Groton Public Schools
Curriculum Map
INTRODUCTION
Course Title: Math
Curriculum Area and Grade: Math – Grade 1
Course Purpose:The purpose of this course is to provide a means to implement meaningful methods to understand mathematical concepts, approach problem solving and learn computation at the first grade level. The course incorporates best practices of both traditional and reform mathematics curricula and strikes a balance between promoting children’s natural solution methods and introducing new and effective mathematical practices. In order to promote and implement natural and new methods, as well as to encourage students to become reflective and resourceful problem solvers, the course will assist teachers in developing lessons that create a progressive and logical mathematical environment.
The Learner at this Level:
The First Grade Child:
- Loves to ask questions.
- Learns best through discovery.
- Likes to “work” and to explain things.
Major Learning Goals and Understandings:
Algebraic Reasoning: The First Grade Child:
- Describes counting and number patterns.
- Identifies, extends and translates one- and two-attribute patterns.
- Rationalizes what belongs in the pattern and what does not.
- Describes and demonstrates equivalence.
- Iterates relative positions (outside, inside, top, bottom, left, right).
- Models real-life situations of addition and subtraction by using models, pictures and open sentences.
- Identifies patterns in counting.
- Explores the patterns of days, months, and seasons.
- Makes the connections in simple ratio patterns (one bird has two legs, two birds have four legs).
- Creates generalizations about patterns.
- Arranges several things one after another in a series or pattern according to their differences.
- Develops number sense by counting real-world objects, sounds and movements.
- Understands that the last number said is the quantity.
- May be able to see at a glance the number of items in a small collection.
- Counts and groups by twos, fives and tens.
- Counts back from 10 by ones.
- Develops a deeper understanding of quantities to 100 by using 10 as a referent.
- Models a two-digit number by making groups of tens and ones with objects, such as sticks or snap cubes, before using commercial base-tenmaterials.
- Understands that counting by ones gives the same number as counting by a combination of tens
- Solves problems with objects or graphic representation and invents their own problem solving strategies.
- Writes number sentences only after many problems have been solved using objects and the solutions have been discussed.
- Sees the part-whole relations in addition and subtraction situations.
- Constructs and understands the different ways a quantity can be represented, e.g., seven is three and four; seven is two and five; seven is three less than10.
- Masters basic adding and subtracting combinations using real-world problems, not by memorizing facts in isolation.
- Begins to solve problems without having real objects to count.
- Describes fractions as fair (equal) shares of the whole (unit) or set.
- Can be confused because the whole may consist of one piece or many pieces.
- Begins using informal units of measure to focus directly on the attribute being measured and discussion will then focus on what it means to measure that attribute.
- Needs frequent opportunities to estimate measures during measurement activities.
- Uses plane, “two-dimensional,” and solid, “three-dimensional” figures and their appropriate geometric names, position and direction while putting together and taking part figures (e.g., such as two squares put together can make a rectangle).
- Describes sorting and classifying criteria by moving from simple feature description, (e.g., “short” or “like a box”), to the description of geometric features, (e.g., “it has four sides” or “it is squarish”).
- Creates groupings based on how shapes are alike and different using one or two attributes.
- Tells time by counting the hours.
- Creates two- and three-dimensional designs/patterns and replicates them from memory.
- Records work through multiple representations in written symbols and/or drawings.
- Becomes a more flexible thinker when experiencing many different ways to graph information.
- Can see that graphs and charts display information about attributes and data and that different types of graphic representations tell differentthings about the same data.
- Constructs individual graphs and summarizes the results.
- Makes and discusses predictions about probability experiments.
Units/Concepts for the Year
- Pattern and Quantity
- Addition and Subtraction
- Story Problems
- Tens and Ones Place Value
- Money: Dimes and Pennies
- Graphing and Measuring
- Fractions, Circles Graphs and Clocks
- Working with Money
- Analyzing Story Problems
- Measurement and Estimation
Part 1 – Unit 1
Grade:
1 / Subject:
Math / Course:
Pattern and Quantity / Length of Unit:
About 30 days
Essential Questions and Big Ideas
EQ – What is a pattern?
