Physics - Ewing Public Schools



MATHEMATICS – GRADE 1

EWING PUBLIC SCHOOLS

2099 Pennington Road

Ewing, NJ 08618

BOE Approval Date: 8/29/11 Michael Nitti

Revised by: Donald Wahlers Superintendent

|In accordance with The Ewing Public Schools’ Policy 2230, Course Guides, this curriculum has been reviewed and found to be in compliance with |

|all policies and all affirmative action criteria. |

TABLE OF CONTENTS

Page

Course Description and Rationale 1

Scope of Essential Learning:

Unit 1: How Many Of Each? (Addition, Subtraction and the

Number System 1) [32 Days] 2

Unit 2: Making Shapes (2-D Geometry) [16 Days] 7

Unit 3: Solving Story Problems (Addition, Subtraction and

the Number System 2) [32 Days] 11

Unit 4: What Would You Rather Be? (Data Analysis) [14 Days] 16

Unit 5: Fish Lengths and Animal Jumps (Measurement) [18 Days] 20

Unit 6: Number Games and Crayon Puzzles (Addition, Subtraction

and the Number System 3) [28 Days] 24

Unit 7: Twos, Fives and Tens (Addition, Subtraction and the

Number System 4) [28 Days] 29

Unit 8: Blocks and Books (3-D Geometry) [11 Days] 34

COURSE DESCRIPTION AND RATIONALE

THE EWING PUBLIC SCHOOLS’

MATH VISION

The Ewing Public Schools will deliver an instructional program in mathematics where students are actively engaged in the discovery of math concepts and are applying these concepts in ways that they find meaningful and relevant.

Ewing students will be mathematical thinkers who can reason, communicate and solve problems.

Ultimately, Ewing students will master and will be able to utilize these math concepts and skills throughout their lives.

In this first grade course in mathematics, students will delve into the base ten structure of our number system, uncovering and discovering patterns which they will utilize to develop visual images of quantities, compose and decompose numbers, and begin to formulate strategies for the numerical operations of addition and subtraction. Students will also investigate the characteristics and attributes of 2-dimensional and 3-dimensional shapes, collect and analyze data, and explore the role of standardizing units in measuring length.

While students will utilize a constructivist approach to investigate relationships in math, this approach will be balanced with a level of practice needed to attain skill mastery. Throughout the course, students will be actively engaged in problem solving through reasoning. Students will be expected to communicate their reasoning and problem solving on a daily basis though written and verbal formats.

In the end, the goal of this course is to develop young mathematicians with the habits of mind enabling them to meet the vision shared above; enabling their future success in mathematics.

UNIT 1: HOW MANY OF EACH? (ADDITION, SUBTRACTION AND THE

NUMBER SYSTEM 1) [32 DAYS]

Why Is This Unit Important?

This is the first unit in this grade level where students continue to develop ideas about counting and quantity, the composition of numbers, including work with place value, the structure of the base-ten number system, and the operations of addition and subtraction. In this unit students will focus on building number sense through counting and comparing quantities, and through composing and decomposing numbers. Students also work with the operation of addition, developing strategies for combining quantities. The big ideas embedded in this unit are:

▪ The base ten structure of the number system

▪ Numbers can be decomposed into other numbers and then composed into the original amount

▪ Addition is a process for finding the total of separate parts

▪ Subtraction being the inverse of addition is a process for finding the amounts of separated parts of the total

▪ Addition is commutative, while subtraction is not.

Enduring Understandings:

1. Developing strategies for accurately counting a set of objects by ones

2. Developing an understanding of the magnitude and position of numbers

3. Composing numbers up to 10 with 2 addends

4. Making sense of and developing strategies to solve addition problems with small numbers

5. Using manipulatives, drawings, tools, and notation to show strategies and solutions

Essential Questions:

1. What patterns do you see in our number line?

2. In ‘real-life’ when we add what are we doing?

3. When we add two numbers, does it matter which number we start with?

Acquired Knowledge:

1. Connecting number names and written numbers to the quantities they represent

2. Developing an understanding of how the quantities in the counting sequence are related: each number is 1 more or 1 less than the number before or after it

3. Finding and exploring relationships among combinations of numbers up to 10

4. Seeing that adding the same two numbers (e.g., 4 and 3) results in the same total, regardless of context (e.g., number cubes, cards, objects)

Acquired Skills:

1. Counting a set of up to 20 objects by ones

2. Practicing the rote counting sequence forward and backward, from 1 to 30

3. Identifying number names and written numbers to the quantities they represent

4. Developing and analyzing visual images for quantities up to 10

5. Ordering a set of numbers and quantities up to 12

6. Comparing two quantities up to 20 to see which is larger

7. Finding and exploring relationships among combinations of numbers up to 10

8. Recording combinations of two numbers that make a certain total

9. Solving a problem with multiple solutions

10. Solving a problem in which the total and one part are known

11. Visualizing and retelling the action in an addition situation

12. Modeling the action of an addition problem with counters or drawings

13. Finding the total of two or more quantities up to a total of 20 by counting all, counting on, or using number combinations

14. Using the number line as a tool for counting

15. Introducing standard notation for comparing quantities (greater than, less than, and equal to)

16. Introducing and using standard notation (1 and 5) to represent addition situations

17. Recording a solution to a problem

18. Representing number combinations with numbers, pictures, and/or words

Instructional Materials:

• Investigations in Number, Data, and Space, Pearson Education, Inc., 2012

• Investigations in Number, Data, and Space, Manipulatives Kit for Grade 1

• Investigations in Number, Data, and Space, Cards Package for Grade 1

Differentiation:

Enrichments

• Counting Quantities to 20 Extension

• Mystery Boxes with Larger Numbers Extension

• Solving Story Problems with Larger Numbers Extension

• Dogs and Cats Extension

Supplements

• Investigation 1 Quiz

• Using a 20 Frame to Count Intervention

• Counting to 20 Practice

• Investigation 2 Quiz

• What’s in the Mystery Box? Intervention

• Missing Steps Practice

• Investigation 3 Quiz

• Solving Story Problems with Objects Intervention

• Solving Story Problems Practice

• Investigation 4 Quiz

• Five Blueberries and Strawberries Intervention

• Pencils and Crayons Practice

Assessed Benchmarks:

1. Count a set of up to 20 objects

2. Demonstrate that the two digits of a two digit number represent the amount of tens and ones:

o 10 can be thought of as a bundle of ten ones called a “ten”

o The numbers from 11 to 19 are compose of a ten and a specific number of ones

3. Compare and order quantities up to 12

4. Combine two small quantities

5. Relate counting to addition (skip counting on)

6. Interpret (retell the action and sequence) and solve addition story problems

7. Find more than one combination of two addends for a number up to 10 (e.g., 7 is 4 and 3 and is also 5 and 2)

List of Applicable Common Core State Standards for Mathematics Covered in This Unit:

1.0A.1-8

1.NBT.1, 3

1.MD.4

MP 1-6, 8

Suggested Learning Experiences and Instructional Activities:

1. Morning Meeting: Calendar

2. Introducing Math Tools

3. Exploring Connecting Cubes

4. Exploring Pattern Blocks

5. Exploring Geoblocks

6. Exploring Power Polygons

7. Morning Meeting: Weather

8. Collect 20 Together

9. Start With/Get To

10. Staircases

11. Mystery Boxes

12. Compare Dots

13. Compare

14. Plus or Minus 1 Bingo

15. Quick images

16. Counting 20

17. Quick Images

18. Ordering Numbers

19. Double Compare

20. Double Compare Dots

21. Five-in-a-Row

22. Roll and Record

23. Story Problems Aloud

24. Addition Story problems

25. Today’s Number 10

26. An Addition Story Problem

27. Finding How Many in All?

28. Seven Peas and Carrots

29. Three Towers

30. Heads and Tails

31. How Many Am I Hiding?

32. Nine Peas and Carrots

Technology:

• Fun 4 The Brain Addition Games:

• Fun 4 The Brain Subtraction Games:

• Great site for elementary level online math games:

• Arithmetic Baseball:

• MathBlaster Adventures. (requires a registration which is free):

• Jumpstart Math Adventures. (requires a registration which is free):

• Virtual Manipulatives and Games:

Classroom Routines:

• Developing strategies for counting accurately

• Using the calendar as a tool for keeping track of time

• Developing vocabulary to talk about time (morning, noon, midday, afternoon, etc.) and sequence (first, next, last, before, after, and so on)

• Collecting and recording data

• Estimating quantities up to about 30

• Adding or subtracting small amounts to/from a familiar number

• Connecting written numbers and number names

• Using the number line as a tool for counting

• Practicing the rote counting sequence forward and backward

• Developing and analyzing visual images for quantities up to 10

• Recreating an arrangement of objects

• Finding the total of two or more single digit quantities

UNIT 2: MAKING SHAPES (2-D GEOMETRY) [16 DAYS]

Why Is This Unit Important?

Geometry is a part of mathematics that students experience every day. Students bring with them a good deal of informal experience with geometry. Young children use their eyes and hands to interact with shapes and images in their world, they are developing an intuitive sense of how those shapes and images are the same and how they are different. Part of young students’ work in developing mathematical understanding is to begin to observe, describe, compare, and represent the shapes they see around them. This is the first of two units in this grade level where students will extend upon the explorations and learning from kindergarten in the areas of shape composition and structure. The big ideas embedded in this unit are:

▪ 2-D shapes can be decomposed into other smaller 2-D shapes. Likewise 2-D shapes can be composed into a larger 2-D shape

▪ 3-D shapes can be decomposed into other smaller 3-D shapes. Likewise 3-D shapes can be composed into a larger 3-D shape

▪ The faces of a 3-D shape are 2-D shapes

▪ Shapes are composed of attributes which can be used to sort, classify, compare and identify shapes.

Enduring Understandings:

1. Describing, identifying, and comparing 2-D shapes

2. Composing and decomposing 2-D shapes

Essential Questions:

1. Where do you see this 2-D shape out in the world?

2. In what ways is this 2-D shape the same as other 2-D shapes?

3. In what ways is this 2-D shape different from other 2-D shapes?

4. What shapes can this 2-D shape be made of?

Acquired Knowledge:

1. Developing visual images of and language for describing 2-D shapes

2. Recognizing that there are many types of quadrilaterals (e.g., rectangles, trapezoids, squares, rhombi)

3. Understanding how shapes can be combined to make other shapes

4. Seeing relationships between squares and triangles

Acquired Skills:

1. Identifying shapes in the environment

2. Describing, comparing, and naming 2-D shapes

3. Developing visual images of and language for describing 2-D shapes

4. Identifying common attributes of a group of shapes

5. Identifying characteristics of triangles and quadrilaterals

6. Identifying and making triangles and quadrilaterals of different shapes and sizes

7. Covering a region without gaps or overlaps using multiple shapes

8. Decomposing shapes in different ways

9. Finding different combinations of shapes that fill the same area

10. Altering designs to use more or fewer pieces to cover the same space

Instructional Materials:

• Investigations in Number, Data, and Space, Pearson Education, Inc., 2012

• Investigations in Number, Data, and Space, Manipulatives Kit for Grade 1

• Investigations in Number, Data, and Space, Cards Package for Grade 1

Differentiation:

Enrichments

• Shape Puzzles Extension

• Making Triangles Extension

Supplements

• Investigation 1 Quiz

• Describing 2-D Shapes Intervention

• Identifying Shapes Practice

• Investigation 2 Quiz

• Geoboard Triangles Intervention

• Find the Rule Practice

Assessed Benchmarks:

1. Fill a given region in different ways with a variety of shapes

2. Use geometric language to describe and identify important features of familiar 2-D shapes

3. Identify and describe triangles

4. Describe and sort 2-D shapes

5. Distinguish between defining attributes (number of sides, closed sides, etc) and non-defining attributes (color, orientation, over-all size)

