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Category: Grade 1 Math

  • Grade 1 Math Unit 5

    Geometry

    Unit description: Students will learn to distinguish attributes of shapes and compose shapes with given attributes. They will identify and divide shapes into halves and fourths/quarters,

    Essential Outcomes of the Unit

    Geometry- Reason with shapes and their attributes

    1.G.1 Distinguish between defining attributes versus non-defining attributes for a wide variety of shapes. Build and/or draw shapes to possess defining attributes.

    1.G.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. Note: Students do not need to learn formal names such as “right rectangular prism.”

    1.G.3 . 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, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

    Essential Questions and Big Ideas

    How do we identify shapes?

    • Two and three dimensional shapes have attributes that allow them to be identified.
    • Some shapes are composed from other shapes. Some shapes can be decomposed into smaller shapes.

    How do we recognize wholes and parts?

    • Composite shapes can be composed and decomposed into parts.
    • Some shapes can be broken into smaller equal parts.
    • Two equal parts of a whole are called halves.
    • Four equal parts of a whole are called quarters or fourths.
    • The more equal parts a whole is broken into, the smaller each part is.

    Download the complete Grade 1 Math Unit 5 framework to customize for your own planning.

  • Grade 1 Math Unit 4

    Measurement and Data

    Unit description: In this unit students will learn to tell time to the hour and half-hour using analog and digital clocks. The students will learn to identify coins and their values and to use the cent (¢) sign. The students will count combinations of dimes and pennies within 100 cents.The students also learn to measure and compare lengths using standards and nonstandard measuring tools. The students will organize, represent and interpret data, including asking and answering questions and comparing amounts across categories.

    Essential Outcomes of the Unit

    Measurement and Data- Tell and write time and money

    1.MD.3a . Tell and write time in hours and half-hours using analog and digital clocks. Develop an understanding of common terms, such as, but not limited to, o’clock and half past.

    1.MD.3b Recognize and identify coins (penny, nickel, dime, and quarter) and their value and use the cent symbol (¢) appropriately. 

    1.MD.3c Count a mixed collection of dimes and pennies and determine the cent value (total not to exceed 100 cents)

    Measurement and Data- Represent and interpret data.

    1.MD.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

    Other Standards Addressed in the Unit

    Measurement and Data- Measure lengths indirectly and by iterating length units

    1.MD.1 Order three objects by length; compare the lengths of two objects indirectly by using a third object.

    1.MD.2 Measure the length of an object using same-size “length units” placed end to end with no gaps or overlaps. Express the length of an object as a whole number of “length units.” 

    Essential Questions and Big Ideas

    How do we know the time?

    • Analog and digital clocks tell us the time.

    What is money and how do we know its worth?

    • Money is made up of bills and coins that have a certain value that can be exchanged for goods and services.
    • American money is valued in dollars(bills) and cents(coins).
    • The coins are:
      • Penny: 1 cent, 1¢
      • Nickel: 5 cents, 5¢
      • Dime: 10 cents, 10¢
      • Quarter: 25 cents, 25¢

    How do we measure and compare lengths?

    • Standard and non-standard tools can be used to measure lengths.
    • Lengths of objects can be compared when measured.

    How can data be displayed and analyzed?

    • Data can be displayed using charts and graphs.
    • Data can be analyzed by asking and answering questions and comparing amounts across categories.

    Download the complete Grade 1 Math Unit 4 framework to customize for your own planning.

  • Grade 1 Math Unit 3

    Place Value Comparison- Addition and Subtraction Beyond 20

    In this unit, students will learn to use their number sense to compare (using symbols  >, =, and <.) and order values of two two-digit numbers. They will model, write and solve addition and subtraction equations within 100 including composing new tens when necessary when adding. The students will apply mental math strategies when adding and subtracting multiples of ten.

    Essential Outcomes of the Unit

    Number and Operations in Base Ten- Understand place value

    NBT.3 Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

    Number and Operations in Base Ten- Use place value understanding and properties of operations to add and subtract

    NBT.4 Add within 100, including • a two-digit number and a one-digit number, • a two-digit number and a multiple of 10. Use concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones, and sometimes it is necessary to compose a ten. Relate the strategy to a written representation and explain the reasoning used.

