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clear Content Area: Mathematics // Grade Level: First Grade // Standard Category: All Standards Categories

Mathematics

First Grade, Standard 1. Number and Quantity

• MP7. Look for and make use of structure.

1.NBT.A. Number & Operations in Base Ten: Extend the counting sequence.

Evidence Outcomes:

Students Can:

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. (CCSS: 1.NBT.A.1)

Colorado Essential Skills and Mathematical Practices:

1. Make use of the base-ten counting structure when using special words at the decades, like “sixty” and “seventy.” (MP7)

Inquiry Questions:

1. When might someone want to count by tens instead of ones?
2. Which numbers can be written with two numerals and which numbers are written with three?

Coherence Connections:

1. This expectation represents major work of the grade.
2. In kindergarten, students count to $100$ by ones and tens, count forward from a given number, and connect counting to cardinality.
3. In Grade 1, this expectation connects with understanding place value and with adding and subtracting within $20$.
4. In Grade 2, students extend their place value understanding to hundreds and three-digit numbers, and use this along with the properties of operations to add and subtract within $1000$ and fluently add and subtract within $100$.

• MP1. Make sense of problems and persevere in solving them.
• MP2. Reason abstractly and quantitatively.
• MP4. Model with mathematics.
• MP7. Look for and make use of structure.

1.NBT.B. Number & Operations in Base Ten: Understand place value.

Evidence Outcomes:

Students Can:

1. Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: (CCSS: 1.NBT.B.2)
1. $10$ can be thought of as a bundle of ten ones — called a "ten." (CCSS: 1.NBT.B.2.a)
2. The numbers from $11$ to $19$ are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. (CCSS: 1.NBT.B.2.b)
3. 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). (CCSS: 1.NBT.B.2.c)
2. Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols $>$, $=$, and $<$. (CCSS: 1.NBT.B.3)

Colorado Essential Skills and Mathematical Practices:

1. Make sense of quantities and their relationships in problem situations. (MP1)
2. Abstract $10$ ones into a single conceptual object called a ten. (MP2)
3. Model ones and tens with objects and mathematical representations. (MP4)
4. See the structure of a number as its base-ten units. (MP7)

Inquiry Questions:

1. What does the position of a digit tell you about its value?
2. What are two ways to describe the number $30$?
3. Why was a place value system developed? What might numbers look like without it?

Coherence Connections:

1. This expectation represents major work of the grade.
2. In kindergarten, students decompose numbers from $11$ to $19$ into ten ones and further ones.
3. In Grade 1, this expectation connects with extending the counting sequence and using place value understanding and properties of operations to add and subtract within 100.
4. In Grade 2, students understand hundreds and place value of three-digit numbers, and use this along with the properties of operations to add and subtract.

• MP1. Make sense of problems and persevere in solving them.
• MP7. Look for and make use of structure.

1.NBT.C. Number & Operations in Base Ten: Use place value understanding and properties of operations to add and subtract.

Evidence Outcomes:

Students Can:

1. Add within $100$, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of $10$, 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. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. (CCSS: 1.NBT.C.4)
2. Given a two-digit number, mentally find $10$ more or $10$ less than the number, without having to count; explain the reasoning used. (CCSS: 1.NBT.C.5)
3. Subtract multiples of $10$ in the range $10$–$90$ from multiples of $10$ in the range $10$–$90$ (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 to a written method and explain the reasoning used. (CCSS: 1.NBT.C.6)

Colorado Essential Skills and Mathematical Practices:

1. Perform computation with addition and subtraction while making connections to the properties of operations and to place value structure. (Entrepreneurial Skills: Critical Thinking/Problem Solving)
2. Model quantities with drawings or equations to make sense of place value. (MP1)
3. Use the base-ten structure to add and subtract, including adding and subtracting multiples of ten. (MP7)

Inquiry Questions:

1. Can you add or subtract ten without having to count by ones?
2. How does modeling addition look different if you add tens and ones separately compared to counting on by tens then by ones?