BI – A pattern is numbers or drawings that are related to one another that allow predictions about the next number or drawing.
EQ – What is quantity?
BI – A quantity represents a group of objects.
Part 2 – Standards and State Frameworks
Algebraic Reasoning: Patterns and Functions
1.1 Understand and describe patterns and functional relationships.
Numerical and Proportional Reasoning
2.1 Understand that a variety of numerical representations can be used to describe quantitative relationships.
2.2 Use numbers and their properties to compute flexibly and fluently.
Geometry and Measurement
3.1 Use properties and characteristics of two-dimensional shapes.
Grade Level Expectations / The Students will be able to: / CMT Correlations
1.1.1Sort, classify and order numbers and objects by one and two attributes including size, shapes, color, texture, orientation, position, and use and explain the reason or rule used.
1.1.2Recognize, extend, and create one-attribute patterns. Describe the pattern and the rule.
1.1.4Develop and test generalizations based on observations of patterns and relationships.
1.2.5. Model real-life situations that represent the result of counting, combining and separation of sets of objects (addition and subtraction of whole numbers) with objects, pictures, symbols and open-ended sentences.
2.1.2 Compare and order quantities of up to 100 objects, including naming a number that is one or 10 more or less than a given number.
2.1.4 Identify ordinal numbers up to 10th with an ordered set of objects (e.g., point to the fifth crayon lined up on the table).
2.2.11 Count and group at least 100 objects by tens.
2.2.12Identify read and write numerals to 100.
2.2.14 Solve contextual problems using all addition sums to 18 and subtraction differences from 10 with flexibility and fluency. /
- Sort, classify and order numbers and objects.
- Identify and extend repeating patterns
- Develop and test generalizations.
- Model real-life situations using addition and subtraction of whole numbers.
- Compare and order numbers to 10 and identify a number as one or 10 more or less than a given number.
- Identify ordinal numbers, and even and odd in numbers to 10.
- Find and identify pairs of numbers embedded in numbers through 10.
- Identify, read and write numerals to 100.
- Solve contextual problems using addition and subtraction.
- Identify and draw two-dimensional solids including circles, triangles, rectangles and squares.
- Copy designs from memory.
2A. Relate whole numbers to pictorial representations of base ten blocks and vice versa.
4A. Order two-and three-digit whole numbers.
4B. Describe magnitude of two- and three-digit whole numbers.
5B. Identify the appropriate operation or number sentence to solve a story problem.
5C. Write story problems from addition or subtraction number sentences.
6A. Add and subtract facts to 18.
7A. Add and subtract one- and two-digit whole numbers without regrouping.
7B. Add one- and two-digit whole numbers with regrouping.
9A. Solve simple story problems involving addition (with/without regrouping) or subtraction (without regrouping).
9B. Solve simple story problems involving addition (with/without regrouping) or subtraction (without regrouping) with extraneous information.
17A. Identify and recognize two-dimensional geometric shapes and figures, including number of angles and sides of polygons.
17B. Draw two-dimensional geometric shapes and figures.
22A. Extend or complete patterns, or identify rules using numbers and attributes.
22B. Extend or complete patterns and state rules using numbers and attributes.
24A. Identify objects that are the same or different by one attribute.
24B. Sort objects into two groups by a common attribute.
25A. Solve extended numerical and statistical problems.
Part 3 – Common Unit Assessments
Pre Assessment:
Math Expressions Assessment Guide
Unit 1 Test Form B (multiple choice)
Post Assessment:
Math Expressions Assessment Guide
Unit 1 Test Form A (short response)
Weekly Math Review Quiz
Part 4 – Common/Assured Learning Experiences
Promethean Board Activity: Student Work
Common Vocabulary:
Number, shapes- triangles, circles, rectangles, squares, ovals, patterns, number words, 0-10, more, less, equal, partner( addend), total, ordinal number words
Suggested Literature::
Ten Little Rabbits
Circles and Squares Everywhere by Max Grover
Any counting or shape books
Daily Math Review (Computational review)
Math Journaling (End of Unit)
Part 5-Teacher Notes
Teacher Resources
Differentiated Instruction
LESSON PLANS
FLIP CHARTS
Electronic Resources:
Part 1 – Unit 2
Grade:
1 / Subject:
Math / Course:
Addition and Subtraction / Length of Unit:
About 25 days
Essential Questions and Big Ideas
EQ - What is addition?