    Other Standards Addressed in the Unit

    Number and Operations in Base Ten- Understand place value

    NBT.2c Understand the numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

    Number and Operations in Base Ten- Use place value understanding and properties of operations to add and subtract

    NBT.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

    NBT.6 . Subtract multiples of 10 from multiples of 10 in the range 10-90 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 representation and explain the reasoning

    Essential Questions and Big Ideas

    How can we compare values of numbers?

    • Numbers sense and understanding of place value are used to compare values of numbers.
    • The symbols symbols  > means more than, = means equal to, and < means less than when comparing two numbers.

    How do we add and subtract within 100?

    • Concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction can be used to add and subtract within 100.
    • Sometimes it is necessary to compose a new ten when adding within 100.

    How can we use number sense and understanding of place value to add and subtract using mental math?

    • Understanding number pairs that make ten help to add and subtract mentally.
    • Understanding place value and being able to count by tens and add ones can be used to add and subtract mentally.

    Download the complete Grade 1 Math Unit 3 framework to customize for your own planning.

  • Grade 1 Math Unit 2

    Intro to Place Value through Addition and Subtraction within 20

    Unit description: This unit serves as a bridge from problem solving within 10 to work within 100 as students begin to solve addition and subtraction problems involving teen numbers. In unit 1, students were encouraged to move beyond the beginning strategy of counting all to the more efficient counting on. Now, they go beyond that level to decomposition and composition strategies, informally called make ten or take from ten. Students will work on the concept of addition and subtraction within 20 and focus on building fluency within 10. Mastery of facts is not expected at this point in the year. They will develop an understanding of ten as a unit to analyze teens as ten and some ones and use modalities to build individual numbers with tens/ones while counting. Students will compare two two-digit numbers using symbols (<,>,=).

    Essential Outcomes of the Unit

    Numbers in Base Ten

    Understand place value
    • 1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones.
    • 1.NBT.2a Understand 10 can be thought of as a bundle of ten ones, called a “ten”.
    • 1.NBT.2b Understand the numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
    • 1.NBT.3 Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

    Other Standards Addressed in this Unit

    Operations in Algebraic Thinking

    Represent and solve problems involving addition and subtraction.
    • 1.OA.1 Use addition and subtraction within 20 to solve one-step word problems involving situations of adding to, taking from, putting together, taking apart, and/or comparing, with unknowns in all positions.
      • Note: Problems should be represented using objects, drawings, and equations with a symbol for the unknown number. Problems should be solved using objects or drawings, and equations.
    • 1.OA.2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20.
    Understand and apply properties of operations and the relationship between addition and subtraction.
    • 1.OA.3 Apply properties of operations as strategies to add and subtract.
      • (Note: Students need not use formal terms for these properties. When students use the making ten strategy (NY-1.OA.6), they are applying the Associative property of addition.
    • 1.OA.4 Understand subtraction as an unknown-addend problem within 20.

    All work with properties (NY-1.OA.3) and place value (e.g., NY-1.NBT.2 & 4) should be seen as an investigation and use of the structure of the number system and of arithmetic.

    Add and subtract within 20.
    • 1.OA.5 Relate counting to addition and subtraction.
    • 1.OA.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. e.g., Which of the following equations are true and which are false?
      6 = 6   7 = 8 – 1   5 + 2 = 2 + 5   4 + 1 = 5 + 2
    • 1.OA.8 Determine the unknown whole number in an addition or subtraction equation with the unknown in all positions. e.g., Determine the unknown number that makes the equation true in each of the equations
      8 + ? = 11   – 3 = 5   6 + 6 = □

    Essential Questions and Big Ideas

    1. Why is it important to know multiple strategies in solving addition/subtraction problems?

      • Strategies can be used to decompose complex problems to make an easier problem.
      • Strategies help to solve addition and subtraction problems within 20 quicker.

    2. How are problem solving strategies connected to number relationships?

      • Problem solving structures reinforce part/part/whole and number combinations within 20.
      • Each type of word problem situation (adding to, taking from, putting together, taking apart, comparing) reflects number relationships.

