Content Area: Mathematics

Course: Math

Grade Level: One

Vision of the Graduate

• Communicator & Collaborator
• Critical Thinking
• Life Long Learner
• Responsible Citizen

 Standards for Mathematical Practice

1. Make Sense of Problems and Persevere in Solving Them
2. Reason Abstractly and Quantitatively
3. Construct Viable Arguments and Critique the Reasoning of Others
4. Model w/ Mathematics
5. Use Appropriate Tools Strategically
6. Attend to Precision
7. Look For and Make Use of Structure
8. Look For and Express Regularity in Repeated Reasoning

Unit Titles

Length of Unit

• Unit 1:  Numbers within 10-Addition and Subtraction

9 - 10 weeks

• Unit 2:  Numbers within 20- Addition and Subtraction and Representing Data

8 - 9 weeks

• Unit 3: Tens & Ones: Counting, Place Value

4 - 5 weeks

• Unit 4:  Operations with Tens and Ones: Addition and Subtraction

5 - 6 weeks

• Unit 5:  Length: Comparing, Ordering and Measuring

3 - 4 weeks

• Unit 6:  Geometry: Analyzing, Composing, and Partitioning Shapes
• Unit 3:  Time and Money

3 - 4 weeks

Course Overview

Summary of Year

In Grade 1, instructional time should focus on four critical areas: (1) developing understanding of addition, subtraction, and strategies for addition and subtraction within 20; (2) developing understanding of whole number relationships and place value, including grouping in tens and ones; (3) developing understanding of linear measurement and measuring lengths as iterating length units; and (4) reasoning about attributes of, and composing and decomposing geometric shapes. (The Core Standards Gr 1)

Key Areas of Focus for Grade 1: Addition and subtraction – concepts, skills, and problem solving; place value

Required Fluency: 1.OA.C.6 - Add/subtract within 10

Overview/Big Ideas:  (The Core Standards Gr 1)

Operations and Algebraic Thinking

• Represent and solve problems involving addition and subtraction.
• Understand and apply properties of operations and the relationship between addition and subtraction.
• Add and subtract within 20.
• Work with addition and subtraction equations.

Number and Operations in Base Ten

• Extend the counting sequence.
• Understand place value.
• Use place value understanding and properties of operations to add and subtract.

Measurement and Data

• Measure lengths indirectly and by iterating length units.
• Tell and write time.
• Represent and interpret data.

Geometry

• Reason with shapes and their attributes.

Unit Title / Summary

Unit 1: Numbers Within 10 Addition and Subtraction

In this unit, students are introduced to addition strategies and properties of addition as they extend their knowledge of adding within 10.  They develop more efficient ways to add and build fluency within 10 as they move beyond counting all to find sums. Students also build on what they know about counting and the meaning of subtraction to count on to subtract. They solve subtraction word problems involving take away, take apart, and comparison situations with 10.  

Length of Unit

9 - 10 weeks

Essential Questions

• How can counting on solve addition problems and subtraction problems?
• How does reading and modeling a problem help decide whether to add or subtract?
• How can using what you know about parts of numbers help you develop and choose addition and subtraction strategies?
• How do you know if an equation is true?

Focus Standards*

Operations and Algebraic Expressions

 *1.OA.C.5*, 1.OA.C.6*, 1.OA.B.3*, 1.OA.D.8*, 1.OA.B.4*, 1.OA.A.1*,  1.OA.D.7*

Unit Themes

The big ideas students will be learning are:

• You can count on to solve addition problems and subtraction problems.
• Knowing how to read and model a problem can help you decide whether to add or subtract.
• Numbers can be broken into parts. You can use what you know about parts of numbers to help

you develop and choose addition and subtraction strategies.

Key Vocabulary

add, addend, addition equation, column, compare,  count on, doubles, doubles plus 1, equal sign, equation, fewer, more, more than, number bond, row,  subtract, subtraction equation, total

Critical Content:

My students will Know…  

Key Skills:

My students will be able to (Do)…  

• Add within 10
• Apply the counting on strategy
• Analyze counting strategies
• Use fingers, counters, and connecting cubes to model the counting on strategy
• Explain how to use the counting on strategy to add two numbers
• Relate an image of two equal groups to doubles
• Relate an image of two equal groups with one left over to doubles plus one.
• Write addition equations for doubles and doubles plus one.
• Use properties to write a double plus one expression (3 addends) as an expression with 2 addends
• Use visual models or counters to create equations and solve doubles  or doubles plus one problem.
• Demonstrate fluency for addition within 10 using strategies such as counting on.
• Use the strategy for applying properties of operations to add.
• Determine the unknown addend that makes the addition equation true for sums to 10.
• Add numbers in any order to find the same total.
• Understand the relationship between addition and subtraction.
• Write a missing addend equation for a corresponding subtraction equation.
• Connect addition and subtraction equations to a number bond.
• Relate subtraction equations and missing addend equations to a problem situation.
• Fluently add and subtract number partners for 10.
• Apply the commutative property as a strategy for adding and subtracting number partners for 10.
• Understand the relationship between addition and subtraction to determine the unknown whole number in an addition or subtraction equation.
• Apply the counting on strategy to subtract within 10.
• Model the counting on strategy using physical and visual models.
• Connect the counting on strategy to an equation.
• Complete addition and subtraction equations to solve word problems.
• Understand a comparison problem situation as subtraction and/or related addition.
• Compare two quantities, determining which is greater or lesser and identifying how many more or how many fewer one quantity is than the other.
• Write and solve subtraction and addition equations to solve comparison word problems.
• Understand that the equal sign is used to indicate that one quantity is the same as another.
• Match equivalent expressions.
• Write and identify true and false equations.
• Rewrite a false equation to make it true.
• Fluently add and subtract within 10.

I can . . .

• Count on to add and subtract.
• Use doubles and doubles plus 1 facts.
• Add in any order.
• Find missing addends.
• Find number partners for 10.
• Solve addition and subtraction word problems.
• Subtract to compare.
• Tell if an equation is true or false.

Unit Title /Summary

Unit 2: Numbers Within 20: Addition and Subtraction and Representing Data

In this unit, students explore the structure of the numbers 11 to

19, refining their understanding of these numbers as “ten ones

and some more ones” to begin to see them as “one ten and

some number of ones.” Students develop and use the make

a ten strategy and other addition strategies to add within 20.

Then they use several strategies and models to subtract

within 20, relating these strategies to similar strategies used

for addition. Students find the value of unknown numbers in

equations and solve addition and subtraction word problems,

including problems about data.

Length of Unit

 8 - 9 weeks

Essential Questions

• How do you name and write teen numbers?
• How can you make a ten to add and subtract?
• How do you find an unknown number in an equation?
• How do you solve word problems within 20?
• How do you collect and compare data?

Focus Standards*

Operations and Algebraic Expressions

1.OA.C.6*, 1.OA.A.2*, 1.OA.B.3*, 1.OA.D.8*, 1.OA.A.1*

Number and Operations in Base Ten

1.NBT.B.2a*, 1.NBT.B.2b*

Measurement & Data

1.MD.C.4

Unit Themes

The big ideas students will be learning are:

• Ten is an important number.
• Teen numbers are made up of a ten and some ones.
• Numbers can be put together and broken apart in different ways.
• You can use what you know about adding and subtracting up to 10 to add and subtract up to 20.

Key Vocabulary

addend, compare, count on, data, doubles, equal sign, equation, make a ten, ones, picture graph, sort, tally chart, tally marks, teen number, tens,

Critical Content:

My students will Know…

Key Skills:

My students will be able to (Do)…

• Recognize that 10 ones and 1 ten represent the same quantity.
• Understand that numbers between 10 and 20 are composed of 1 ten and some ones.
• Model teen numbers.
• When adding 2 one-digit numbers, understand the rationale for decomposing one addend to make ten.
• Use the strategy of making ten to add numbers within 20
• Use and articulate mental math strategies to add.
• Use strategies including counting on, doubles, doubles plus 1, and make a ten to solve addition problems.
• Recognize different ways that addends can be decomposed and composed.
• Write addition equations for doubles and doubles plus one facts.
• Use properties to write a doubles plus one expression(3 addends) as an expression with 2 addends.
• Write addition expressions with three addends to represent word problems.
• Find the total of three addends, using strategies such as making a ten and using doubles by grouping any two addends.
• Use the associative and commutative properties to group addends strategically in order to use known facts.
• Recognize that teen numbers can be decomposed and composed to subtract.
• Choose strategies to subtract single-digit numbers from teen numbers.
• Make a ten to subtract single-digit numbers from teen numbers.
• Find the missing number in an addition or subtraction equation(missing number in all positions)
• Use familiar number facts and strategies to help find a missing number in an addition or subtraction equation.
• Use related addition and subtraction facts to solve for an unknown number in an equation.
• Relate addition and subtraction equations to word problems and choose strategies to solve them.
• Solve addition and subtraction word problems within 20 with unknowns in all positions.
• Define meaningful categories for a given set of objects and sort the objects according to the categories.
• Count to find the number of objects in each category.
• Represent categorical data using tally charts, charts with numbers, and picture graphs.
• Answer questions about data in charts and graphs.
• Compare quantities represented in charts and graphs.

