Great Meadows Regional
Mathematics Curriculum
First Grade
CURRICULUM GUIDE
Approved
August 22, 2017
Mr. David C. Mango, Superintendent
Mrs. Debra Grigoletti, Director of Curriculum & Instruction
Developed by:
Colleen Schubert
Jennifer Daly
This curriculum may be modified through varying techniques,
strategies and materials, as per an individual student’s
Individualized Education Plan (IEP).
Approved by the Great Meadows Regional Board of Education
at the regular meeting held on August 22, 2017
and
Aligned with the New Jersey Common Core Standards and New Jersey Student Learning Standards
Table of Contents
Component / PagePhilosophy and Rationale / 3
Mission Statement / 3
Scope and Sequence / 3
Units:
- Addition and Subtraction Concepts
2. Addition and Subtraction Strategies / 11
3. Addition and Subtraction Relationships / 15
4. Count, Model, and Compare Numbers / 18
5. Two-Digit Addition and Subtraction / 21
6. Measurement and Data / 24
7. Three-Dimensional and Two-Dimensional Geometry / 28
NJ Content Standards Link / 31
21st Century Skills Link / 32
Philosophy and Rationale
For students to build critical thinking and problem solving skills in mathematics, they must develop an understanding of addition and subtraction that includes strategies for solving problems; an understanding of whole number relationships, including place value and its representation; an understanding of measurement and time to engage in real-world solutions; and an understanding of attributes to compose and decompose geometric shapes. An effective standards-based environment will push students to explore multiple strategies, use appropriate tools, and pursue the application of a range of skills in daily life.
Mission Statement
The Great Meadows Regional School District will provide quality educational opportunities that ensure the individual success of all students within a safe and supportive environment and to build lifelong learners who will meet society’s challenges into and beyond the 21st century. To that end, it is anticipated that all students will achieve the New Jersey Student Learning Standards at all grade levels.
Scope and Sequence
Unit 1: Addition and Subtraction Concepts
Lesson Skills and Strategies
●Chapter 1
●Use pictures to add to
●Model adding to
●Model putting together
●Model addition
●Add zero
●Add in any order
●Put together numbers to ten
●Addition to ten
●Chapter 2
●Use pictures to show taking from
●Model taking from
●Model taking apart
●Model subtraction and problem solving
●Use pictures and subtraction to compare
●Subtract to compare
●Subtract all or zero
●Take apart numbers
●Subtraction from ten or less
Vocabulary
●Chapter 1
●Add, addends, addition sentence, is equal to =, order, plus +, sum, zero
●Chapter 2
○Compare, difference, fewer, minus -, more, subtract, subtraction sentence
Time Allotment: 30 to 35 school days
Unit 2:Addition and Subtraction Strategies
Lesson Skills and Strategies
●Chapter 3
●Add in any order
●Count on
●Add doubles
●Use doubles to add
●Doubles plus 1 and minus 1
●Practice the strategies
●Add 10 and more
●Make a 10 to add
●Use make a 10 to add
●Hands on: Add 3 numbers
●Add 3 numbers
●Use addition strategies
●Chapter 4
●Count back
●Hands on: Think addition to subtract
●Think addition to subtract
●Use 10 to subtract
●Break apart to subtract
●Use subtraction strategies
Vocabulary
●Chapter 3
●Count on, doubles, doubles plus 1, doubles minus 1, make a ten
Vocabulary
●Chapter 4
●Count back
Time Allotment: 35 to 40 school days
Unit 3:Addition and Subtraction Relationships
Lesson Skills and Strategies
●Chapter 5
●Problem Solving: Add or Subtract?
