First Grade
Overview
In Grade 1 there are 4 critical areas:
Critical Area 1
Developing understanding of addition, subtraction, and strategies for addition and subtraction within 20: Students develop strategies for adding and subtracting whole numbers based on their prior work with small numbers. They use a variety of models, including discrete objects and lengthbased models (e.g., cubes connected to form lengths), to model addto, takefrom, puttogether, takeapart, and compare situations to develop meaning for the operations of addition and subtraction, and to develop strategies to solve arithmetic problems with these operations. Students understand connections between counting and addition and subtraction (e.g., adding two is the same as counting on two). They use properties of addition to add whole numbers and to create and use increasingly sophisticated strategies based on these properties (e.g., "making tens") to solve addition and subtraction problems within 20. By comparing a variety of solution strategies, children build their understanding of the relationship between addition and subtraction.

Critical Area 2
Developing understanding of whole number relationships and place value, including grouping in tens and ones: Students develop, discuss, and use efficient, accurate, and generalizable methods to add within 100 and subtract multiples of 10. They compare whole numbers (at least to 100) to develop understanding of and solve problems involving their relative sizes. They think of whole numbers between 10 and 100 in terms of tens and ones (especially recognizing the numbers 11 to 19 as composed of a ten and some ones). Through activities that build number sense, they understand the order of the counting numbers and their relative magnitudes.
Critical Area 3
Developing understanding of linear measurement and measuring lengths as iterating length units: Students develop an understanding of the meaning and processes of measurement, including underlying concepts such as iterating (the mental activity of building up the length of an object with equalsized units) and the transitivity principle for indirect measurement
Critical Area 4
Reasoning about attributes of, and composing and decomposing geometric shapes: Students compose and decompose plane or solid figures (e.g., put two triangles together to make a quadrilateral) and build understanding of partwhole relationships as well as the properties of the original and composite shapes. As they combine shapes, they recognize them from different perspectives and orientations, describe their geometric attributes, and determine how they are alike and different, to develop the background for measurement and for initial understandings of properties such as congruence and symmetry.
Unit 1
First Grade Mathematics
Unit 1
Operations and Algebraic Thinking
During Unit 1, your children will develop strategies for adding and subtracting whole numbers based on their prior work with small numbers. They will use a variety of models, including discrete objects and lengthbased models (e.g., cubes connected to form lengths), to model addto, takefrom, puttogether, takeapart, and compare situations to develop meaning for the operations of addition and subtraction, and to develop strategies to solve arithmetic problems with these operations. Your children will understand connections between counting and addition and subtraction (e.g., adding two is the same as counting on two). They will use properties of addition to add whole numbers and to create and use increasingly sophisticated strategies based on these properties (e.g., "making tens") to solve addition and subtraction problems within 20. By comparing a variety of solution strategies, your children will build their understanding of the relationship between addition and subtraction. 
Students Need To
 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.
 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
 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.
 Apply properties of operations as strategies to add and subtract.2 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.)
 Understand subtraction as an unknownaddend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8. Add and subtract within 20.
 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 + ? = 11, 5 = _ – 3, 6 + 6 = _.
 Relate counting to addition and subtraction (e.g., by counting on 2 to add 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).
 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.
Ways Parents Can Help
 Tell your child an addition or subtraction word problem. Encourage them to "retell" the problem in their own words in order to build comprehension of the situation. Then have them use objects (Legos, pasta shapes, cereal, etc…) to act out the addition or subtraction word problem.
 Encourage your child to represent word problems using words, numbers, and pictures/models when solving them.
 Keep a set of flash cards in the car to practice as you run errands. Encourage your child to explain the strategy that they used to solve the problem.
 With a deck of cards, use the number cards to play Fact War. Each player flips 1 card and the player to say the sum first, gets both cards
 Have your child sort a set of flashcards based on the strategy that they would use to solve the problem. Have them select one strategy pile to solve.
