:
  • Angles are geometric shapes formed when two rays share a common endpoint.
  • How to draw points, lines, line segments, and rays

Skills

Students are able to:
  • Identify an angle as two rays with a common endpoint.

Understanding

Students understand that:
  • angles are geometric shapes made of two rays that are infinite in length and are measured with reference to a circle with its center at the common endpoint of the rays.

Vocabulary

  • Angle
  • Ray
  • Endpoint
  • Geometric shape
  • Vertex
  • Line
  • Point
  • Line segment

MA19.4.25

Use a protractor to measure angles in whole-number degrees and sketch angles of specified measure.

Unpacked Content

Knowledge

Students know:
  • Measurable attributes of geometric shapes, specifically angle size.
  • Units of measurement, specifically one-degree angle (degrees).
  • An angle is measured by the number or iterations of one-degree angles that exactly cover the rotation of the angle.

Skills

Students are able to:
  • Sketch angles given a specified measure.
  • Use appropriate tools to find angle measure.

Understanding

Students understand that:
  • the rotation of an angle is measured by the number of one-degree angles that exactly cover the rotation of the angle.

Vocabulary

  • Protractor
  • Angle
  • Whole number
  • Degree
  • Center
  • Circle
  • Intersect
  • Arc
  • Point
  • Ray
  • One-degree angle
  • Vertex

MA19.4.26

Decompose an angle into non-overlapping parts to demonstrate that the angle measure of the whole is the sum of the angle measures of the parts.

Unpacked Content

Knowledge

Students know:
  • Angles are measured in degrees from 0 to 360.
  • Protractor orientation does not affect an angle measurement.

Skills

Students are able to:
  • Decompose an angle into non-overlapping parts and demonstrate that the sum of the angle measure parts is the same as the measure of the whole angle.
  • Use addition and subtraction to find unknown angles on a diagram in real-world or mathematical problems.

Understanding

Students understand that:
  • The rotation of an angle is measured by the number of one-degree angles that exactly cover the rotation of the angle.
  • Angle measurement is additive of the non-overlapping parts of a decomposed angle.

Vocabulary

  • Decompose
  • Angle
  • Non-overlapping
  • Angle measure
  • Sum
  • Diagram
  • Adjacent
  • Compose
  • Degrees
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