●Record related facts
●Identify related facts
●Use addition to check subtraction
●Unknown numbers
●Use related facts
●Choose an operation
●Ways to make numbers to 20
●Equal and not equal
●Facts practice to 20
Vocabulary
●Chapter 5
●Related facts, add, subtract
Time Allotment: 20 to 25 school days
Unit 4:Count, Model, and Compare Numbers
Lesson Skills and Strategies
●Chapter 6
●Count by ones to 120
●Count by tens to 120
●Understand tens and ones
●Make ten and ones
●Hands on: Tens
●Tens and ones to 50
●Tens and ones to 100
●Show numbers in different ways
●Model, read, and write numbers from 100-110
●Model, read, and write numbers from 111-120
●Chapter 7
●Greater than >
●Less than <
●Use symbols to compare
●Compare numbers
●10 less, 10 more
Vocabulary
●Chapter 6
●digits, ones, ten, hundred
●Chapter 7
●is greater than >, is less than <, is equal to =
Time Allotment: 30 to 35 school days
Unit 5: Two Digit Addition and Subtraction
Lesson Skills and Strategies
●Chapter 8
●Add and subtract within 20
●Add tens
●Subtract tens
●Use a hundred chart to add
●Use models to add
●Make ten to add
●Use place value to add
●Addition word problems
●Related addition and subtraction
Vocabulary
●Chapter 8
●Add, addends, addition sentence, is equal to =, order, plus +, sum, zero, Compare, difference, fewer, minus -, more, subtract, subtraction sentence, tens, ones
Time Allotment: 20 to 25 school days
Unit 6: Measurement and Data
Lesson Skills and Strategies
●Chapter 9
●Order objects by length
●Indirect measurement
●Measure length using nonstandard units
●Make a nonstandard measuring tool
●Measure and compare
●Time to the hour
●Time to the half hour
●Tell time to the hour and half hour using analog and digital clocks
●Use the hour hand to draw and write times on analog and digital clocks
●Chapter 10
●Read picture graphs
●Make picture graphs
●Read bar graphs
●Make bar graphs
●Read tally charts
●Make tally charts
●Represent data
Vocabulary
●Chapter 9
●Longest, shortest, hour hand, half hour, hour, minute hand, minutes
●Chapter 10
●Picture graph, bar graph, tally chart, tally mark
Time Allotment: 25 to 30 school days
Unit 7: Three-Dimensional and Two-Dimensional Geometry
Lesson Skills and Strategies
●Chapter 11
●Identify and describe three-dimensional shapes
●Combine three-dimensional shapes
●Make new three-dimensional shapes
●Take apart three-dimensional shapes
●Identify two-dimensional shapes on three-dimensional shapes
●Chapter 12
●Sort two-dimensional shapes
●Describe two-dimensional shapes
●Combine two-dimensional shapes
●Combine more shapes
●Make new two-dimensional shapes
●Find shapes in shapes
●Decompose two-dimensional shapes into parts
●Identify Equal and unequal parts
●Halves (2 equal shares)
●Fourths (4 equal shares)
Vocabulary
●Chapter 11
●Cone, cube, curved surface, cylinder, flat surface, rectangular prism, sphere
●Chapter 12
●Circles, rectangles, sides, square, triangles, vertices, hexagon, trapezoid, equal parts, equal shares, unequal parts, unequal shares, half of, halves, fourth of, fourths, quarter of, quarters
Time Allotment: 20 to 30 school days
Stage 1: Desired Results
Unit: 1
Topic: Addition and Subtraction Concepts
Content Standards
1.OA.A.1
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, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem
1.OA.B.3
Apply properties of operations as strategies to add and subtract.
1.OA.C.6
Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
1.OA.D.8
Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.
Essential Questions
●How do pictures show adding to?
●How do you model adding to a group?
●How do you model putting together?
●How do you solve addition problems by making a model?
●What happens when you add zero to a number?
●Why can you add addends in any order?
●How can you show all the ways to make a number?
●Why are some addition facts easy to add?
●How can you show taking from with pictures?
●How do you model taking from a group?
●How do you model taking apart?
●How do you solve subtraction problems by making a model?
●How can you use pictures to compare and subtract?
●How can you use models to compare and subtract?
●What happens when you subtract zero from a number?
●How can you show all of the ways to take apart a number?
●Why are some subtraction facts easy to subtract?