Coherence Connections:

1. This expectation represents major work of the grade.
2. In kindergarten, students model and describe addition as putting together and adding to, and subtraction as taking part and taking from, using objects or drawings. Students also work with numbers $11$–$19$ to gain foundations for place value.
3. In Grade 1, this expectation connects with understanding place value and adding and subtracting within $20$.
4. In Grade 2, students understand place value for three-digit numbers and use that understanding and properties of operations to add and subtract within $1000$ and fluently add and subtract within $100$.

Mathematics

First Grade, Standard 2. Algebra and Functions

• MP1. Make sense of problems and persevere in solving them.
• MP4. Model with mathematics.

1.OA.A. Operations & Algebraic Thinking: Represent and solve problems involving addition and subtraction.

Evidence Outcomes:

Students Can:

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. (CCSS: 1.OA.A.1)
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. (CCSS: 1.OA.A.2)

Colorado Essential Skills and Mathematical Practices:

1. Make sense of problems by relating objects, drawings, and equations. (MP1)
2. Use cubes, number racks, ten frames and other models to represent addition and subtraction situations in real-world contexts. (MP4)

Inquiry Questions:

1. How can you use cubes to help you compare two numbers?
2. (Given a representation of a value less than ten) How many more do you need to make ten?

Coherence Connections:

1. This expectation represents major work of the grade.
2. In kindergarten, students add and subtract within $10$ by using objects or drawings to represent problems.
3. In Grade 1, this expectation connects with comparing, adding, and subtracting numbers, including measurement and data activities.
4. In Grade 2, students represent and solve real-world problems involving addition and subtraction within $100$, with fluency expected within $20$.

• MP1. Make sense of problems and persevere in solving them.
• MP7. Look for and make use of structure.

1.OA.B. Operations & Algebraic Thinking: Understand and apply properties of operations and the relationship between addition and subtraction.

Evidence Outcomes:

Students Can:

1. Apply properties of operations as strategies to add and subtract. (Students need not use formal terms for these properties.) Examples: 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.) (CCSS: 1.OA.B.3)
2. Understand subtraction as an unknown-addend problem. For example, subtract $10 - 8$ by finding the number that makes $10$ when added to $8$. (CCSS: 1.OA.B.4)

Colorado Essential Skills and Mathematical Practices:

1. Make sense of addition and subtraction by applying properties of operations and working with different problem types (see Appendix, Table 1). (MP1)
2. Use properties of operations to recognize equivalent forms of equations. (MP7)

Inquiry Questions:

1. How could you explain why $3+8$ and $8+3$ both equal $11$?
2. How can you use the number line to show how you might use adding OR subtracting to solve the same problem?

Coherence Connections:

1. This expectation represents major work of the grade.
2. In previous grades, students model and describe addition as putting together and adding to, and subtraction as taking apart and taking from, using objects or drawings.
3. In Grade 1, this expectation connects with representing and solving problems involving addition and subtraction and with adding and subtracting within $20$.
4. In future grades, students use place value understanding and properties of operations to add and subtract within larger number ranges, then to perform multi-digit arithmetic. Later, students use these concepts to build fractions from unit fractions, and to apply and extend their understandings of arithmetic to algebraic expressions.

• MP7. Look for and make use of structure.

1.OA.C. Operations & Algebraic Thinking: Add and subtract within 20.

Evidence Outcomes:

Students Can:

1. Relate counting to addition and subtraction (e.g., by counting on $2$ to add $2$). (CCSS: 1.OA.C.5)
2. 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 $6 + 6 + 1 = 12 + 1 = 13$). (CCSS: 1.OA.C.6)

Colorado Essential Skills and Mathematical Practices:

1. Use multiple strategies to think about problems and see how the quantities involved support the use of some strategies over others. (Entrepreneurial Skills: Critical Thinking/Problem Solving)
2. Make use of the structure of numbers when making tens or when creating equivalent but easier or known sums. (MP7)

Inquiry Questions:

1. Which would you prefer when adding $4 + 7$: starting with $7$ and counting up $4$ or starting with $4$ and counting up $7$? Why?
2. Why does knowing doubles like $4 + 4$ or $5 + 5$ help when adding $4 + 5$?
3. How does counting on to add and subtract within $20$ make it easier to use fingers even though we have only $10$ fingers?

