MA19.1.1c
Put together/take apart with addend unknown to solve word problems within 20.
Put together/take apart with addend unknown to solve word problems within 20.
MA19.1.1c
MA19.1.1d
Compare quantities, with difference unknown, bigger unknown, and smaller unknown while solving word problems within 20.
Compare quantities, with difference unknown, bigger unknown, and smaller unknown while solving word problems within 20.
MA19.1.2
Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 by using concrete objects, drawings, or equations with a symbol for the unknown number to represent the problem.
Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 by using concrete objects, drawings, or equations with a symbol for the unknown number to represent the problem.
Unpacked Content
Knowledge
Students know:
- The relationship between addition and subtraction.
- how to explain subtraction as an unknown addend.
Skills
Students are able to:
- use symbols such as blanks, boxes, or letters to represent unknown quantities in equations.
- Communicate the connections between subtraction and addition.
- Use the inverse relationship between addition and subtraction to find differences.
- Choose and apply addition and subtraction strategies to accurately determine sums and differences within 20.
Understanding
Students understand that:
- addition and subtraction have an inverse relationship that can be used to solve problems.
Vocabulary
- Addend
MA19.1.3
Apply properties of operations as strategies to add and subtract.
COS Examples
Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known (commutative property of addition).
To add 2 + 6 + 4, the second and third numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12 (associative property of addition).
When adding 0 to a number, the result is the same number (identity property of zero for addition).
Apply properties of operations as strategies to add and subtract.
COS Examples
Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known (commutative property of addition).
To add 2 + 6 + 4, the second and third numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12 (associative property of addition).
When adding 0 to a number, the result is the same number (identity property of zero for addition).
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
MA19.1.4
Explain subtraction as an unknown-addend problem.
COS Examples
Example: subtracting 10 - 8 by finding the number that makes 10 when added to 8
Explain subtraction as an unknown-addend problem.
COS Examples
Example: subtracting 10 - 8 by finding the number that makes 10 when added to 8
Unpacked Content
Knowledge
Students know:
- The relationship between addition and subtraction.
- how to explain subtraction as an unknown addend.
Skills
Students are able to:
- use symbols such as blanks, boxes, or letters to represent unknown quantities in equations.
- Communicate the connections between subtraction and addition.
- Use the inverse relationship between addition and subtraction to find differences.
- Choose and apply addition and subtraction strategies to accurately determine sums and differences within 20.
Understanding
Students understand that:
- addition and subtraction have an inverse relationship that can be used to solve problems.
Vocabulary
- Addend
MA19.1.5
Relate counting to addition and subtraction.
COS Examples
Example: counting on 2 to add 2
Relate counting to addition and subtraction.
COS Examples
Example: counting on 2 to add 2
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
MA19.1.6
Add and subtract within 20.
Add and subtract within 20.
Unpacked Content
Knowledge
Students know:
- Strategies for finding sums and differences within 20.
Skills
Students are able to:
- Use addition and subtraction strategies.
Understanding
Students understand that:
- Addition and subtraction strategies can be used to compute sums and differences, and how.
Vocabulary
- Fluency
MA19.1.6a
Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by counting on.
Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by counting on.
MA19.1.6b
Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by making ten.
Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by making ten.
MA19.1.6c
Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by decomposing a number leading to a ten.
COS Examples
Example: 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9
Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by decomposing a number leading to a ten.
COS Examples
Example: 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9
MA19.1.6d
Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by using the relationship between addition and subtraction.
COS Examples
Example: Knowing that 8 + 4 = 12, one knows 12 - 8 = 4.
Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by using the relationship between addition and subtraction.
COS Examples
Example: Knowing that 8 + 4 = 12, one knows 12 - 8 = 4.
MA19.1.6e
Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by creating equivalent but easier or known sums.
COS Examples
Example: adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13
Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by creating equivalent but easier or known sums.
COS Examples
Example: adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13
MA19.1.7
Explain that the equal sign means the same as.“ Determine whether equations involving addition and subtraction are true or false.“
COS Examples
Example: determining which of the following equations are true and which are false: 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2
Explain that the equal sign means the same as.“ Determine whether equations involving addition and subtraction are true or false.“
COS Examples
Example: determining which of the following equations are true and which are false: 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2
Unpacked Content
Knowledge
Students know:
- strategies for finding the value of simple addition and subtraction equations.