6. Compose and decompose shapes

7. Build and draw shapes to possess defining attributes

8. Compose 2 dimensional shapes (rectangles, squares, trapezoids, half-circles, and quarter circles) to create a composite shape, and create new shapes from the composite shape

List of Applicable Common Core State Standards for Mathematics Covered in This Unit:

1.NBT.1

1.G.1-2

MP 2, 3, 5, 7

Suggested Learning Experiences and Instructional Activities:

1. Morning Meeting: Calendar

2. Quick Images: Shapes

3. Start With/Get To

4. Pattern Block Fill Ins

5. Describing Shapes

6. Fill the Hexagons

7. Shapes poster: Hexagon and Rhombus

8. Three Ways to Fill an Outline

9. Filling with More and Fewer

10. Guess My Rule with Shapes

11. Sorting Shapes

12. Making Triangles

13. Looking at Power Polygons: Quadrilaterals

Technology:

• Investigations ‘Shapes’ software

• A site that launches into all kinds of fun geometry applications:

• Great site for elementary level online math games:

• Geometry math games:

• Know your shapes? Test yourself by picking off the correct shapes:

• Geometry resources for teachers:

• Interactive geometry Website:

• Virtual manipulatives and games for geometry:

Classroom Routines:

• Developing strategies for counting accurately

• Using the calendar as a tool for keeping track of time

• Developing vocabulary to talk about time (morning, noon, midday, afternoon, etc.) and sequence (first, next, last, before, after, during, and so on.)

• Collecting and recording data

• Estimating quantities up to about 30

• Adding or subtracting small amounts to/from a familiar number

• Connecting written numbers and number names

• Using the number line as a tool for counting

• Practicing the rote counting sequence forward and backward

• Identifying names and attributes of 2-D shapes

UNIT 3: SOLVING STORY PROBLEMS (ADDITION, SUBTRACTION AND

THE NUMBER SYSTEM 2) [32 DAYS]

Why Is This Unit Important?

This is the second unit in this grade level where students continue to develop ideas about counting and quantity, the composition of numbers, including work with place value, the structure of the base-ten number system, and the operations of addition and subtraction. In this unit students will focus on building number sense through counting and comparing larger quantities, and through composing and decomposing numbers into several parts. There is also the added challenge of finding all of the two addend combinations of a number. Students also extend their work on the operation of addition and are introduced to the operation of subtraction. The big ideas embedded in this unit are:

▪ The base ten structure of the number system

▪ Numbers can be decomposed into other numbers and then composed into the original amount

▪ Addition is a process for finding the total of separate parts

▪ Subtraction being the inverse of addition is a process for finding the amounts of separated parts of the total

▪ Addition is commutative, while subtraction is not

Enduring Understandings:

1. Composing numbers up to 15 with two or more addends

2. Making sense of and developing strategies to solve addition and subtraction problems with small numbers

3. Representing numbers by using equivalent expressions

4. Developing strategies for accurately counting a set of objects by ones

5. Using manipulatives, drawings, tools, and notation to show strategies and solutions

Essential Questions:

1. In what ways are addition and subtraction related?

2. Describe the strategy you used for addition. Does anyone have a suggested name for this strategy? How is it similar to other strategies we have seen?

3. Describe the strategy you used for subtraction. Does anyone have a suggested name for this strategy? How is it similar to other strategies we have seen?

Acquired Knowledge:

1. Proving that all of the possible combinations have been found

2. Understanding the relationships among combinations of numbers up to 15

3. Seeing that subtracting the same two numbers (e.g., 6 from 10) results in the same difference regardless of context (e.g., number and dot cubes, cards, objects)

4. Seeing the 100 chart as a representation of the counting numbers to 100

Acquired Skills:

1. Finding as many 2-addend combinations of a number as possible

2. Proving that all of the possible combinations have been found

3. Solving a problem in which the total and one part are known

4. Finding and exploring relationships among combinations of numbers up to 15

5. Developing the strategy of counting on

6. Developing counting on as a strategy for combining two numbers

7. Visualizing and retelling the action in addition and subtraction situations involving removal

8. Finding the total of two or more quantities up to a total of 20 by counting all, counting on, or using number combinations

9. Estimating whether an amount is more or less than a given quantity

10. Modeling the action of an addition or subtraction (removal) problem with counters or drawings

11. Subtracting one number from another, with initial totals of up to 12

12. Developing strategies for solving addition and subtraction (removal) problems

13. Generating equivalent expressions for a number

14. Practicing the rote counting sequence forward and backward, starting from any number 1–60

15. Developing and analyzing visual images for quantities

16. Accurately counting a set of objects by ones, up to 60

17. Practicing the oral counting sequence from 1 to 100

18. Writing the sequence of numbers (as high as students know)

19. Identifying and using patterns in the sequence of numbers to 100

20. Recording solutions to a problem

21. Using numbers and standard notation (+, -, =) to record

22. Connecting written numbers and standard notation (+, -, =) to the quantities and actions they represent

23. Using the equal sign to show equivalent expressions

24. Using the number line as a tool for counting

25. Developing methods for recording addition and subtraction (removal) strategies

Instructional Materials:

• Investigations in Number, Data, and Space, Pearson Education, Inc., 2012

• Investigations in Number, Data, and Space, Manipulatives Kit for Grade 1

• Investigations in Number, Data, and Space, Cards Package for Grade 1

Differentiation:

Enrichments

• Dot Addition D and E Extension

• How Many Fish Extension

• Solving Challenging Story Problems Extension

• More Missing Numbers Extension

Supplements

• Investigation 1 Quiz

• Dot Addition with Smaller Numbers Intervention

• How Many Rocks? Practice

• Investigation 2 Quiz

• More Solving Subtraction Story Problems Intervention

• Subtracting Dots Practice

• Investigation 3 Quiz

• Addition and Subtraction with Counters Intervention

• How Many? Practice

• Investigation 4 Quiz

• Covering and Counting with Pattern Blocks Intervention

• What Went Wrong Practice

Assessed Benchmarks:

1. Find at least five combinations of two addends for a number up to 15

2. Combine two small quantities

3. Interpret (retell the action and sequence) and solve addition and subtraction story problems

4. Subtract one small quantity from another

5. Understand subtraction as an unknown addend problem

6. Relate counting to subtraction (skip counting down)

7. Represent numbers by using equivalent expressions

8. Understand that the two digits of a two digit number represent the amount of tens and ones:

- 10 can be thought of as a bundle of ten ones called a “ten”

- The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to a bundle of a specific

number of tens and 0 ones

9. Count a set of 40 to 50 objects

10. Rote count, read, and write numbers to 65

List of Applicable Common Core State Standards for Mathematics Covered in This Unit:

1.0A.1-8

1.NBT.1, 3

1.MD.4

MP 1-8

Suggested Learning Experiences and Instructional Activities:

1. Start With/Get To

2. How Many of Each?

3. Counters in a Cup

4. Nine Toys: How Many of Each?

5. How Many Am I Hiding?

6. Roll and Record

7. Five in a Row

8. Ten Toys: How Many of Each?

9. Dot Addition

10. Solving an Addition Story Problem

11. Solving a Subtraction Story Problem

12. Roll and Record: Subtraction

13. Five in a Row: Subtraction

14. Today’s Number

15. Tell a Story

16. Today’s Number

17. How Big Are Our Feet?

18. Covering and Counting

19. Counting Strips

20. Counting to 100

21. Missing Numbers

22. True or False

Technology:

• Fun 4 The Brain Addition Games:

• Fun 4 The Brain Subtraction Games:

• Great site for elementary level online math games:

• Arithmetic Baseball:

• MathBlaster Adventures. (requires a registration which is free):

• Jumpstart Math Adventures. (requires a registration which is free):

• Virtual Manipulatives and Games:

Classroom Routines:

• Using the calendar as a tool for keeping track of time

• Collecting and recording data

• Connecting written numbers and number names

• Using the number line as a tool for counting

• Practicing the forward and backward counting sequences with numbers up to 60

• Developing and analyzing visual images for quantities

• Recreating an arrangement of objects

• Finding the total of two or more single digit quantities

• Exploring relationships among combinations

• Finding the total of two or more equal groups

UNIT 4: WHAT WOULD YOU RATHER BE? (DATA ANALYSIS) [14 DAYS]

Why Is This Unit Important?

In kindergarten and grade 1, students were engaged in a variety of sorting activities. Students began to develop their own representations of the data. In this unit students will further explore attributes which can be used to sort and collect data about objects. Students will also use surveys to collect data which they will represent. Students will analyze their data with the goal of answering “What do the data tell us about our class?” The big ideas embedded in this unit are:

▪ Data can be collected, represented, and analyze to discover trends that exist

▪ Differing representations of data differ in their usefulness for discovering and analyzing trends. The usefulness of any given representation technique is context based

Enduring Understandings:

1. How to sort and classify data

2. How to represent data

3. How to describe data

4. How to design and carry out a data investigation

Essential Questions:

1. What attributes does this object possess? Which of them do the other objects also have?

2. What categories can you use to sort the data? Are there other categories that would work for this data? In this case which categories are better to use? Why?

3. What are some possible ways to represent the data? Which way do you think would be best? Why?

4. What trends in the data do you see?

Acquired Knowledge:

1. Understanding that the sum of the pieces of data in all the categories equals the number of people surveyed

Acquired Skills:

1. Describing attributes of objects

2. Using attributes to sort a set of objects

3. Looking carefully at a group of objects to determine how they have been sorted

4. Making a representation to communicate the results of a survey

5. Making sense of data representations, including pictures, bar graphs, tallies, and Venn diagrams

6. Comparing what different representations communicate about a set of data

7. Using equations to show how the sum of the responses in each category equals the total responses collected

8. Organizing data in numerical order

9. Describing and comparing the number of pieces of data in each category or at each value and interpreting what the data tell you about the group

10. Using data to compare how two groups are similar or different

Instructional Materials:

• Investigations in Number, Data, and Space, Pearson Education, Inc., 2012

• Investigations in Number, Data, and Space, Manipulatives Kit for Grade 1

• Investigations in Number, Data, and Space, Cards Package for Grade 1

Differentiation:

Enrichments

• Guess My Rule with 2 Rules Extension

• Different Ways of Showing Data Extension

• What Pencil Color? Extension

Supplements

• Investigation 1 Quiz

• Sorting Shapes Intervention

• Guess My Rule with Objects Practice

• Investigation 2 Quiz

• Representing Data Intervention

• Analyzing Data Practice

• Investigation 3 Quiz

• More Age Data Intervention

• What Do You Know Practice

Assessed Benchmarks:

1. Sort a group of objects according to a given attribute

2. Represent a set of data with three categories

3. Interpret a variety of data representations with three categories

4. Describe a set of data, including how many are in each group, which group is greater (and how much more or less are in one group than in another), and how many people responded to the survey

Jumps

List of Applicable Common Core State Standards for Mathematics Covered in This Unit:

1.NBT.1, 3

1.MD.3-4

1.G.1

MP 3, 7

Suggested Learning Experiences and Instructional Activities:

1. Sorting Shapes

2. Sorting Buttons

3. Guess my Rule with People

4. Quick Survey: Brushing Your Teeth

5. Eagle or Whale

6. Deep Sea or Outer Space

7. Quick Survey: Child or Grown-Up

8. Quick Survey: What Color are your Shoes?

9. Quick Survey: About Your Class

10. Pocket Plot

11. Making a Plan

12. Teeth Data from Other Classes

13. Mystery Teeth Data

14. Which Class Is It?

Technology:

• Teacher website for data analysis resources for games in the classroom:

• NCTMs Calculation Nation. Free registration to log on and play other kids from around the world in online math games:

•

• Virtual manipulatives:

Classroom Routines:

• Developing strategies for counting accurately

• Using the calendar as a tool for keeping track of time

• Developing vocabulary to talk about time (morning, noon, midday, afternoon, etc.) and sequence (first, next, last, before, after, etc.)