Coherence Connections:

1. This expectation represents major work of the grade.
2. In kindergarten, students understand the relationship between numbers and quantities and connect counting to cardinality.
3. In Grade 1, this expectation connects with place value understanding, properties of addition and subtraction, the relationship between addition and subtraction, and with representing and solving problems involving addition and subtraction.
4. In Grade 2, students fluently add and subtract within $20$ using mental strategies and know from memory all sums of two one-digit numbers.

• MP2. Reason abstractly and quantitatively.
• MP3. Construct viable arguments and critique the reasoning of others.

1.OA.D. Operations & Algebraic Thinking: Work with addition and subtraction equations.

Evidence Outcomes:

Students Can:

1. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? $6 = 6$, $7 = 8 - 1$, $5 + 2 = 2 + 5$, $4 + 1 = 5 + 2$. (CCSS: 1.OA.D.7)
2. Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations $8 + \mbox{?} = 11$, $5 = \mbox{_} - 3$, $6 + 6 = \mbox{_}$. (CCSS: 1.OA.D.8)

Colorado Essential Skills and Mathematical Practices:

1. Make sense of quantities and their relationships in problem situations. (MP2)
2. Question assumptions about the meaning of the equals sign and construct viable arguments. (MP3)

Inquiry Questions:

1. What does it mean for two sides of an equation to be “equal”? How can $2 + 3$ “equal” $5$?
2. (Given $4=4$ If you add $2$ more to the $4$ on the right, how many do you need to add on the left to make a true statement? How would you write that as an equation?

Coherence Connections:

1. This expectation represents major work of the grade.
2. In kindergarten, students represent addition and subtraction with equations without needing to understand the meaning of the equal sign.
3. In Grade 1, this expectation connects with representing and solving problems involving addition and subtraction.
4. In Grade 2, students work with equal groups of objects to gain foundations for multiplication. In Grade 4, students build fractions from unit fractions and apply addition and subtraction to concepts of angle and angle measurement.

Mathematics

First Grade, Standard 3. Data, Statistics, and Probability

• MP2. Reason abstractly and quantitatively.
• MP3. Construct viable arguments and critique the reasoning of others.
• MP5. Use appropriate tools strategically.
• MP6. Attend to precision.

1.MD.A. Measurement & Data: Measure lengths indirectly and by iterating length units.

Evidence Outcomes:

Students Can:

1. Order three objects by length; compare the lengths of two objects indirectly by using a third object. (CCSS: 1.MD.A.1)
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. (CCSS: 1.MD.A.2)

Colorado Essential Skills and Mathematical Practices:

1. Abstract comparisons between lengths using statements like $A \gt B$. (MP2)
2. Use the transitive property to explain if $A$ is longer than $B$, and $B$ is longer than $C$, then $A$ must be longer than $C$. (MP3)
3. Devise different ways to represent the same data set and discuss the strengths and weaknesses of each representation. (MP5)
4. Consider the endpoints of objects when measuring and making comparisons. (MP6)

Inquiry Questions:

1. How is it possible for $5$ sticks placed end-to-end to be equal in length to $6$ sticks placed end-to-end?
2. Which is longer, the total length of two sticks placed end-to-end vertically or the same two sticks placed end-to-end horizontally?
3. What objects in this classroom are the same length as (or longer than, or shorter than) your forearm?

Coherence Connections:

1. This expectation represents major work of the grade.
2. In kindergarten, students directly compare two objects with a measurable attribute in common.
3. In Grade 1, this expectation is part of a progression of learning that develops conceptions of comparison, conservation, seriation, and iteration.
4. In Grade 2, students measure and estimate lengths in standard units.

• MP6. Attend to precision.

1.MD.B. Measurement & Data: Tell and write time.

Evidence Outcomes:

Students Can:

1. Tell and write time in hours and half-hours using analog and digital clocks. (CCSS: 1.MD.B.3)

Colorado Essential Skills and Mathematical Practices:

1. Tell and manage time to be both personally responsible and responsible to the needs of others. (Personal Skills: Personal Responsibility)
2. Recognize that time is a quantity that can be measured with different degrees of precision. (MP6)

Inquiry Questions:

1. How long is two half-hours?
2. If the time is 2:30, where would the minute hand be pointing on an analog clock?

Coherence Connections:

1. This expectation is in addition to the major work of the grade.
2. In kindergarten, students are not expected to learn how to tell and write time.
3. In Grade 2, students tell and write time from analog and digital clocks to the nearest five minutes.

• MP1. Make sense of problems and persevere in solving them.
• MP2. Reason abstractly and quantitatively.
• MP5. Use appropriate tools strategically.
• MP6. Attend to precision.

1.MD.C. Measurement & Data: Represent and interpret data.

Evidence Outcomes:

Students Can:

1. 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. (CCSS: 1.MD.C.4)

Colorado Essential Skills and Mathematical Practices:

2. Group similar individual objects together and abstract those objects into a new conceptual group. (MP2)
3. Devise different ways to display the same data set then discuss relative strengths and weaknesses of each scheme. (MP5)
4. Use appropriate labels and units of measure. (MP6)

Inquiry Questions:

1. How do different representations of data indicate there are more objects in one category than in another category?
2. How can objects be categorized in different ways?
3. How can an object’s attributes determine if it does not belong with other objects in a group?

Coherence Connections:

1. This expectation supports the major work of the grade.
2. In kindergarten, students classify objects into given categories, count the numbers of objects in each category, and sort the categories by count.
3. In Grade 1, this expectation supports representing and solving problems involving addition and subtraction, which is major work of the grade.
4. In Grade 2, students draw a picture graph and a bar graph to represent a data set with up to four categories, and solve put-together, take-apart, and compare problems using the information in a bar graph.

Mathematics

• MP1. Make sense of problems and persevere in solving them.
• MP2. Reason abstractly and quantitatively.
• MP3. Construct viable arguments and critique the reasoning of others.
• MP7. Look for and make use of structure.

1.G.A. Geometry: Reason with shapes and their attributes.

Evidence Outcomes:

Students Can:

1. Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. (CCSS: 1.G.A.1)
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. (Students do not need to learn formal names, such as "right rectangular prisms.") (CCSS: 1.G.A.2)
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. (CCSS: 1.G.A.3)

Colorado Essential Skills and Mathematical Practices:

1. Demonstrate flexibility, imagination, and inventiveness in composing two-dimensional and three-dimensional shapes to create composite shapes. (Entrepreneurial Skills: Informed Risk Taking)
2. Sort, classify, build, or draw shapes in terms of defining attributes versus non-defining attributes. (MP1)
3. Determine how to partition a given circle or rectangle into two and four equal shares and describe the whole in terms of equal shares. (MP2)
4. Justify whether a shape belongs in a given category by differentiating between defining attributes and non-defining attributes. (MP3)
5. Analyze how composite shapes can be formed by, or decomposed into, basic shapes. (MP7)

Inquiry Questions:

1. Which properties of shapes are most important when you decide if a shape belongs in a group with other shapes?
2. What kinds of objects can you find in your school or home that are made up of two or more different shapes being put together?
3. In how many different ways can you create two or four equal shares in a rectangle?

Coherence Connections:

1. This expectation is an addition to the major work of the grade.
2. In kindergarten, students identify, describe, analyze, compare, create, and compose shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
3. In Grade 2, students recognize and draw shapes having specified attributes and partition circles and rectangles into two, three, or four equal shares. In Grade 3, students develop understanding of fractions as numbers.

Need Help? Submit questions or requests for assistance to bruno_j@cde.state.co.us