MA19.2.16b
Using Venn diagrams, pictographs, and yes-no “charts analyze data to predict an outcome.”
Using Venn diagrams, pictographs, and yes-no “charts analyze data to predict an outcome.”
MA19.2.16b
MA19.2.17
Measure the length of an object by selecting and using standard units of measurement shown on rulers, yardsticks, meter sticks, or measuring tapes.
Measure the length of an object by selecting and using standard units of measurement shown on rulers, yardsticks, meter sticks, or measuring tapes.
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 (inches, feet, yards, centimeters and meters).
- choose and accurately use appropriate measurement tools and units of measure.
Understanding
Students understand that:
- without overlaps or gaps.
- the length of the object is expressed as the number of unit lengths needed to cover the same distance.
Vocabulary
- Standard units of measurement
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.
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.
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.
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.
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.
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.
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.
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.
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.
MA19.2.24a
Identify nickels and quarters by name and value.
Identify nickels and quarters by name and value.
MA19.2.24b
Find the value of a collection of quarters, dimes, nickels, and pennies.
Find the value of a collection of quarters, dimes, nickels, and pennies.
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¢
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¢
MA19.2.25
Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
Unpacked Content
Knowledge
Students know:
- defining characteristics of basic shapes (triangles, rectangles, squares, circles).
Skills
Students are able to:
- identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
- recognize shapes with specified attributes.
- draw shapes having specified attributes.
- determine shapes based on their attributes.
Understanding
Students understand that:
- shapes may be sorted by many sets of attributes, but their geometric classification is based on certain defining attributes.
Vocabulary
- Attributes
MA19.2.25a
Recognize and draw shapes having specified attributes.
COS Examples
Examples: a given number of angles or a given number of equal faces
Recognize and draw shapes having specified attributes.
COS Examples
Examples: a given number of angles or a given number of equal faces
MA19.2.26
Partition a rectangle into rows and columns of same-size squares, and count to find the total number of squares.
Partition a rectangle into rows and columns of same-size squares, and count to find the total number of squares.
Unpacked Content
Knowledge
Students know:
- how to partition a rectangle into equal-size squares and count those squares.
Skills
Students are able to:
- use repeated addition to tell how many total squares in an equally partitioned rectangle.
Understanding
Students understand that:
- repeated addition connects to the conceptual understanding of multiplication.
Vocabulary
- Partition
MA19.2.27
Partition circles and rectangles into two, three, or four equal shares. Describe the shares using such terms as halves, thirds, half of, or a third of, and describe the whole as two halves, three thirds, or four fourths.
Partition circles and rectangles into two, three, or four equal shares. Describe the shares using such terms as halves, thirds, half of, or a third of, and describe the whole as two halves, three thirds, or four fourths.
Unpacked Content
Knowledge
Students know:
- strategies for partitioning shapes into two, three, or four equal shares and reason about these shares.
Skills
Students are able to:
- decompose circles and rectangles into halves, thirds, and fourths.
- communicate the size of pieces using the appropriate fraction terminology.
- recognize that equal shares may be different shapes within the same whole.
Understanding
Students understand that:
- shapes can be equally partitioned into halves, thirds, and fourths.
Vocabulary
- Partition
MA19.2.27a
Explain that equal shares of identical wholes need not have the same shape.
Explain that equal shares of identical wholes need not have the same shape.
MA19.3.1
Illustrate the product of two whole numbers as equal groups by identifying the number of groups and the number in each group and represent as a written expression.
Illustrate the product of two whole numbers as equal groups by identifying the number of groups and the number in each group and represent as a written expression.
Unpacked Content
Knowledge
Students know:
- that in multiplication, one factor represents the number of groups and the other factor represents the number of items in each group, and the product represents the total number of items in all of the groups.
Skills
Students are able to:
- Use a model or drawing to illustrate the product of two whole numbers.
- Write an expression or equation to represent the product of two whole numbers identifying the number of equal groups and the group size.
Understanding
Students understand that:
- a multiplication problem can be interpreted as x groups of y objects.
Vocabulary
- Equal groups
- Equation
- Expression
- Factor
- Product
- Array
- Row
- Column
- Skip count
MA19.3.2
Illustrate and interpret the quotient of two whole numbers as the number of objects in each group or the number of groups when the whole is partitioned into equal shares.
Illustrate and interpret the quotient of two whole numbers as the number of objects in each group or the number of groups when the whole is partitioned into equal shares.