Enduring Understandings
●Drawing a picture acts as a representation of a number and/or part of an operation.
●Making a model acts as a representation of a number and/or part of an operation.
●Subtracting zero from a number does not change the difference.
●Versatile mathematical thinkers apply numerous strategies to solve problems using addition and subtraction.
Knowledge and Skills (SWBAT embedded course proficiencies)
Students will be able to:
●Use pictures to “add to” and find sums.
●Use concrete objects to solve “adding to” addition problems.
●Use concrete objects to solve “putting together” addition problems.
●Solve adding to and putting together situations using the strategy make a model.
●Understand and apply the additive identity property for addition.
●Explore the commutative property of addition.
●Model and record all the ways to put together numbers within ten.
●Build fluency for addition within ten.
●Use pictures to show “taking from” and find differences.
●Use concrete objects to solve “taking from” subtraction problems.
●Use concrete objects to solve “taking apart” subtraction problems.
●Solve “taking from” and “taking apart” subtraction problems.
●Compare pictorial groups to understand subtraction.
●Model and compare groups to show the meaning of subtraction.
●Identify how many are left when subtracting all or 0.
●Model and record all the ways to take apart numbers within 10.
●Build fluency for subtraction within 10
Stage 2: Evidence of Understanding, Learning Objectives and Expectations
Benchmarks (embedded student proficiencies)
Assessment Methods (formative, summative, other evidence and/or student self- assessment)
●Chapters 1 and 2 summative assessments
●Math games for fluency (Scoot!, Around the Room) as formative assessments
●Teacher observation
●Teacher created lesson checks
●Mid-chapter checkpoint assessment
●Homework and practice pages as formative assessments
Stage 3: Learning Plan
Students will be engaged through large and small group discussion allowing students to revise, rethink, and refine their understanding of topics covered. Students will be challenged and engaged through applicable real life problems and projects. Integrating the Standards for Mathematical Practice (MP1-8) will support student development of topics and skillsets.
Differentiation will be provided through written, visual, auditory, and hands-on activities to meet all learning styles. We will use various learning centers, differentiated lesson materials, and Go Math! Grab-and-Go resources including modified worksheets for individual needs. Students will be provided with individualized instruction as needed. Introduction of new vocabulary will help students express their ideas, opinions, and feelings. These activities allow students to participate in collaborative conversations with diverse partners and adults in small and large groups.
Students will deepen learning through activities such as Smartboard lessons (Go Math! created and teacher created), mathematical games, use of classroom computers, computer mathematics programs, educational songs and video clips from YouTube and Brain POP Jr., manipulatives such as counters, magnetic numbers, and school website links to online educational games. Related read alouds will engage students and provide a cross curricular learning experience (Examples: The Class Party, Math Club, Join Us, Busy Bugs, Milk for Sale)
In this Unit, the students will practice the 21st Century Skills of Communication and Collaboration, Critical Thinking and Problem Solving, as well as Creativity and Innovation. We will also focus on Life and Career Skills by supporting students’ interactions with peers and teachers throughout their school day and by assigning students real life mathematical problems to solve. Unit performance tasks build on these skillsets. We will integrate digital tools through use of the Smartboard and classroom computers.
Time Allotment
30-35 school days
Resources
Houghton-Mifflin Go Math! mathematics series for first grade (Chapter 1 and 2 student book and teacher editions)
Supplementary Resources:Go Math! Curriculum Materials such as:
Mathematics Readers, Smartboard Interactive Lessons, Grab-and-Go, Family Connections, Teacher Websites, Chapter Resources (Reteach and Enrich)
Supplemental texts, Brain Pop, Jr., related read alouds
Differentiation
Whole Group Instruction, Small Group Instruction, One-on-one Instruction, Hands-on manipulatives (counters, connecting cubes), Math Centers, Mathematics Readers, Starfall, ABCYA, ABC Mouse, PBS Kids, Flashcards, Scholastic Core Clicks, Learning Games, Multi-Sensory explorations, In-Class Support, Think Central (Dashboard), Smartboard (Smart Exchange), Go Math! Chapter Resources
Stage 1: Desired Results
Unit: 2
Topic: Addition and Subtraction Strategies
Content Standards
1.OA.A.1
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, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
1.OA.A.2
Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
1.OA.B.3
Apply properties of operations as strategies to add and subtract.