• Collecting and recording data

• Making sense of a variety of representations of data

• Connecting written numbers and number names

• Using the number line as a tool for counting

• Using the 100 chart as a tool for counting

• Practicing the forward and backward counting sequences with numbers up to 60

• Developing and analyzing visual images for quantities

• Identifying and naming coins

UNIT 5: FISH LENGTHS AND ANIMAL JUMPS (MEASUREMENT) [18 DAYS]

Why Is This Unit Important?

Young children are often curious about and interested in questions about measurement. It is not unusual to see children comparing heights to find out who is taller nor is it unusual to hear students talk about the sizes of dinosaurs, whales, or tadpoles. However, young people need many opportunities to develop their understanding of the particular attribute they are comparing or measuring. This conceptual development is important for students to truly understand length and its measurement. In kindergarten students made direct comparisons between the lengths of objects and began exploring the use of non-standard units. In this unit students will build upon the work they did with non-standard units and explore the use of and need for more standardization. The big ideas embedded in this unit are:

▪ Measurement is a process used to determine the relative amount of a physical attribute of an object

▪ There are specific practices which must be followed during the process of measurement to yield consistent results

▪ Standardized units help society to have a consistent process of comparison of measured attributes

Enduring Understandings:

1. Understanding length

2. Using linear units

3. Measuring with standard units

Essential Questions:

1. What are some ways we can measure length?

2. Where on an object can you measure length?

3. Did we get the same answer for the length of the object? Why did some get a different length when they measured the same object? What can we do when we measure so that our answers can be the same for the same object?

Acquired Knowledge:

1. Understanding what length is and how it can be measured

2. Understanding the meaning of at least in the context of linear measurement

3. Understanding that measurements of the same length should be the same when they are measured twice or by different people using the same unit

4. Understanding that measuring an object using different-length units will result in different measurements

5. Understand that for these examples that decomposing into more equal shares creates smaller shares

Acquired Skills:

1. Measuring lengths using different-sized units

2. Identifying the longest dimension of an object

3. Comparing lengths to determine which is longer

4. Identifying contexts in which measurement is used

5. Developing accurate measurement techniques

6. Describing measurements that are in between whole numbers of units

7. Measuring length by iterating a single unit

8. Using inch tiles to measure objects in inches

9. Partition circles and rectangles into two and four equal shares. Describe the shares using the words halves, fourths, and quarters and use the phrases half of, fourth of, and quarter of. Describe the whole as two of and four of the shares.

Instructional Materials:

• Investigations in Number, Data, and Space, Pearson Education, Inc., 2012

• Investigations in Number, Data, and Space, Manipulatives Kit for Grade 1

• Investigations in Number, Data, and Space, Cards Package for Grade 1

Differentiation:

Enrichments

• Measuring 3 Ways Extension

• How Much Longer? Extension

Supplements

• Investigation 1 Quiz

• Measuring Markers, Pencils, and Crayons Intervention

• Measuring with Tiles Practice

• Investigation 2 Quiz

• Measuring with Shoes Intervention

• Measuring with Kid Steps Practice

Assessed Benchmarks:

1. Order three objects by length;

2. Compare the length of two objects indirectly by using a third object

3. Demonstrate accurate measuring techniques when measuring a distance with nonstandard or standard units. These techniques include starting at the beginning, ending at the end, leaving no gaps or overlaps, measuring in a straight line, and keeping track of the number of units.

4. Understand that the same results should be obtained when the same object is measured twice, or when two different people measure the same object (using the same unit)

5. Understand that using different-sized units will result in different numbers

6. Partition circles and rectangles into two and four equal shares. Describe the shares using the words halves, fourths, and quarters and use the phrases half of, fourth of, and quarter of. Describe the whole as two of and four of the shares. Understand that for these examples that decomposing into more equal shares creates smaller shares

List of Applicable Common Core State Standards for Mathematics Covered in This Unit:

1.0A.1

1.NBT.1, 3

1.MD.1-4

1.G.1

MP 3, 5, 6

Suggested Learning Experiences and Instructional Activities:

1. Measuring with Connecting Cubes

2. Measuring with Cubes, Tiles, or Paper Clips

3. Measuring Fish

4. Fish Stories

5. Making Keepers

6. Measuring in Kid Steps

7. Big Steps, Little Steps, and Craft Sticks

8. What Did We Find?

9. Animal Jumps

10. Jumping Story Problems

11. Half-and-Half Pizzas

12. Telling Time to the Half Hour

13. Halves of Squares

14. Half-and-Half Rugs

15. Designing More Rugs: Fourths

Technology:

• Great site for elementary level online math games:

• Teacher resources for measurement:

• Wacky Rulers Games Central:

• Games to measure length, width, and time:

• Virtual manipulatives and games:

Classroom Routines:

• Developing strategies for counting accurately

• Using the calendar as a tool for keeping track of time

• Developing vocabulary to talk about time (morning, noon, midday, afternoon, etc.) and sequence (first, next, last, before, after, and so on)

• Collecting and recording data

• Connecting written numbers and number names

• Using the 100 chart as a tool for counting

• Practicing the forward and backward counting sequences with numbers up to 60

• Developing and analyzing visual images for quantities

• Identifying and naming coins

• Collecting, counting, representing, describing, and comparing data

• Interpreting different representations of data including: pictures, bar graphs, tallies, and Venn diagrams

UNIT 6: NUMBER GAMES AND CRAYON PUZZLES (ADDITION, SUBTRACTION

AND THE NUMBER SYSTEM 3) [28 DAYS]

Why Is This Unit Important?

