# Sequenced Units for the Common Core State Standards in Mathematics Grade 1

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3 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. Page 2

5 1. Make sense of problems and persevere in solving them. 4. Model with mathematics. 1.MD.4.9. Ask questions about collected data. 1 For additional information, see page 5 in the Categorical Data progressions document. Page 4

6 Unit 3: Ordering and comparing lengths Suggested number of days: 5 In this unit students explore length comparisons both directly and indirectly. They build and expand upon the direct comparison that they learned in Kindergarten to compare and order three objects directly, and then extend this to indirect comparisons through the use of a third object. 2 This concrete experience with length comparisons supports students' understanding of number comparisons and comparison problem solving. Measurement and Data - l.md A. Measure lengths indirectly and by iterating length units. 1. Order three objects by length; compare the lengths of two objects indirectly by using a third object. 3. Construct viable arguments and critique the reasoning of others. 5. Use appropriate tools strategically. 1.MD.1.1 Order 3 objects by length. 1.MD.1.2 Compare 3 objects with different lengths. l.md.a.l involves measuring non-standard units. 3 Comparison is the focus of this unit, whereas iterating length units (l.md.a.2), is addressed in unit 16. Students need to use the tools appropriately (MP.5), but this unit should also provide an opportunity for students to explain their reasoning about length comparisons (MP.3). Page 5

7 Unit 4: Exploring quantities to 99 Suggested number of days: 8 This unit is focused on counting and writing two-digit numbers. This unit provides student opportunities to practice making groups of ten to efficiently represent and count objects. Number and Operations in Base Ten - l.nbt A. Extend the counting sequence. 1. Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. 6. Attend to precision. 7. Look for and make use of structure. 1.NBT.1.1 Count from a given number to NBT.1.2 Read from a given number to NBT.1.3 Write from a given number to NBT.1.4 Look at a number of objects from and write the correct numeral to represent that number of objects. The focus of this unit is numbers within 99. l.nbt.a.l will be repeated in unit 8, in which the number range will be extended to 120. In this unit students can focus on the uniformity of how tens and ones change as you count larger quantities. In this unit students recognize and apply number patterns (MP.7) and communicating this understanding precisely in reading, writing, and representing numbers (MP.6). 2 For more details on how this understanding is developed, see page 8 in the K-5, Geometric Measurement progressions document. 3 For more details, see page 13 in the Common Core State Standards for Mathematics under "MathematicsI ". Page 6

8 Unit 5: Telling and writing time to the hour Suggested number of days: 5 This is students' first experience in the classroom telling and writing time. In this unit students are not doing any operations with time. Students identify the different parts of the clock, making connections between these parts and the time in hours. Measurement and Data - l.md B. Tell and write time. 3. Tell and write time in hours and half-hours using analog and digital clocks. 5. Use appropriate tools strategically. 6. Attend to precision. 1.MD.3.1 Identify the parts of a clock. (hour hand, minute hand, and second hand) 1.MD.3.2 Tell the difference between analog and digital clocks. 1.MD.3.3 Tell time to the hour using analog and digital clocks. 1.MD.3.4 Tell time to the ½ hour using analog and digital clocks. 1.MD.3.5 Write the time correctly in hours and ½ hours using the colon correctly. The focus of l.md.b.3 in this unit is telling time in hours. Students will extend this skill to telling time to the half hour in unit 10. Precisely communicating the roles of the different components of the clock is the focus of this unit (MP.5, MP.6). Page 7

11 Unit 7: Distinguishing attributes of shapes. Suggested number of days: 5 In this unit students extend their understanding of attributes-e.g. orientation, size, and number of sides-they learned in Kindergarten to distinguish between defining attributes and non-defining attributes. Students need to explore various examples in different ways so that their experiences with shapes are not limited to single examples (e.g. if a student has only worked with equilateral triangles, it may be difficult for them to develop more general understandings of triangles). 7 Geometry - l.g A. Reason with shapes and their attributes. 1. Distinguish between defining attributes (e.g., triangles are closed and threesided) versus non- defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. 3. Construct viable arguments and critique the reasoning of others. 7. Look for and make use of structure. 1.G.1.1 Identify shapes according to their characteristics that define them (number of sides, open or closed, etc.). 1.G.1.2 Identify open and closed shapes. 1.G.1.3 Build and draw identified shapes. Although building and drawing shapes can support students understanding of defining attributes, this part of l.g.a.l is not required until unit 12. This unit gives students opportunities to construct arguments and justify their conclusions based on defining attributes and the structure of geometric figures (MP.3, MP.7). 7 For more information about developing spatial reasoning, see page 3 in the Geometry progressions document. Page 10

12 Unit 8: Using place value to read, write, represent, and compare numbers Suggested number of days: 10 In this unit students extend their understanding from unit 1, to a larger number range. Students apply the structure of teen numbers to reason about larger quantities and their relative magnitude. Number and Operations in Base Ten - l.nbt A. Extend the counting sequence. 1. Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. B. Understand place value. 2. Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: c. 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). 3. Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols», =, and <. 2. Reason abstractly and quantitatively. 7. Look for and make use of structure. 1.NBT.1.1 Count from a given number to NBT.1.2 Read from a given number to NBT.1.3 Write from a given number to NBT.1.4 Look at a number of objects from and write the correct numeral to represent that number of objects. 1.NBT.2c.1 Demonstrate that 10, 20, 30, 40, 50, 60, 70, 80, 90 represent a certain number of tens bundles and zero ones units. 1.NBT.3.1 Compare two, 1 digit numbers using symbols >,<, or = 1.NBT.3.2 Compare two, 2 digit numbers using symbols >,<, or =. 1.NBT.3.3 I can use <,>, or = to compare two digit numbers. l.nbt.a.l involves relating the structure of numbers 0-20 to the numbers In this unit l.nbt.b.3 focuses on students using comparative language to describe numerical comparisons. Mathematical comparison symbols (< and») will be introduced in unit 13. Students continue to explore the structure of place value (MP.7); namely that the two digits of a twodigit number represent amounts of tens and ones and that to compare numbers relies on their relative magnitudes. Students make sense of the relationships between the numerals and the quantities (MP.2). Page 11