BI - Addition means combining groups.
EQ - What is subtraction?
BI - Subtraction means separating groups.
EQ – What is a number sentence?
BI - A number sentence represents a relationship between a quantity and a number.
Part 2 – Standards and State Frameworks
Algebraic Reasoning: Patterns and Functions
1.2 Represent and analyze quantitative relationships in a variety of ways.
1.3 Use operations, properties, and algebraic symbols to determine equivalence and solve problems.
Numerical and Proportional Reasoning
2.2 Use numbers and their properties to compute flexibly and fluently, and to reasonably estimate measures and quantities.
Geometry and Measurement
3.2 Use spatial reasoning, location and geometric relationships to solve problems.
Grade Level Expectations / The Students will be able to: / CMT Correlations
1.2.5.1.2.5Model real life situations that represent the result of counting, combining and separation of sets of objects (addition, and subtraction of whole numbers) with objects, pictures, symbols and open-ended sentences.
1.3.6 Demonstrate understanding of equivalence or balance with objects, models, diagrams, operations or numbers, using a balance scale, or arm balance showing the same amount on both sides.
2.2.9 Count by rote to at least 100.
2.2.10 Count on from a given amount, orally and with models, and count back from 10.
2.2.12 Identify, read and write numerals to 100.
2.2.13 Create problems and write one- and two-digit number sentences that reflect contextual situations and real world experiences. Solve the problems using a variety of method including models, pictures, pencil and paper estimation and mental computation, and describe the reasoning and strategies used. For example: Tell a story or draw a picture for the problem that can be solved using a number sentence 10+6=16.
2.2.14 Solve contextual problems using all addition sums to 18 and subtraction differences from 10 with flexibility and fluency.
2.2.16 Identify and name pennies, nickels, dimes, and quarters.
2.2.17 Determine and compare sets of pennies and dimes valued up to $1.00; trade sets of pennies for dimes and vice versa. For example: Jose’ has three dimes and eight pennies. Andrea has two dimes and 17 pennies. If they do not have the same amount of money, who has more or less? How much more or less.
3.2.5. Describe location, direction, and position of objects using terms such as left, right, and opposite. /
- Use pictures to show simple addition and subtraction problems.
- Demonstrate understanding of equivalence or balance.
- Count to and identify, read and write numerals to 100.
- Count on and back by ten.
- Create problems and write one- and two-digit number sentences.
- Solve contextual problems.
- Identify, determine and compare sets of pennies and dimes.
- Describe location, direction and position of objects.
2B. Relate fractions of regions and sets to pictures and vice versa.
2C. Label and/or shade fractional parts of regions and/or sets.
3A. Relate equivalent fractions to pictorial representations.
5B. Identify the appropriate operation or number sentence to solve a story problem.
5C. Write story problems from addition or subtraction number sentences.
6A. Add and subtract facts to 18.
7A. Add and subtract one- and two-digit whole numbers without regrouping.
7B. Add one- and two-digit whole numbers with regrouping.
8A. Add and subtract fractions with like denominators.
9A. Solve simple story problems involving addition (with/without regrouping) or subtraction (without regrouping).
9B. Solve simple story problems involving addition (with/without regrouping) or subtraction (without regrouping) with extraneous information.
10A. Identify the best expression to find an estimate.
11A. Identify a reasonable estimate to a problem.
15A. Estimate lengths and areas by comparing.
17B. Draw two-dimensional geometric shapes and figures.
25A. Solve extended numerical and statistical problems.
Part 3 – Common Unit Assessments
Pre Assessment:
Math Expressions Assessment Guide
Unit 2 Test Form B (multiple choice)
Post Assessment:
Math Expressions Assessment Guide
Unit 2 Test Form A (short response)
Weekly Math Review Quiz
Part 4 – Common/Assured Learning Experiences
Promethean Board Activity: Student Work
Common Vocabulary:
Number, addition, subtraction, total, partners (addends), minus, more, less, equal, number sentence, counting on, penny, nickel, coin, story problem
Suggested Suggested Literature::
Count On Your Fingers African Style by Claudia Zaslavsky.