Unpacked Content
Knowledge
Students know:
- that division is related to multiplication in terms of finding a missing factor. The missing factor being either the number of groups or the number of items in each group.
Skills
Students are able to:
- Interpret quantities in a division situation as the number of objects in each groupor the number of equal groups.
- Use a model or drawing to illustrate a quotient.
- Write word problems for division context involving equal groups and fair shares.
Understanding
Students understand that:
- a division expression represents either the number of objects in each group when the total number is partitioned evenly into a given number of groups or the number of groups when the total number is partitioned into groups that each contain a given number.
Vocabulary
- Partitive division
- Measurement division
- Missing factor
- Factor
- Quotient
- Partition
- Product
- Divisor
- Dividend
- Equal share
MA19.3.3
Solve word situations using multiplication and division within 100 involving equal groups, arrays, and measurement quantities; represent the situation using models, drawings, and equations with a symbol for the unknown number.
Solve word situations using multiplication and division within 100 involving equal groups, arrays, and measurement quantities; represent the situation using models, drawings, and equations with a symbol for the unknown number.
Unpacked Content
Knowledge
Students know:
- Multiplication situations can be related to division contexts by identifying the total number of groups and the number of items in a group.
- Strategies to solve problems involving multiplication and division.
Skills
Students are able to:
- Use models, drawings, and equations to represent a multiplication or division situation.
- Use symbols to represent unknownquantities in equations.
- Solve word situations with multiplication and division within 100 involving equal groups, arrays, and measurement quantities.
Understanding
Students understand that:
- a word problem with an unknown product is a multiplication problem, and a word problem with an unknown number of groups or an unknown group size can be thought of as a division problem or a multiplication problem with an unknown factor.
Vocabulary
- Equal groups
- Arrays
- Measurement division
- Factor
- Product
- Quotient
- Partitive division
- Represent
- Unknown
MA19.3.4
Determine the unknown whole number in a multiplication or division equation relating three whole numbers.
Determine the unknown whole number in a multiplication or division equation relating three whole numbers.
Unpacked Content
Knowledge
Students know:
- how to use the meaning of multiplication and division and the relationship between the two operations to determine an unknown number in a given equation.
Skills
Students are able to:
- Relate three whole numbers to determine the unknown factor in a multiplication equation.
- Relate three whole numbers to determine the unknown whole number in a division equation.
Understanding
Students understand that:
- the unknown number in a multiplication or division equation is the number that makes the equation true.
Vocabulary
- Unknown
- Multiplication
- Division
- Divisor
- Dividend
- Equation
- Product
MA19.3.5
Develop and apply properties of operations as strategies to multiply and divide.
Develop and apply properties of operations as strategies to multiply and divide.
Unpacked Content
Knowledge
Students know:
- When any factor, x, is multiplied by a factor of 1, the product is the value of x.
- If one factor is zero, then there are zero groups or zero items in a group and the product is zero.
- The commutative property of multiplication shows a x b = c and b x a = c.
- The associative property of multiplication shows that when multiplying three or more numbers, the product is always the same regardless of the grouping.
- The distributive property will help in finding products of more difficult multiplication facts.
Skills
Students are able to:
- Develop properties as strategies for multiplication and division.
- Apply properties of operations as strategies to multiply and divide.
Understanding
Students understand that:
- applying properties of operations can help develop strategies to find solutions to multiplication and division problems.
Vocabulary
- Product
- Sum
- Property of operations
- Multiplication expression
- Decompose
- Array
- Area model
MA19.3.6
Use the relationship between multiplication and division to represent division as an equation with an unknown factor.
Use the relationship between multiplication and division to represent division as an equation with an unknown factor.
Unpacked Content
Knowledge
Students know:
- Multiplication and division are related operations.
- Using known multiplication facts and the relationship between multiplication and division, will help build fluency with division facts.
Skills
Students are able to:
- Use the relationship between multiplication and division to find quotients.
- Write a multiplication equation with a missing factor to represent a division situation.
- Use symbols to represent an unknown quantity in equations.
Understanding
Students understand that:
- Multiplication and division are related operations.
- The dividend in a division equation is the same as the product in a related multiplication equation.
Vocabulary
- Product
- Quotient
- Equation
- Unknown factor
- Dividend
- Divisor
MA19.3.7
Use strategies based on properties and patterns of multiplication to demonstrate fluency with multiplication and division within 100.
Use strategies based on properties and patterns of multiplication to demonstrate fluency with multiplication and division within 100.
Unpacked Content
Knowledge
Students know:
- Strategies for finding products and quotients.
- How to use multiplication facts in terms of a missing factor to learn division facts.
Skills
Students are able to:
- Use strategies based on properties of operations and patterns of multiplication to find products and quotients.
- Use efficient multiplication and division strategies based on the numbers in the problems. -Use multiplication facts in terms of a missing factor to learn division facts.
Understanding
Students understand that:
- they can use the meaning of the numbers in multiplication and division situations to determine strategies to become fluent with multiplication and division facts.
Vocabulary
- Fluently
- Properties of operations
- Product
- Digit
- Divisor
- Dividend
- Inverse operation
- Derived fact
MA19.3.7a
Fluently determine all products obtained by multiplying two one-digit numbers.
Fluently determine all products obtained by multiplying two one-digit numbers.
MA19.3.7b
State automatically all products of two one-digit numbers by the end of third grade.
State automatically all products of two one-digit numbers by the end of third grade.
MA19.3.8
Determine and justify solutions for two-step word problems using the four operations and write an equation with a letter standing for the unknown quantity. Determine reasonableness of answers using number sense, context, mental computation, and estimation strategies including rounding.
Determine and justify solutions for two-step word problems using the four operations and write an equation with a letter standing for the unknown quantity. Determine reasonableness of answers using number sense, context, mental computation, and estimation strategies including rounding.
Unpacked Content
Knowledge
Students know:
- Characteristics of addition, subtraction, multiplication, and division.
- Strategies for addition, subtraction, multiplication, and division.
- Strategies for mental computation and estimating sums, differences, products, and quotients.
Skills
Students are able to:
- Use a variety of strategies to solve two-step word problems involving all four operations.
- Write an equation to represent the problem context, and use a symbol for the unknown quantity.
- Justify strategy and solutions using mathematical vocabulary.
- Determine and justify reasonableness of solutions using mental computation strategies and estimation strategies.
Understanding
Students understand that:
- Mathematical problems can be solved using a variety of strategies, models, and representations.
- Contextual situations represented by multiplication and division.
- Reasonableness of solutions can be evaluated by using estimation strategies.
Vocabulary
- Unknown quantity
- Mental computation
- Estimation
- Variable
- Reasonableness
- Rounding
- Expression
- Equation
MA19.3.9
Recognize and explain arithmetic patterns using properties of operations.
Recognize and explain arithmetic patterns using properties of operations.
Unpacked Content
Knowledge
Students know:
- that mathematical ideas and concepts build on patterns and recognize and identify those patterns to make sense of math, and the ability to make generalizations is the foundation for algebraic reasoning.
Skills
Students are able to:
- Identify arithmetic patterns in number sequences, in the addition table, or multiplication table.
- Use logical reasoning and properties of numbers and operations to explain characteristics of arithmetic patterns.
Understanding
Students understand that:
- Mathematical concepts build on patterns.
- When consecutive terms always differ by the same amount, an arithmetic pattern is formed.
- Visual patterns can be found in the multiplication table.
Vocabulary
- Arithmetic pattern
- Starting value
- Addition table
- Multiplication table
- Consecutive
- Term
- Decompose
MA19.3.10
Identify the nearest 10 or 100 when rounding whole numbers, using place value understanding.
Identify the nearest 10 or 100 when rounding whole numbers, using place value understanding.
Unpacked Content
Knowledge
Students know:
- Values of the digits in the ones, tens, and hundreds places.
- How to determine what is halfway between two multiples of 10 or 100.
- Strategies for rounding to the nearest 10 or 100.
- Use place value vocabulary and logical reasoning to justify solutions when rounding.
Skills
Students are able to:
- Round whole numbers to the nearest 10 or 100.
- Identify a possible value for a number which will result in a given number rounded to the nearest 10 or 100.
Example: What value will result in 270 when rounded to the nearest 10? Identify the possible values.
Understanding
Students understand that:
- rounding is determining which ten or hundred a number is closer to.
Vocabulary
- Place value
- Round
- Nearest 10
- Nearest 100
- Benchmark number
- Midpoint
MA19.3.11
Use various strategies to add and subtract fluently within 1000.
Use various strategies to add and subtract fluently within 1000.
Unpacked Content
Knowledge
Students know:
- The relationship between addition and subtraction operations.
- How conceptual models support and give understanding to procedures for addition and subtraction.
Skills
Students are able to:
- Use a variety of strategies to solve addition and subtraction problems within 1000.
Understanding
Students understand that:
- Strategies for addition and subtraction will vary depending on the problem.