This is the third unit in this grade level where students continue to develop ideas about counting and quantity, the composition of numbers, including work with place value, the structure of the base-ten number system, and the operations of addition and subtraction. In this unit students will focus on building number sense through number composition, extending to even larger quantities. Students will work with composing and decomposing numbers and combinations of a number to further refine and develop their accuracy with the operations of addition and subtraction. The big ideas embedded through this unit are:

▪ The base ten structure of the number system

▪ Numbers can be decomposed into other numbers and then composed into the original amount

▪ Addition is a process for finding the total of separate parts

▪ Subtraction being the inverse of addition is a process for finding the amounts of separated parts of the total

▪ Addition is commutative, while subtraction is not

Enduring Understandings:

1. Composing numbers up to 20 with 2 or more addends

2. Making sense of and developing strategies to solve addition and subtraction problems with small numbers

3. Using manipulatives, drawings, tools, and notation to show strategies and solutions

Essential Questions:

1. In what ways are addition and subtraction related?

2. Describe the strategy you used for addition. Does anyone have a suggested name for this strategy? How is it similar to other strategies we have seen?

3. Describe the strategy you used for subtraction. Does anyone have a suggested name for this strategy? How is it similar to other strategies we have seen?

Acquired Knowledge:

1. Combinations of 10

2. Standard notation (+, -, =) symbols

Acquired Skills:

1. Developing fluency with the 2-addend combinations of 10

2. Finding relationships among different combinations of numbers up to 20

3. Using 5 + 5 to reason about other combinations of 10

4. Finding as many 2-addend combinations of a number as possible

5. Trying to prove that all the possible 2-addend combinations of a number have been found

6. Solving related story problems

7. Solving a problem in which the total and one part are known

8. Adding 2 or more single-digit numbers

9. Visualizing, retelling, and modeling the action in addition and subtraction (removal) situations

10. Subtracting one number from another, with initial totals of up to 12

11. Developing strategies for solving addition and subtraction story problems

12. Solving addition and subtraction story problems

13. Using numbers and standard notation (+, -, =) to record

14. Developing strategies for recording solutions to story problems

Instructional Materials:

• Investigations in Number, Data, and Space, Pearson Education, Inc., 2012

• Investigations in Number, Data, and Space, Manipulatives Kit for Grade 1

• Investigations in Number, Data, and Space, Cards Package for Grade 1

Differentiation:

Enrichments

• Make 10 with Wild Cards Extension

• Crayon Puzzles About Fewer Extension

• Strategies for Solving Problems Extension

Supplements

• Investigation 1 Quiz

• Make 10 with Ten Frame Cards Intervention

• That’s a 10! Practice

• Investigation 2 Quiz

• Dot Addition with Smaller Numbers Intervention

• Dot and Number Totals Practice

• Investigation 3 Quiz

• Story Problems Intervention

• Story Problem Strategies Practice

Assessed Benchmarks:

1. Find at least five 2-addend combinations of 10

2. Combine two small quantities by at least counting on

3. Add within 20, demonstrating fluency for addition within 10, using strategies such as counting on, making 10, and creating equivalent but easier or known sums

4. Interpret (retell the action and sequence) and solve addition and subtraction story problems

5. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing with unknowns in all positions by using objects, drawings, and equations with a symbol for the unknown number to represent the problem

6. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 by using objects, drawings, and equations with a symbol for the unknown number to represent the problem

7. Subtract one small quantity from another

8. Subtract within 20, demonstrating fluency for subtraction within 10, using strategies such as decomposing a number leading to 10, using the relationship between addition and subtraction, and creating equivalent but easier or known sums

List of Applicable Common Core State Standards for Mathematics Covered in This Unit:

1.0A.1-8

1.NBT.1-3

1.MD.3-4

MP 1-2, 4-6, 8

Suggested Learning Experiences and Instructional Activities:

1. Today’s Number

2. Three Towers

3. Stories about Ten

4. Make 10

5. Quick Images: Ten Frames

6. More Stories about Ten

7. Counters in a Cup

8. How Many Am I Hiding?

9. Tens Go Fish

10. Twelve Crayons in All

11. Crayon Puzzles

12. Dot Addition

13. Five in a Row with Three Cards

14. Addition Story Problems

15. Five in a Row: Subtraction

16. Roll and Record: Subtraction

17. Addition and Subtraction Story Problems

18. Story Problems with Missing Parts

19. True or False?

Technology:

• Fun 4 The Brain Addition Games:

• Fun 4 The Brain Subtraction Games:

• Great site for elementary level online math games:

• Arithmetic Baseball:

• MathBlaster Adventures. (requires a registration which is free):

• Jumpstart Math Adventures. (requires a registration which is free):

• Virtual Manipulatives and Games:

Classroom Routines:

• Developing strategies for counting accurately

• Using the calendar as a tool for keeping track of time

• Developing vocabulary to talk about time (morning, noon, midday, afternoon, etc.) and sequence (first, next, last, before, after, etc.)

• Collecting and recording data

• Estimating quantities up to about 30

• Adding or subtracting small amounts to/from a familiar number

• Investigating numbers that can (and cannot) be made into groups of two

• Counting, describing, and comparing data

• Making sense of a variety of representations of data

• Connecting written numbers and number names

• Using the 100 chart as a tool for counting

• Using the number line as a tool for counting

• Practicing forward and backward counting sequences with numbers up to 100

• Developing and analyzing visual images for quantities

• Finding the total of two or more single digit quantities

• Developing fluency with the addition combinations that make 10

• Using known combinations (i.e., combinations that make 10) to combine numbers

• Using standard notation (+, -, =) to write equations

• Collecting, counting, representing, describing, and comparing data

• Interpreting different representations of data including: pictures, bar graphs, tallies, and Venn Diagrams

UNIT 7: TWOS, FIVES AND TENS (ADDITION, SUBTRACTION AND THE

NUMBER SYSTEM 4) [28 DAYS]

Why Is This Unit Important?