 Students often overuse "counting on" for all math facts. Help your child to generate facts that are efficient for counting on and facts that are not efficient for counting on (you could create a list or use flashcards to make groups). Encourage your child to explain why counting on would not be efficient for a fact (such as 5+7).
Key Vocabulary
Support Sites
Unit 2
First Grade Mathematics
Unit 2
Numbers and Operations in Base Ten
Place Value
Printable Parent Letter
During Unit 2, your children will compare whole numbers (at least to 100) to develop understanding of and solve problems involving their relative sizes. They will think of whole numbers between 10 and 100 in terms of tens and ones (especially recognizing the numbers 11 to 19 as composed of a ten and some ones). Through activities that build number sense, they will understand the order of the counting numbers and their relative magnitudes. 
Students Need To

Ways Parents Can Help
 Use blocks, pasta shapes or other fun objects to model numbers to 120. Have your child bundle groups of ten and identify how many tens and how many ones make up the number. Help your child to mentally find ten more and ten less than the number they built.
 While riding in the car practice counting to 120, starting at any number less than 120.
 Practice stating the number that is ten more or ten less than a given number. Have your child explain how they found the answer.
 When seeing numbers in your surroundings, help your child to say them and tell how many tens and ones are in the number.
 Use objects and/or drawings to represent and solve addition and subtraction word problems.
 Encourage your child to use strategies to solve addition and subtraction facts within 20. Help your child to become fluent (answer orally within 3 seconds or less) with addition and subtraction facts within 10.
Key Vocabulary
Video Support
Unit 3
First Grade Mathematics
Unit 3
Number and Operations in Base 10
Addition and Subtraction
Printable Parent Letter
During Unit 3, your children will continue to solve problems, become more fluent with basic facts to 10, and work with two digit numbers, developing strategies for addition and subtraction. When we were children being taught to add and subtract two digit numbers, we used words such as “borrowing”, “trading”, “cross out” or “put a 1 in the tens place”. Our answers would look like this:
8 0  3 0 5 0 
1 4 8 + 5 5 3 
As your child learns to add and subtract, we will be focusing on place value and how to combine or take away parts of the number. Our instruction will rely heavily on drawing pictures to represent the numbers and operations. For your child, the problems above will look like this.
8 ones and 5 ones equals 13 ones 13 ones equals 1 ten and 3 ones The total is 5 tens and 3 ones or 53 
8 tens take away 3 tens Equals 5 tens 5 tens equals 50 
The pictures above allow us to “see” what is happening with the numbers as we add or subtract. Math work that your child brings home will look like these examples. We ask that you talk with your child about their pictures and encourage them to represent their math with pictures.
Students Need To
 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.
 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.
 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.
 Given a twodigit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.
 Add within 100, including adding a twodigit number and a onedigit number, and adding a twodigit 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 an subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding twodigit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
 Subtract multiples of 10 in the range 1090 from multiples of 10 in the range 1090 (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.
 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).
Ways Parents Can Help
 Practice stating the number that is ten more or ten less than a given number. Have your child explain how they found the answer.
 Practice solving addition problems that contain three addends and whose sum is less than 20. Have your child explain which strategy they used to solve the problem. (ex. 3 + 5 + 3 = 11 Your child might state that they added 3 + 3 first because it is a doubles fact and the 6 + 5 is a doubles +1 fact ( 5 + 5 + 1).
 Use objects and/or drawings to represent and solve addition problems involving a 2 digit number and a 1 digit number.
 Use objects and/or drawings to represent and solve addition problems involving a 2 digit number and a 2 digit number.