- Strategies can include place value, properties of operations, and the relationship between addition and subtraction.
Vocabulary
- Fluently
- Sum
- Difference
- Place value
- Strategy
MA19.3.12
Use concrete materials and pictorial models based on place value and properties of operations to find the product of a one-digit whole number by a multiple of ten (from 10 to 90).
Use concrete materials and pictorial models based on place value and properties of operations to find the product of a one-digit whole number by a multiple of ten (from 10 to 90).
Unpacked Content
Knowledge
Students know:
- a variety of strategies or tools to find products (skip counting, properties of operations, concrete materials, number lines, arrays, etc.).
Skills
Students are able to:
- Find the product of a 1-digit factor and multiple of 10 (from 10 to 90).
- Use concrete materials and pictorial models to find the product.
- Use properties of operations to find the product.
- Justify products.
Understanding
Students understand that:
- A one-digit number multiplied by ten gives a multiple of ten. Ex: 6 x 10 = 60 is the same as that number of ones (60) or that number of tens (6 tens).
- Adding a zero to the product of two non-zero whole numbers does not demonstrate the relationship between the product and its place value.
Vocabulary
- Multiply
- One-digit
- Multiple of ten
- Place value
- Properties of operations
- Product
MA19.3.13
Demonstrate that a unit fraction represents one part of an area model or length model of a whole that has been equally partitioned; explain that a numerator greater than one indicates the number of unit pieces represented by the fraction.
Demonstrate that a unit fraction represents one part of an area model or length model of a whole that has been equally partitioned; explain that a numerator greater than one indicates the number of unit pieces represented by the fraction.
Unpacked Content
Knowledge
Students know:
- Fractional parts of a whole must be of equal size but not necessarily equal shape.
- Denominators represent the number of equal size parts that make a whole.
- The more equal pieces in the whole, the smaller the size of the pieces.
- The numerator represents the number of equal pieces in the whole that are being counted or considered.
Skills
Students are able to:
- Use an area model and length model to show a unit fraction as one part of an equally partitioned whole.
- Explain that given a fraction with a numerator greater than one, the numerator indicates the number of unit fraction pieces represented by the fraction.
Example: 3/4 is the same as 3 units of 1/4 size, or three 1/4 pieces, 3 copies of 1/4, or 3 iterations of 1/4. - Identify and describe the fractional name given a visual fraction model.
- Identify and demonstrate fractional parts of a whole that are the same size but not the same shape using concrete materials.
Understanding
Students understand that:
- Given the same size whole, the larger the denominator, indicating the number of equal parts in the whole, the smaller the size of the pieces because there are more pieces in the whole.
- Fractions are numbers that represent a quantity less than, equal to, or greater than 1.
- Fractions represent equal partitions of a whole.
Vocabulary
- Unit fraction
- Area model
- Interval
- Length (Linear) model
- Partition
- Numerator
- Denominator
- Part
- Point
- Whole
MA19.3.14
Interpret a fraction as a number on the number line; locate or represent fractions on a number line diagram.
Interpret a fraction as a number on the number line; locate or represent fractions on a number line diagram.
Unpacked Content
Knowledge
Students know:
- How to use fraction strips as a model to connect to finding fractional parts on a number line.
- Fractions are numbers that can be represented on a number line.
- Fractions can be placed on the number line by marking off equal parts between two whole numbers.
- Fractions equal to 1 have the same numerator and same denominator.
- Fractions greater than 1 have a numerator that will be greater than the denominator.
Skills
Students are able to:
- Represent fractions on a number line.
- Locate fractions on a number line.
- Use a number line and partition an interval from 0 to 1 into equal parts as specified by the denominator of a fraction.
- Represent a non unit fraction on a number line by marking off unit fraction lengths as specified by the numerator from zero.
- Extend the number line to include fractions greater than one as a continuation of counting unit fractions.
Understanding
Students understand that:
- A number line is a length model.
- Fractions are numbers that represent a quantity less than, equal to, or greater than 1 and can be placed on a number line.
- A number line can be partitioned to represent equal parts of a whole.
Vocabulary
- Fraction
- Number line
- Number line diagram
- Unit fraction
- Interval
- Partition
- Point
- Denominator
- Numerator
MA19.3.14a
Represent a unit fraction $(\frac{1}{b})$ on a number line by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts as specified by the denominator.
Represent a unit fraction $(\frac{1}{b})$ on a number line by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts as specified by the denominator.