I can . . .

• Name and write teen numbers.
• Make a ten to add and subtract.
• Find totals greater than 10.
• Add three numbers.
• Find the unknown number in an equation.
• Solve word problems within 20.
• Collect and compare data.

Unit Title / Summary

Unit 3:  Tens and Ones: Counting, Place Value, and Time

In this unit, students are introduced to place value to extend

their understanding of two-digit numbers to those beyond

19. They develop an understanding that 10 can be shown as

one group of 10 or as 10 individual ones and that the digit in

the tens place of a two-digit number denotes a number of

tens. They compare two-digit numbers and look for patterns

that show relationships between numbers when counting

to 120. Students are also introduced to telling time and to

money. They learn to recognize minutes and hours on both

analog and digital clocks and read and write time to the hour

and half hour. They identify coins and find the value of sets of

coins (in an optional lesson).

Length of Unit

4 - 5 weeks

Essential Questions

• How can you show numbers as tens?
• How can you show numbers as tens and ones?
• How do you compare numbers?
• How do you tell time to the hour and half hour?

Focus Standards*

Numbers and Operations

1.NBT.B.2a*, 1.NBT.B.2c*, 1.NBT.A.1*, 1.NBT.B.3*

Measurement and Data

1.MD.B.3

Unit Themes

The big ideas students will be learning are:

• Two-digit numbers are made of tens and ones.
• Knowing how to express two-digit numbers as tens and ones in different ways will help you understand the value of that number.
• You can use what you know about tens and ones in two-digit numbers to compare their values.

Key Vocabulary

cent, column, compare, digit, digital clock, dime, dollar, equal sign =, fewer, greater than, greater than symbol<, half hour, half past,  hour, hour hand, less than, less than symbol >, minute, minute hand, more, more than, nickel, o’clock, ones, penny, place value, quarter, row, tens,

Critical Content:

My students will Know…

Key Skills:

My students will be able to (Do)…

• Understand that the digits of a two-digit number represent numbers of tens and ones.
• Organize 10 ones in to a group of ten.
• Express 10 ones as 1 ten and 1 ten as 10 ones.
• Identify and write multiples of ten in terms of tens and ones.
• Count on from any number on the 120 chart.
• Identify missing numbers in a sequence within 20.
• Count by 10’s within 120.
• Represent two-digit numbers as tens and ones.
• Decompose a two-digit number as some tens and some ones in multiple ways.
• Model a two-digit number in multiple ways.
• Understand the meaning of the symbols < and >.
• Compare the values of 2 two-digit numbers using tens and ones.
• Write the symbols <, >, and = to compare 2 two-digit numbers.
• Tell time to the hour and to the half hour using analog and digital clocks.
• Write the time to the hour and half hour.
• Understand that 30 minutes is the same as a half hour.
• Identify coins(pennies, nickels, dimes, and quarters).
• Know the value of each coin.
• Relate the value of coins(pennies, dimes, and quarters), to the value of one dollar.
• Count on to find the value of a set of dimes and pennies.

I can . . .

• Show numbers as tens.
• Count on a 120 chart.
• Show numbers as tens and ones.
• Compare numbers.
• Tell time to the hour and half hour.

Unit Title / Summary

Unit 4 Operations with Tens and Ones: Addition and Subtraction

In this unit, students are introduced to operations with

two-digit numbers. They build on what they know about

composing and decomposing numbers 11 to 19 and

strategies for adding and subtracting within 20 to add

two-digit numbers. Students extend their knowledge

of counting by tens to mentally find 10 more or 10 less

and explore adding multiples of 10. They deepen their

understanding of place-value concepts, beginning to see

how adding tens and adding ones relate to each other as

they regroup to add two-digit numbers.

Length of Unit

 5 - 6 weeks

Essential Questions

• How do you add and subtract tens?
• How do you add one-digit and two-digit numbers?

Focus Standards*

Number and Operations in Base Ten

1.NBT.C.4*, 1.NBT.C.6*, 1.NBT.C.5*, 1.NBT.C.4*

Unit Themes

The big ideas students will be learning are:

• You can use what you know about tens and ones to add or subtract tens from any number.
• When adding two-digit numbers, you can add tens to tens, and ones to ones.
• Sometimes you need to regroup 10 ones to make a ten when you add.