Counting Our Way to Maine by Maggie Smith
Additional Suggested Literature:-Math Expressions- Volume 1 p. T17
Daily Math Review (Computational review)
Math Journaling (End of Unit)
Part 5-Teacher Notes
Teacher Resources
Differentiated Instruction
LESSON PLANS
FLIP CHARTS
Electronic Resources:
Part 1 – Unit 3
Grade:
1 / Subject:
Math / Course:
Story Problems / Length of Unit:
About 25 days
Essential Questions and Big Ideas
EQ - What is a story problem?
BI - A story problem is a math problem using everyday situations with symbols and pictures.
Part 2 – Standards and State Frameworks
Algebraic Reasoning: Patterns and Functions
1.2 Represent and analyze quantitative relationships in a variety of ways.
1.3 Use operations, properties, and algebraic symbols to determine equivalence and solve problems.
Numerical and Proportional Reasoning
2.2 Use numbers and their properties to compute flexibly and fluently, and to reasonably estimate measures and quantities.
Grade Level Expectations / The Students will be able to: / CMT Correlations
1.2.5 Model real life situations that represent the result of counting, combining, and separation of objects (addition and subtraction of whole numbers) with objects, pictures, symbols, and open sentences.
1.3.6. Demonstrate understanding of equivalence or balance with objects, models, diagrams, operations or numbers, using a balance scale, or arm balance showing the same amount on both sides.
2.2.9 Count by rote to at least 100.
2.2.10 Count on from a given amount, orally and with models, and count back from 10.
2.2.12Identify, read and write numerals to 100.
2.2.13 Create problems and write one- and two-digit number sentences that reflect contextual situations and real world experiences. Solve the problems using a variety of methods including models, pictures, pencil and paper estimation and mental computation, and describe the reasoning and strategies used. For example: Tell a story or draw a picture for the problem that can be solved using a number sentence 10+6=16. /
- Model and identify the appropriate operation or number sentence to solve a story problem.
- Demonstrate understanding of equivalence or balance.
- Create and write story problems from addition and subtraction number sentences.
- Count to, identify, read and write numerals to 100.
- Add and subtract facts to 10.
- Solve word problems using a variety of methods.
5C. Write story problems from addition or subtraction number sentences.
6A. Add and subtract facts to 18.
7A. Add and subtract one- and two-digit whole numbers without regrouping.
7B. Add one- and two-digit whole numbers with regrouping.
9A. Solve simple story problems involving addition (with/without regrouping) or subtraction (without regrouping).
9B. Solve simple story problems involving addition (with/without regrouping) or subtraction (without regrouping) with extraneous information.
25A. Solve extended numerical and statistical problems.
Part 3 – Common Unit Assessments
Pre Assessment:
Math Expressions Assessment Guide
Unit 3 Test Form B (multiple choice)
Post Assessment:
Math Expressions Assessment Guide
Unit 3 Test Form A (short response)
Weekly Math Review Quiz
Part 4 – Common/Assured Learning Experiences
Promethean Board Activity: Student Work
Common Vocabulary:
Addition, subtraction, total, partners (addends), equation, story problems, equivalence, number sentence, counting on.
Suggested Suggested Literature::
Too Many Dinosaurs by Bob Barner (addition concepts)
Domino Addition by Lynette Long
Additional Suggested Literature:-Math Expressions-Houghton Mifflin Harcourt Volume 1 p. T17
Daily Math Review (Computational review)
Math Journaling (End of Unit)
Part 5-Teacher Notes
Teacher Resources
Differentiated Instruction
LESSON PLANS
FLIP CHARTS
Electronic Resources:
Part 1 – Unit 4
Grade:
1 / Subject:
Math / Course:
Tens and Ones
Place Value / Length of Unit:
About 20 days
Essential Questions and Big Ideas
EQ – How do you determine a value of a number?