This is the fourth of four units in this grade level where students continue to develop ideas about counting and quantity, the composition of numbers, including work with place value, the structure of the base-ten number system, and the operations of addition and subtraction. In this unit students extend their work in the number system to beyond 100 formulating more efficient ways to count by groups utilizing the base-ten structure of our number system. Students will develop fluency with two addend combinations and are introduced to the concept of equivalency. The big ideas embedded within this unit are:

▪ The base ten structure of the number system

▪ Numbers can be decomposed into other numbers and then recomposed into the original amount

▪ Addition is a process for finding the total of separate parts

▪ Subtraction being the inverse of addition is a process for finding the amounts of separated parts of the total

▪ Addition is commutative, while subtraction is not

Enduring Understandings:

1. Developing strategies for accurately counting a set of objects by ones and by groups

2. Using manipulatives, drawings, tools, and notation to show strategies and solutions

3. Knowing addition combinations of 10

Essential Questions:

1. What patterns do you see in the 100s chart?

2. How can these patterns be used to make counting easier?

3. How can these patterns be used to make adding easier? How about making subtraction easier?

4. In what ways are addition and subtraction related?

5. Describe the strategy you used for addition. Does anyone have a suggested name for this strategy? How is it similar to other strategies we have seen?

6. Describe the strategy you used for subtraction. Does anyone have a suggested name for this strategy? How is it similar to other strategies we have seen?

Acquired Knowledge:

1. Relationship of numbers up to 20 in terms of how they relate to 10 (e.g., 10 + __ or < 10)

2. Considering a 2-digit number as tens and ones

Acquired Skills:

1. Counting and keeping track of amounts up to 60

2. Counting on from a known quantity

3. Organizing objects to count them more efficiently

4. Identifying and using patterns in the number sequence and on the 100 chart

5. Identifying, reading, writing and sequencing numbers to 100 and beyond

6. Counting and combining things that come in groups of 1, 2, 4, 5, and 10

7. Counting by 2s, 5s, and 10s

8. Exploring a 2:1 (the number of hands in a group of people) and a 5:1 relationship

9. (the number of fingers and hands in a group)

10. Counting by numbers other than 1

11. Developing strategies for organizing sets of objects so that they are easy to count and combine

12. Developing meaning for counting by groups of 10

13. Using addition notation (+, =) to record

14. Recording strategies for counting and combining

15. Utilizing notation for equivalent expressions (e.g., 7 + 8 = 10 + 5)

16. Developing fluency with the 2-addend combinations of 10

17. Solving a problem in which the total (10) and one part are known

18. Adding single-digit numbers

19. Describe numbers to 20 in terms of how they relate to 10 (e.g., 10 + __ or < 10)

20. Determining equivalent expressions for a given expression (e.g., 7 + 8 = 10 + __)

21. Represent a 2-digit number as tens and ones

Instructional Materials:

• Investigations in Number, Data, and Space, Pearson Education, Inc., 2012

• Investigations in Number, Data, and Space, Manipulatives Kit for Grade 1

• Investigations in Number, Data, and Space, Cards Package for Grade 1

Differentiation:

Enrichments

• Missing Numbers Between 101 and 200 Extension

• How Many in All? Extension

• Roll Tens with a 100 Mat Extension

Supplements

• Investigation 1 Quiz

• Ten Turns with Ten Frames Intervention

• Counting Strips Practice

• Investigation 2 Quiz

• How Many Hands? Intervention

• How Many Do I See? Practice

• Investigation 3 Quiz

• Roll Tens in a Small Group Intervention

• Solving Ten Plus Problems Practice

Assessed Benchmarks:

1. Identify, read, write, and sequence numbers to 120 (starting from any number less than 120)

2. Begin to count by groups in meaningful ways

3. Gain fluency with the 2-addend combinations of 10

4. Apply properties of operations as strategies to add and subtract: Example if 8+3=11 then 3+8=11 (commutative property) and adding numbers to make 10 such as 2+6+4 as 2+10 (associative property)

5. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.

6. Determine the unknown whole number in an addition or subtraction equation relating three whole numbers

7. Compare two digit numbers based on the meanings of the tens and ones digits, recording the results of the comparisons with the symbols

8. Given a two digit number find 10 more or 10 less than the number, without counting

9. Add within 100, using concrete models or drawings and strategies based on place value (emphasis should be placed on the understanding that tens and tens are added, ones and ones are added, and sometimes it is necessary to compose tens), properties of operations, and/or the relationship between addition and subtraction (relate the strategy used to a written method and explain the reasoning used) including:

- a two digit number and a one digit number

- two digit number and a multiple of 10

10. Subtract multiples of 10 in the range of 10-90 from multiples of 10 in the range of 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 used to a written method and explain the reasoning used)

11. Explain why addition and subtraction strategies work, using place value and the properties of operations

List of Applicable Common Core State Standards for Mathematics Covered in This Unit:

1.0A.1-3, 5-8

1.NBT.1-6

1.MD.3-4

MP 1, 4, 7, 8

Suggested Learning Experiences and Instructional Activities:

1. Ten Turns

2. Revisiting the 100s Chart

3. Missing Numbers

4. What’s Missing?

5. Counting Strips

6. How Many Hands?

7. Problems About Eyes, Ears, and Elbows

8. Counting Body Parts

9. Problems About Fours

10. How Many Fingers?

11. Counting Fingers

12. How Many Squares

13. Problems About Twos, Fours, and Fives

14. Make 10

15. Tens Go Fish

16. Roll Tens

17. Ten Plus

18. How Many Cubes?

19. Plus or Minus 10

20. Adding One to Ten Cubes

21. Adding Tens

22. How Many Now?

Technology:

• Fun 4 The Brain Addition Games:

• Fun 4 The Brain Subtraction Games:

• Arithmetic Baseball:

• MathBlaster Adventures. (requires a registration which is free):

• Jumpstart Math Adventures. (requires a registration which is free):

• Virtual Manipulatives and Games:

Classroom Routines:

• Developing strategies for counting accurately

• Using the calendar as a tool for keeping track of time

• Developing vocabulary to talk about time (morning, noon, midday, afternoon, etc.) and sequence (first, next, last, before, after, etc.)