    3. What is significant about the teen numbers (related to 10)?

      • Explain the value of each digit in a two digit number.
      • Represent a 2 digit numeral using “tens” and “ones.”
      • Build and decompose numbers into tens and ones.
      • Identify a bundle of 10 ones as a “ten”.

    4. How is counting connected to quantity in a number?

      • Use comparison words greater than, less than, and equal to communicate understanding of the relationship between the numbers.

    5. How does using objects and drawings help me represent problems in multiple ways?

      • Use models to represent 2 sets of numbers.
      • When given a set of objects (ranging from 0-120), represent the quantity with a written numeral.
      • Represent a problem situation involving 2-digit numbers using any combination of words, numbers, physical objects, or symbols.

    Download the complete Grade 1 Math Unit 2 framework to customize for your own planning.

  • Grade 1 Math Unit 1 – Parts 1-2

    Operations and Algebraic Thinking

    Unit description: In this unit, students will progress towards fluency with addition and subtraction of numbers to 10 (1.OA.6) using strategies to advance them from counting all to counting on, which leads many students then to decomposing and composing addends and total amounts. They will represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), and act out situations, verbal explanations, expressions, or equations. They will understand the relationship between addition and subtraction and the meaning of the equal sign. Applying all of this knowledge and skill, students will use problem solving structures to solve addition and subtraction word problems within 10 (using both two and three whole numbers for addition) involving all situations using objects, drawings, and equations.

    Download the complete Grade 1 Math Unit 1 frameworks to customize for your own planning:

    Operations and Algebraic Thinking

    NY-1.OA.1 – Use addition and subtraction within 20 to solve one-step word problems involving situations of adding to, taking from, putting together, taking apart, and/or comparing, with unknowns in all positions. Note: Problems should be represented using objects, drawings, and equations with a symbol for the unknown number. Problems should be solved using objects or drawings, and equations

    NY-1.OA.5 – Relate counting to addition and subtraction. e.g., by counting on 2 to add 2

    NY-1.OA.6a –  Add and subtract within 20. Use strategies such as: • counting on; • making ten; • decomposing a number leading to a ten; • using the relationship between addition and subtraction; and • creating equivalent but easier or known sums. 

    NY-1.OA.6b – Fluently add and subtract within 10.

    NY-1.OA.7 – Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. e.g., Which of the following equations are true and which are false? 6 = 6 7 = 8 – 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2 

    NY-1.OA.8 – Determine the unknown whole number in an addition or subtraction equation with the unknown in all positions. e.g., Determine the unknown number that makes the equation true in each of the equations 8 + ? = 11 ＿ – 3 = 5 6 + 6 = □

    Other Standards Addressed in this Unit

    Operations and Algebraic Thinking

    NY-1.OA.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

    NY-1.OA.3 – Apply properties of operations as strategies to add and subtract. e.g.,

    • If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.)
    • To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)

    Note: Students need not use formal terms for these properties.

    NY-1.OA.4 – Understand subtraction as an unknown addend problem within 20. e.g., subtract 10 – 8 by finding the number that makes 10 when added to 8.

    Essential Questions and Big Ideas

    What is the relationship of addition and subtraction?

    • Addition and subtraction are related/inverse operations.

    Why do we take apart and put together numbers?

    • Numbers are composed of other numbers.
    • Taking apart and putting together are the foundation of addition and subtraction.

    How can the structure of a word problem or equation help us to solve it? 

    • Word problems have basic problem solving structures: adding to, taking from, putting together, taking apart, comparing.
    • Unknowns can be in various locations (start, change, result) in equations and develop from combinations of numbers.

    Why are properties important in solving equations?

    • Various strategies can be used to quickly add numbers. 

    What is the purpose of the equal sign?

    • The equal sign is used to represent quantities that have the same value.

    Prerequisite Standards:

    • K.CC.2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1).
    • K.CC.4b Understand that the last number name said, tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were
    • counted.
    • K.CC.4c Understand that each successive number name refers to a quantity that is one larger.
    • K.OA.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or writing an equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
    • K.OA.4 For any number from 1 to 9, find the number that makes 10 when added to the given number. (e.g., by using objects or drawings, and record the answer with a drawing or equation.)
    • K.OA.5 Fluently add and subtract within 5.

    Download the complete Grade 1 Math Unit 1 frameworks to customize for your own planning: