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Operations and Algebraic Thinking
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Represent and solve problems involving addition and subtraction.
Note: Students use properties of operations and different strategies to find the sum of three whole numbers, such as counting on, making tens, decomposing numbers, doubles, and near doubles. | |||||||||||||
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1. Use addition and subtraction to solve word problems within 20 by using concrete objects, drawings, and equations with a symbol for the unknown number to represent the problem.
a. Add to with change unknown to solve word problems within 20.
b. Take from with change unknown to solve word problems within 20.
c. Put together/take apart with addend unknown to solve word problems within 20.
d. Compare quantities, with difference unknown, bigger unknown, and smaller unknown while solving word problems within 20. Alabama Alternate Achievement Standards
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2. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 by using concrete objects, drawings, or equations with a symbol for the unknown number to represent the problem. Alabama Alternate Achievement Standards
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Understand and apply properties of operations and the relationship between addition and subtraction.
Note: Students need not use formal terms for these properties. | |||||||||||||
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3. Apply properties of operations as strategies to add and subtract.
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 and third numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12 (associative property of addition). When adding 0 to a number, the result is the same number (identity property of zero for addition). Alabama Alternate Achievement Standards
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4. Explain subtraction as an unknown-addend problem.
Example: subtracting 10 - 8 by finding the number that makes 10 when added to 8 Alabama Alternate Achievement Standards
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Add and subtract within 20.
Note: Fluency involves a mixture of "just knowing" answers, knowing answers from patterns, and knowing answers from the use of strategies. The word fluently is used in the standards to mean accurately, efficiently, and flexibly. | |||||||||||||
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5. Relate counting to addition and subtraction.
Example: counting on 2 to add 2 Alabama Alternate Achievement Standards
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6. Add and subtract within 20.
a. Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by counting on.
b. Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by making ten.
c. Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by decomposing a number leading to a ten.
Example: 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9
d. Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by using the relationship between addition and subtraction.
Example: Knowing that 8 + 4 = 12, one knows 12 - 8 = 4.
e. Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by creating equivalent but easier or known sums.
Example: adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13 Alabama Alternate Achievement Standards
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Work with addition and subtraction equations.
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7. Explain that the equal sign means "the same as." Determine whether equations involving addition and subtraction are true or false.
Example: determining which of the following equations are true and which are false: 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2 Alabama Alternate Achievement Standards
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8. Solve for the unknown whole number in various positions in an addition or subtraction equation, relating three whole numbers that would make it true.
Example: determining the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = ? - 3, and 6 + 6 = ? Alabama Alternate Achievement Standards
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9. Reproduce, extend, and create patterns and sequences of numbers using a variety of materials. Alabama Alternate Achievement Standards
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Operations with Numbers: Base Ten
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Extend the counting sequence.
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10. Extend the number sequence from 0 to 120.
a. Count forward and backward by ones, starting at any number less than 120.
b. Read numerals from 0 to 120.
c. Write numerals from 0 to 120.
d. Represent a number of objects from 0 to 120 with a written numeral. Alabama Alternate Achievement Standards
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Understand place value.
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11. Explain that the two digits of a two-digit number represent amounts of tens and ones.
a. Identify a bundle of ten ones as a "ten."
b. Identify the numbers from 11 to 19 as composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
c. Identify the numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 as one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). Alabama Alternate Achievement Standards
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12. Compare pairs of two-digit numbers based on the values of the tens and ones digits, recording the results of comparisons with the symbols >, =, and < and orally with the words "is greater than," "is equal to," and "is less than." Alabama Alternate Achievement Standards
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Use place value understanding and properties of operations to add and subtract.
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13. Add within 100, using concrete models or drawings and strategies based on place value.
a. Add a two-digit number and a one-digit number.
b. Add a two-digit number and a multiple of 10.
c. Demonstrate that in adding two-digit numbers, tens are added to tens, ones are added to ones, and sometimes it is necessary to compose a ten.
d. Relate the strategy for adding a two-digit number and a one-digit number to a written method and explain the reasoning used. Alabama Alternate Achievement Standards
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14. Given a two-digit number, mentally find 10 more or 10 less than the number without having to count, and explain the reasoning used. Alabama Alternate Achievement Standards
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15. Subtract multiples of 10 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. Alabama Alternate Achievement Standards
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Data Analysis
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Collect and analyze data and interpret results.
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16. Organize, represent, and interpret data with up to three categories.
a. Ask and answer questions about the total number of data points in organized data.
b. Summarize data on Venn diagrams, pictographs, and "yes-no" charts using real objects, symbolic representations, or pictorial representations.
c. Determine "how many" in each category using up to three categories of data.
d. Determine "how many more" or "how many less" are in one category than in another using data organized into two or three categories. Alabama Alternate Achievement Standards
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Measurement
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Describe and compare measurable attributes.
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17. Order three objects by length; compare the lengths of two objects indirectly by using a third object. Alabama Alternate Achievement Standards
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18. Determine the length of an object using non-standard units with no gaps or overlaps, expressing the length of the object with a whole number. Alabama Alternate Achievement Standards
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Work with time and money.
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19. Tell and write time to the hours and half hours using analog and digital clocks. Alabama Alternate Achievement Standards
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20. Identify pennies and dimes by name and value. Alabama Alternate Achievement Standards
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Geometry
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Reason with shapes and their attributes.
Note: Students do not need to learn formal names such as "right rectangular prism." | |||||||||||||
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21. Build and draw shapes which have defining attributes.
a. Distinguish between defining attributes and non-defining attributes.
Examples: Triangles are closed and three- sided, which are defining attributes; color, orientation, and overall size are non-defining attributes. Alabama Alternate Achievement Standards
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22. 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. Alabama Alternate Achievement Standards
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23. Partition circles and rectangles into two and four equal shares and describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of.
a. Describe "the whole" as two of or four of the shares of circles and rectangles partitioned into two or four equal shares.
b. Explain that decomposing into more equal shares creates smaller shares of circles and rectangles. Alabama Alternate Achievement Standards
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