- Strategies for comparing quantities between 0 and 20.
- Strategies to show equality or inequality.
Skills
Students are able to:
- efficiently apply strategies for determining the value of simple addition and subtraction equations.
- Justify and explain their thinking.
Understanding
Students understand that:
- the equal sign represents a relationship of balance between numerical expressions rather than performing an operation.
Vocabulary
- Equation
- Meaning of the equal sign
MA19.1.8
Solve for the unknown whole number in various positions in an addition or subtraction equation, relating three whole numbers that would make it true.
COS Examples
Example: determining the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = ? - 3, and 6 + 6 = ?
Solve for the unknown whole number in various positions in an addition or subtraction equation, relating three whole numbers that would make it true.
COS Examples
Example: determining the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = ? - 3, and 6 + 6 = ?
Unpacked Content
Knowledge
Students know:
- Strategies for solving simple addition or subtraction equations with one unknown.
Skills
Students are able to:
- solve simple addition and subtraction equations.
- Justify and explain their thinking.
Understanding
Students understand that:
- equalities contain expressions that name the same amount on each side of the equal sign, even with quantities unknown.
Vocabulary
MA19.1.9
Reproduce, extend, and create patterns and sequences of numbers using a variety of materials.
Reproduce, extend, and create patterns and sequences of numbers using a variety of materials.
Unpacked Content
Knowledge
Students know:
- how to duplicate simple patterns.
- how to extend simple patterns.
Skills
Students are able to:
- reproduce given patterns.
- Extend given patterns.
- Create patterns.
- Create sequences of numbers.
Understanding
Students should understand that:
- looking for, describing, and extending patterns can be used to help them develop skills in all mathematical situations.
Vocabulary
- Number patterns
MA19.1.10
Extend the number sequence from 0 to 120.
Extend the number sequence from 0 to 120.
Unpacked Content
Knowledge
Students know:
- number/numeral correspondence (from 0-120).
- Strategies for counting sets of objects.
- how to read numbrs from 0 - 120.
- how to write numbers from 0 - 120.
Skills
Students are able to:
- strategically apply counting strategies.
- Write numerals 0-20.
Understanding
Students understand that:
- there are patterns in our base ten number system.
- quantities can be represented both physically and symbolically (numerals).
Vocabulary
- Number
- Numeral
MA19.1.10a
Count forward and backward by ones, starting at any number less than 120.
Count forward and backward by ones, starting at any number less than 120.
MA19.1.10b
Read numerals from 0 to 120.
Read numerals from 0 to 120.
MA19.1.10c
Write numerals from 0 to 120.
Write numerals from 0 to 120.
MA19.1.10d
Represent a number of objects from 0 to 120 with a written numeral.
Represent a number of objects from 0 to 120 with a written numeral.
MA19.1.11
Explain that the two digits of a two-digit number represent amounts of tens and ones.
Explain that the two digits of a two-digit number represent amounts of tens and ones.
Unpacked Content
Knowledge
Students know:
- how to decompose numbers 11-19.
Skills
Students are able to:
- Use place value models or mental strategies to decompose numbers.
Understanding
Students understand that:
- a two-digit number represents amounts of tens and ones.
- Ten things can be represented as one ten or as ten ones.
Vocabulary
- Base ten
- Decompose
MA19.1.11a
Identify a bundle of ten ones as a ten.““
Identify a bundle of ten ones as a ten.““
MA19.1.11b
Identify the numbers from 11 to 19 as composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
Identify the numbers from 11 to 19 as composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
MA19.1.11c
Identify the numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 as one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).
Identify the numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 as one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).
MA19.1.12
Compare pairs of two-digit numbers based on the values of the tens and ones digits, recording the results of comparisons with the symbols >, =, and < and orally with the words “is greater than,” “is equal to,” and “is less than.”