Key Vocabulary
Video Support
https://www.carrollk12.org/videos/?video=martinbargraph&ViewSetting=E 
Unit 4
First Grade Mathematics
Unit 4
Geometry
Printable Parent Letter
During Unit 4, students work with a variety of shapes in order to identify their attributes. For example, students will group squares, rectangles, rhombi, and other foursided figures together and discuss what they have in common. Students will put together and take apart 2D and 3D shapes to create new composite figures (e.g., put two same sized squares together to make a rectangle or a square and a triangle together make a pentagon or house shape). Students will also divide shapes into halves and fourths to build an early understanding of fractions, but they will not need to record the fractions as ½ or ¼. 
Students Need To
 Identify, name and compare plane geometric figures (triangles, circles, squares, rectangles and rhombi) by sorting and describing their attributes (by shape, number of sides, size or number of angles)
 Use concrete materials to build shapes (rectangles, squares, trapezoids, triangles, halfcircles and quartercircles) that have the defining attributes (attributes that make a shape that specific shape)
 Identify and explain the similarities and differences between two shapes.
 Use concrete materials to create composite shapes from two or threedimensional shapes (cubes, right rectangular prisms, right circular cones and right circular cylinders).
 Use concrete materials to create a new shape from a composite shape.
 Identify equal parts of a partitioned shape with concrete materials and describe the shares using the words halves, fourths, and quarters as well as the phrases half of, fourth of and quarter of.
 Gather and collect data to answer questions
 Interpret data contained in picture graphs using a variety of categories with 1:1 intervals
 Collect, organize, display and interpret data using tally charts, picture graphs, bar graphs and tables
Ways Parents Can Help
 Hunt for shapes around the house that are composite shapes and have your child identify the shapes that make up the composite shape.
 Sort a set of shapes and describe how the shapes are alike and different.
 Take a tissue box, cereal box or other rectangular prism apart and see what two dimensional shapes make up this shape.
 Draw a picture of your room or your house using only basic shapes (circles, squares, rectangles, and triangles). Name the shapes shown in the picture.
 Take food that is in a regular geometric shape (rectangle, square, triangle) and cut the food into equal shares. Describe the shares using words such as halves, fourths, quarters, half of, fourth of, and quarter of.
 Building with blocks or Legos and taking about which shapes (pieces) are used to create the figure.
Key Vocabulary
Video Support
Unit 5
First Grade Mathematics
Unit 5
Measurement
Printable Parent Letter
During Unit 5, your children will develop an understanding of the meaning and processes of measurement. This includes comparing the lengths of objects when you can put them side by side or using another object to compare the lengths of two objects. For example, using your arms to measure the width of a doorway compared to the width of the refrigerator that you need to move through the doorway. The students will use informal units such as paper clips or tiles to measure the length of an object. They will also learn to tell time to the hour and half hour on a digital and analog clock.
Students Need To
 Measure length with nonstandard units (paper clips, toothpicks, unifix cubes, eraser length…) to understand that the length measurement of an object is the number of samesize length units that span it with no gaps or overlaps.
 Order three objects by length.
 Compare the lengths of two objects indirectly by using a third object (concept of transitivity – a is shorter than b and b is shorter than c, so a is shorter than c).
 Use tools to measure time to the hour and half hour intervals
 Apply knowledge of fractional wholes and halves to telling time.
 Compare the same time on analog and digital clocks to measure time to the hour and half hour.
 Gather and collect data to answer questions
 Interpret data contained in picture graphs using a variety of categories with 1:1 intervals
 Collect, organize, display and interpret data using tally charts, picture graphs, bar graphs and tables.
Ways Parents Can Help
 Have your child measure the length of an object by using nonstandard units (paper clips, toothpicks, cereal, candy… and help them to understand that the measurement is the total number of nonstandard units that are placed along the length so that they are touching, leaving no gaps or overlaps.
 Compare the lengths of three household objects such as crayons, pencils and markers.
 Compare the lengths of two objects indirectly by using a third object (a is longer than b and is longer than c so a is longer than c).
 Tell time to the hour and half hour using an analog clock and digital clock.
 Compare the time on an analog clock to the time on a digital clock (to the hour and half hour).