• Collecting and recording data

• Naming and telling time to the hour and half hour on digital and analog clocks

• Associating times on the hour with daily events

• Connecting written numbers and number names

• Using the 100 chart as a tool for counting

• Using the number line as a tool for counting

• Practicing the forward and backward counting sequences with numbers up to 100

• Counting by 5s and 10s

• Connecting standard notation (+, -, =) to the actions and relationships they represent

• Creating a story problem for a given expression

• Developing strategies for adding and subtracting small numbers

• Solving related problems

• Developing and analyzing visual images for quantities

• Finding the total of two or more single digit quantities

UNIT 8: BLOCKS AND BOOKS (3-D GEOMETRY) [11 DAYS]

Why Is This Unit Important?

Geometry is a part of mathematics that students experience every day. Students bring with them a good deal of informal experience with geometry. Young children use their eyes and hands to interact with shapes and images in their world, they are developing an intuitive sense of how those shapes and images are the same and how they are different. Part of young students’ work in developing mathematical understanding is to begin to observe, describe, compare, and represent the shapes they see around them. This is the second of two units in this grade level where students will extend upon their explorations and focus on the relationships between 2-D and 3-D shapes including their characteristics, attributes, how to compose and decompose them in different ways, and how to sort, categorize and name them. The big ideas embedded in this unit are:

▪ 2-D shapes can be decomposed into other smaller 2-D shapes. Likewise 2-D shapes can be composed into a larger 2-D shape

▪ 3-D shapes can be decomposed into other smaller 3-D shapes. Likewise 3-D shapes can be composed into a larger 3-D shape

▪ The faces of a 3-D shape are 2-D shapes

▪ Shapes are composed of attributes which can be used to sort, classify, compare and identify shapes.

Enduring Understandings:

1. Similarities between 2-D and 3-D shapes

2. The relationships between 2-D and 3-D shapes

Essential Questions:

1. Where do you see this 2-D shape out in the world?

2. Where do you see this 3-D shape out in the world?

3. In what ways are 2-D and 3-D shapes similar? How do they differ?

Acquired Knowledge:

1. Vocabulary to describe 3-D shapes and their attributes

2. Characteristics of 3-D objects

3. Knowing shapes identification

Acquired Skills:

1. Describing 3-D shapes and their attributes

2. Comparing size, shape, and orientation of objects

3. Identifying the characteristics of 3-D objects by touch

4. Describing a rectangular prism

5. Comparing rectangular prisms

6. Observing and describing characteristics of 3-D shapes

7. Identify shapes in the world

8. Describing 3-D structures

9. Matching a 3-D object to a 2-D outline of one of its faces

10. Matching a 3-D object to a 2-D picture of the object

11. Making 3-D objects out of 2-D pieces

12. Making a 2-D representation of a 3-D object or structure

13. Building a 3-D construction from a 2-D representation

Instructional Materials:

• Investigations in Number, Data, and Space, Pearson Education, Inc., 2012

• Investigations in Number, Data, and Space, Manipulatives Kit for Grade 1

• Investigations in Number, Data, and Space, Cards Package for Grade 1

Differentiation:

Enrichments

• Matching Footprints Extension

• Drawing My Building Extension

Supplements

• Investigation 1 Quiz

• Geoblock Footprints Intervention

• Is It a Match? Practice

• Investigation 2 Quiz

• Building and Drawing Intervention

• Find the Blocks Practice

Assessed Benchmarks:

1. Attend to features of 3-D shapes, such as overall size and shape, the number and shape of faces, and the number of corners

2. Distinguish between defining attributes (number of sides, closed sides, etc) and non-defining attributes (color, orientation, over-all size)

3. Build and draw shapes to possess defining attributes

4. Match a 2-D representation to a 3-D shape or structure

5. Compose 3 dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and create new shapes from the composite shape students do not need to learn the formal names of the 3-D shapes

List of Applicable Common Core State Standards for Mathematics Covered in This Unit:

1.0A.1, 2, 6, 8

1.NBT.3

1.MD.3-4

1.G.1-2

MP 7

Suggested Learning Experiences and Instructional Activities:

1. Describing Geoblocks

2. Geoblock Footprints

3. Copying Cube Things

4. Build a Wall

5. Block Pictures

6. Blocks in a Sock

7. Drawing Geoblock Buildings

8. Building and Drawing

9. Introducing 3-D Solids

10. Comparing Cones and Cylinders

Technology:

• Investigations ‘Shapes’ software

• A site that launches into all kinds of fun geometry applications:

• Great site for elementary level online math games:

• Geometry math games:

• Know your shapes? Test yourself by picking off the correct shapes:

• Geometry resources for teachers:

• Interactive geometry Website:

• Virtual manipulatives and games for geometry:

Classroom Routines:

• Developing strategies for counting accurately

• Using the calendar as a tool for keeping track of time

• Developing vocabulary to talk about time (morning, noon, midday, afternoon, and so on) and sequence (first, next, last, before, after, and so on)

• Collecting and recording data

• Counting, describing, and comparing data

• Estimating quantities up to about 30

• Adding or subtracting small amounts to/from a familiar number

• Investigating numbers that can (and cannot) be made into groups of two

• Making sense of a variety of representations of data

• Naming and telling time to the hour and half hour on digital and analog clocks Associating times on the hour with daily events

• Developing visual images of, and language for describing, 2-D shapes

• Identifying names and attributes of 2-D shapes

• Collecting, counting, representing, describing, and comparing data

• Interpreting different representations of data, including pictures, bar graphs, tallies, and Venn diagrams

• Connecting standard notation (+, -, =) to the actions and relationships they represent

• Creating a story problem for a given expression

• Developing strategies for adding and subtracting small numbers

• Solving related problems

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