Compare pairs of two-digit numbers based on the values of the tens and ones digits, recording the results of comparisons with the symbols >, =, and < and orally with the words “is greater than,” “is equal to,” and “is less than.”
Unpacked Content
Knowledge
Students know:
- how to compare quantities using the terminology "greater than", "equal to", and "less than".
Skills
Students are able to:
- compare 2-digit numbers.
Understanding
Students understand that:
- numbers can be decomposed to determine if the amount is greater than, equal to, or less than, how that can be done.
Vocabulary
- Equalities
- Inequalities
MA19.1.13
Add within 100, using concrete models or drawings and strategies based on place value.
Add within 100, using concrete models or drawings and strategies based on place value.
Unpacked Content
Knowledge
Students know:
- how to add within 100 using place vaue strategies.
- how to identify tens and ones.
- how to compose two digit numbers.
- how to decompose two digit numbers.
Skills
Students are able to:
- add within 100.
- Model addition problems using visual models.
- Record strategies for solving addition problems.
- Communicate the relationship between models and symbolic (numeric) representations.
Understanding
Students understand that:
- relationships between models of addition problems and written strategies of those models can be used to justify solutions.
Vocabulary
- Compose
- Multiple of 10
MA19.1.13a
Add a two-digit number and a one-digit number.
Add a two-digit number and a one-digit number.
MA19.1.13b
Add a two-digit number and a multiple of 10.
Add a two-digit number and a multiple of 10.
MA19.1.13c
Demonstrate that in adding two-digit numbers, tens are added to tens, ones are added to ones, and sometimes it is necessary to compose a ten.
Demonstrate that in adding two-digit numbers, tens are added to tens, ones are added to ones, and sometimes it is necessary to compose a ten.
MA19.1.13d
Relate the strategy for adding a two-digit number and a one-digit number to a written method and explain the reasoning used.
Relate the strategy for adding a two-digit number and a one-digit number to a written method and explain the reasoning used.
MA19.1.14
Given a two-digit number, mentally find 10 more or 10 less than the number without having to count, and explain the reasoning used.
Given a two-digit number, mentally find 10 more or 10 less than the number without having to count, and explain the reasoning used.
Unpacked Content
Knowledge
Students know:
- how to mentally find 10 more or 10 less of a two digit number and explain reasoning.
- place value vocabulary: tens, ones.
Skills
Students are able to:
- mentally add or subtract 10 from a number in the range from 1
- 100.
- Explain their reasoning using place value understanding and patterns.
Understanding
Students understand that:
- patterns in the place value system can be used to mentally compute sums and differences.
Vocabulary
- Ten more
- Ten less
MA19.1.15
Subtract multiples of 10 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Relate the strategy to a written method and explain the reasoning used.
Subtract multiples of 10 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Relate the strategy to a written method and explain the reasoning used.
Unpacked Content
Knowledge
Students know:
- place value models for adding and subtracting numbers less than 100.
- Strategies for adding and subtracting multiples of 10.
Skills
Students are able to:
- use models and strategies to find and record solutions to problems where a multiple of 10 is subtracted.
- Explain their strategies.
Understanding
Students understand that:
- patterns in the place value system can be used to mentally compute sums and differences.
Vocabulary
- Multiple of 10
MA19.1.16
Organize, represent, and interpret data with up to three categories.
Organize, represent, and interpret data with up to three categories.
Unpacked Content
Knowledge
Students know:
- objects can be grouped into categories based on like characteristics.
- They can gain information from graphs.
Skills
Students are able to:
- Create, analyze, and interpret data.
Understanding
Students understand that:
- questions concerning mathematical contexts can be answered by collecting and organizing data.
Vocabulary
- Tally mark graphs
- Pictographs
- Venn diagrams
- Yes/no charts
- Bar graphs
MA19.1.16a
Ask and answer questions about the total number of data points in organized data.
Ask and answer questions about the total number of data points in organized data.
MA19.1.16b
Summarize data on Venn diagrams, pictographs, and yes-no“ charts using real objects symbolic representations or pictorial representations.“
Summarize data on Venn diagrams, pictographs, and yes-no“ charts using real objects symbolic representations or pictorial representations.“