Key Vocabulary

digit, ones, place value, tens,

Critical Content:

My students will Know…

Key Skills:

My students will be able to (Do)…

• Count tens as 1 ten, 2 tens, 3 tens…or as 10, 20, 330…
• Use counting on, counting back, and strategies based on place value and properties to add and subtract multiples of 10.
• Relate adding tens to adding ones.
• Mentally add 10 to any number and subtract 10 from any number within 100.
• Recognize that adding or subtracting a ten results in a change in the tens digit, but the ones digit remains the same.
• Add multiples of 10 to any two-digit number within 100.
• Apply a strategy based on place value to add a two-digit number and a multiple of 10 and relate it to a written method.
• Model adding a two-digit number and a multiple of 10 using place value understanding.
• Add two-digit and one-digit numbers with and without regrouping.
• Compose a ten when adding ones that total 10 or more.
• Add 2 two-digit numbers with and without grouping.
• Compose a new ten when adding ones that total 10 or greater.
• Develop strategies based on place value for adding two-digit numbers.  

I can . . .

• Add and subtract tens.
• Add or subtract 10 from any number.
• Add tens to any number.
• Add one-digit and two-digit numbers.
• Add 2 two-digit numbers.

Unit Title / Summary

Unit 5 Length: Comparing, Ordering, and Measuring

In this unit, students build on a basic understanding of

length and direct comparison of length to make indirect

comparisons and to order objects by length. Students lay

nonstandard units from end to end of an object with no

gaps or overlaps and understand that the number of units

is a measure of length.

Length of Unit

3 - 4 weeks

Essential Questions

• How can you order objects by length?
• How can you compare lengths of objects?
• How can you measure lengths of objects?                

Focus Standards*

Measurement and Data

1.MD.A.1*

Unit Themes

The big ideas students will be learning are:

• You can compare the length of objects and put them in length order by lining them up at one end.

• Sometimes you can tell which of two objects is longer by comparing both of them to another object.

• You can measure an object with same-sized units to find its length.

Key Vocabulary

compare, length, longer, longest, measure, shorter, shortest, taller, tallest, unit,

Critical Content:

My students will Know…

Key Skills:

My students will be able to (Do)…

• Directly compare the lengths of three objects.
• Order three objects by length.
• Recognize that sometimes it is not possible to compare lengths directly.
• Compare two objects by comparing their lengths to a third reference object.
• Use logical reasoning to indirectly compare the lengths of objects.
• Measure the length of an object using a whole number of nonstandard units of measure.
• Understand that the number of iterated units from end to end is a measure.
• Iterate units with no gaps or overlaps.
• Understand that the length measure of an object is the number of unit laid end to end with no gaps or overlaps.

I can . . .

• Order objects by length.
• Compare lengths of objects.
• Measure lengths of objects.

Unit Title / Summary

Unit 6 Geometry: Analyzing, Composing, and Partitioning Shapes

In this unit, students extend their understanding of

geometric shapes. They build on knowledge of names for

two- and three-dimensional shapes to distinguish between

defining attributes such as the number of sides or corners

and non-defining attributes such as color, orientation,

and size. Students use what they know about composing

and decomposing different shapes to develop a greater

understanding of part-whole relationships. They also

decompose two-dimensional shapes into equal shares (halves and fourths) and describe the relationship between equal shares and the whole and between halves and fourths.

Length of Unit

3 - 4 weeks

Essential Questions

How can you use sides and corners to name shapes?

How can you put shapes together to make new shapes?

How can you break shapes into halves and/or fourths?                        

Focus Standards*

Geometry

1.G.A.1*, 1.G.A.2*, 1.G.A.3*

Unit Themes

The big ideas students will be learning are:

• You can describe and sort shapes by counting the number of sides and corners they have.

• You can put two or more shapes together to make new shapes.

• You can divide shapes into two equal parts (called halves) or four equal parts (called fourths).

Key Vocabulary

circle, cone, corner, cube, cylinder, edge, equal parts, face, fourths, halves, hexagon, quarters, rectangle, rectangular prism, rhombus, side, sphere, square, trapezoid, triangle, unequal parts, whole

Critical Content:

My students will Know…

Key Skills:

My students will be able to (Do)…

• Identify the defining attributes of a shape.
• Distinguish between defining and non-defining attributes.
• Classify a shape based on its defining attributes.
• Compose two-dimensional shapes to create composite shapes, and then compose new shapes from the composite shape.
• Compose three-dimensional shapes to create composite shapes and analyze the parts of a composite shape.
• Divide circles, squares, and rectangles into two and four equal parts.
• Identify the number of equal parts in a divided shape.
• Name the parts as halves, fourths, and quarters.
• Understand that if a whole is divided into more parts, the parts get smaller.

I can . . .

• Use sides and corners to name shapes.
• Put shapes together to make new shapes.
• Break shapes into halves.
• Break shapes into fourths.