1.OA.B.4
Understand subtraction as an unknown-addend problem.
1.OA.C.5
Relate counting to addition and subtraction (e.g., by counting on 2 to add 2)
1.OA.C.6
Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
Essential Questions
●What happens if you change the order of the addends when you add?
●How do you count on one, two, or three?
●What are doubles facts?
●How can you use doubles to help you add?
●How can you use what you know about doubles to find other sums?
●What strategies can you use to solve addition fact problems?
●How can you use a ten frame to add ten and some more?
●How do you use the make a ten strategy to add?
●How can you make a ten to help you add?
●How can you add three addends?
●How can you group numbers to add three addends?
●How do you solve addition word problems by drawing a picture?
●How can you count back one, two, or three?
●How can you use an addition fact to find the answer to a subtraction fact?
●How can you use addition to help you find the answer to a subtraction fact?
●How can you make a ten to help you subtract?
●How do you break apart a number to subtract?
●How can acting out a problem help you solve the problem?
Enduring Understandings
●Subtraction means separating two or more.
●A subtraction answer is called a difference.
●Addition means joining or putting together two or more numbers.
●An addition answer is called a sum.
●Addition and subtraction is facilitated by making groups of 10.
●Versatile mathematical thinkers apply numerous strategies to solve problems using addition and subtraction.
Knowledge and Skills (SWBAT embedded course proficiencies)
Students will be able to:
●Understand and apply the Commutative Property of Addition for sums within 20
●Use count on 1, 2, or 3 as a strategy to find sums within 20
●Use doubles as a strategy to solve addition facts with sums within 20
●Use doubles to create equivalent but easier sums
●Use doubles plus 1 and doubles minus 1 as strategies to find sums within 20
●Use the strategies count on, doubles, doubles plus 1, and doubles minus 1 to practice addition facts within 20
●Use a ten frame to add 10 and an addend less than 10
●Use make a ten as a strategy to find sums within 20
●Use numbers to show how to use the make a ten strategy to add
●Use the Associative Property of Addition to add three addends
●Understand and apply the Associative Property or Commutative Property of Addition to add three addends
●Solve adding to and putting together situations using the strategy draw a picture
●Use count back 1, 2, or 3 as a strategy to subtract
●Recall addition facts to subtract numbers within 20
●Use addition as a strategy to subtract numbers within 20
●Use make a 10 as a strategy to subtract
●Subtract by breaking apart to make a ten
●Solve subtraction problem situations using the strategy act it out
Stage 2: Evidence of Understanding, Learning Objectives and Expectations
Benchmarks (embedded student proficiencies)
Assessment Methods (formative, summative, other evidence and/or student self- assessment)
●Chapters 3 and 4 summative assessments
●Math games for fact fluency (Scoot!, Around the Room) as formative assessments
●Teacher observation
●Teacher created lesson checks
●Mid-chapter checkpoint assessment
●Homework and practice pages as formative assessments
Stage 3: Learning Plan
Students will be engaged through large and small group discussion allowing students to revise, rethink, and refine their understanding of topics covered. Students will be challenged and engaged through applicable real life problems and projects. Integrating the Standards for Mathematical Practice (MP1-8) will support student development of topics and skillsets.
Differentiation will be provided through written, visual, auditory, and hands-on activities to meet all learning styles. We will use various learning centers, differentiated lesson materials, and Go Math! Grab-and-Go resources including modified worksheets for individual needs. Students will be provided with individualized instruction as needed. Introduction of new vocabulary will help students express their ideas, opinions, and feelings. These activities allow students to participate in collaborative conversations with diverse partners and adults in small and large groups.