Colorado Academic Standards Online

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 $20$.

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.

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.

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.