15 Unit 10: Telling and writing time to the half hour Suggested number of days: 5 In this unit students extend their understanding of telling and writing time from unit 5 to include situations that deal with telling time to the half hour. Measurement and Data - 1.MD B. Tell and write time. 3. Tell and write time in hours and half-hours using analog and digital clocks. 5. Use appropriate tools strategically. 6. Attend to precision. 1.MD.3.1 Identify the parts of a clock. (hour hand, minute hand, and second hand) 1.MD.3.2 Tell the difference between analog and digital clocks. 1.MD.3.3 Tell time to the hour using analog and digital clocks. 1.MD.3.4 Tell time to the ½ hour using analog and digital clocks. 1.MD.3.5 Write the time correctly in hours and ½ hours using the colon correctly. As in unit 5, precisely communicating the roles of the different components of the clock is the focus of this unit (MP.5, MP.6). Page 14

17 Unit 12: Composing and drawing shapes Suggested number of days: 8 In this unit students transition from using trial and error to applying their understanding of different attributes in order to draw and compose shapes. 10 Composing and decomposing figures supports students' understanding of part-whole relationships. Geometry - 1.G A. Reason with shapes and their attributes. 1. Distinguish between defining attributes (e.g., triangles are closed and threesided) versus non- defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. 2. Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter- circles) or threedimensional 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. 4 NOTE: 4 Students do not need to learn formal names such as "right rectangular prism." 2. Reason abstractly and quantitatively. 4. Model with mathematics. 1.G.1.1 Identify shapes according to their characteristics that define them (number of sides, open or closed, etc.). 1.G.1.2 Identify open and closed shapes. 1.G.1.3 Build and draw identified shapes. 1.G.2.1 Create two-dimensional shapes. 1.G.2.2 Identify three-dimensional shapes. 1.G.2.3 Design/compose shapes to make a new shape. 1.G.2.4 Separate/Decompose shapes from a given shape. 1.G.2.5 Create new shapes from the combined shape. 1.G.2.6 Compose trapezoids, half-circles, and quarter circles. 1.G.2.7 Compose rectangular prisms, right circular cones, and right circular cylinders. Students model these geometric figures (MP.4) in meaningful ways that highlight defining attributes in an abstract way (MP.2). For example, students understand that a new shape can be composed from two other shapes and can simultaneously see both the composite shape and the component shapes For more information about students work with geometric attributes, see page 3 in the Geometry progressions document. Page 16

20 6. Subtract multiples of 10 in the range from multiples of 10 in the range (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 to a written method and explain the reasoning used. 1.NBT.6.1 Choose and tell in my own words how to subtract patterns of ten in the range NBT.6.2 Use what I know about place value to show that only the tens place changes when adding/subtracting multiples of Attend to precision. 8. Look for and express regularity in repeated reasoning. 12 For more information about the expectations for this grade level, see page 7 in the Number and Operations in Base Ten progressions document. Page 19

22 Unit 16: Measuring lengths with non-standard units Suggested number of days: 10 This unit lays the groundwork for the use of standard measurement units in Grade 2 and the general concept of length. They learn about the meaning and processes of measurement, including underlying concepts such as iterating (the mental activity of building up the length of an object with equal-sized units). Measurement and Data - 1.MD A. Measure lengths indirectly and by iterating length units. 2. Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps. 1.MD.2.1 Use non-standard units to measure length. 1.MD.2.2 Use standard units to measure to length. (inches, centimeters) Giving students opportunities to use and select appropriate tools (MP.S) and justify and critique strategies for measurement (MP.3) supports conceptual understanding of measurement rather than just procedural skills. 3. Construct viable arguments and critique the reasoning of others. 5. Use appropriate tools strategically. Page 21

23 Unit 17: Finding equal shares of shapes Suggested number of days: 5 In this unit students partition shapes into equal shares. The focus is fair shares and equal area to support initial understandings of properties such as congruence and symmetry in area-not to discuss fractions. The terms "halves, fourths, and quarters" name the amount of area that is represented to describe the part-whole relationship. Fraction notation is first used in Grade 3. Geometry - 1.G A. Reason with shapes and their attributes. 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. 3. Construct viable arguments and critique the reasoning of others. 1.G.3.1 Identify equal parts of a shape. 1.G.3.2 Describe the parts of a shape with the terms half, fourth, and quarter. 1.G.3.3 Break apart circles and rectangles into two or four equal parts. 1.G.3.4 Place the parts back together to make a whole. Students construct arguments to support their own partitioning, but also distinguish correct reasoning from that which is flawed (MP.3). Page 22

25 3. Construct viable arguments and critique the reasoning of others. 8. Look for and express regularity in repeated reasoning. Page 24

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