Courses of Study : Mathematics

Students:

• Count correctly from 0 to 100 by ones without skipping numbers, repeating numbers, or hesitating.
• Count correctly from 0 to 100 by tens without skipping numbers, repeating numbers, or hesitating.
• Count backwards from 10 to 0 by ones without skipping numbers, repeating numbers, or hesitating.

Students know:

• how to count by ones and tens orally. This includes counting forward and counting backward.

Students are able to:

• orally count forward.
• orally count backward.

Students understand that:

• Counting from 0 to 100 is a sequence.

Learning Objectives:
M.K.1.1: Count backwards from 5 to 0 by ones.
M.K.1.2: Mimic counting backwards from 5 to 0 by ones.
M.K.1.3: Count to 50 by ones.
M.K.1.4: Count to 50 by tens.
M.K.1.5: Count to 20 by ones.
M.K.1.6: Count to 10 by ones.
M.K.1.7: Mimic counting by tens.
M.K.1.8: Mimic counting by ones.

Students:

• Count correctly to 100 by ones starting with any given number other than 0 without skipping numbers, repeating numbers, or hesitating.

Students know:

• how to rote count from 0 to 100 starting with any given number.

Students are able to:

• orally count.

Students understand that:

• Counting from 0 to 100 is a sequence and you can begin with any number.

Learning Objectives:
M.K.2.1: Count forward to 100 from a number over 50.
M.K.2.2: Count forward to 100 from a number between 2 and 50.
M.K.2.3: Count forward to 50 from a given number.
M.K.2.4: Count to 100 by ones.
M.K.2.5: Mimic counting to 100 by ones.
M.K.2.6: Count to 50 by ones.
M.K.2.7: Mimic counting to 50 by ones.

Students:

• Write numerals correctly from 0 to 20.
• Represent numbers using concrete objects when given a written numeral from 0 to 20.

Students know:

• how to match numeral name with sets of objects.

Students are able to:

• write numerals from 0 to 20.
• Represent numbers from 0 to 20.

Students understand that:

• a written numeral represents a number of objects.

Learning Objectives:
M.K.3.1: Write numbers 0 to 10.
M.K.3.2: Match numerals to quantity 11 to 20.
M.K.3.3: Match numerals to quantity 0 to 10.
M.K.3.4: Recognize written numerals 0 to 20.
M.K.3.5: Demonstrate one to one correspondence for a group of objects 6 to 20.
M.K.3.6: Demonstrate one to one correspondence for a group of objects 0 to 5.
M.K.3.7: Trace numerals 0 to 20.
M.K.3.8: Make purposeful marks such as lines and circles.

Students:

• Count an object saying the number name.
• Tell the number of objects in a set.
• Specify the number of objects in a set regardless of arrangement.
• Explain "one more".

Students know:

• Use one to one correspondence when counting objects.
• how to rote count in consecutive order.

Students are able to:

• count objects with one to one correspondence.
• Indicate the number of objects.
• Explain one more.

Students understand that:

• a number represents a quantity.

Learning Objectives:
M.K.4.1: Define number and counting.
M.K.4.2: Identify correct number of objects for a given number up to 20.
M.K.4.3: Identify different size groups of objects up to 10.

a.
M.K.4.4: Count to 20 by ones.
M.K.4.5: Mimic counting objects.

b.
M.K.4.6: Know that the last number tells how many when counting 0 to 5 objects.
M.K.4.7: Mimic counting objects up to 20.
M.K.4.8: Count to 20 by ones.
M.K.4.9: Mimic counting to 20 by ones.

c.
M.K.4.10: Define one larger/one more.
M.K.4.11: Count objects in a group and identify total after adding one more.
M.K.4.12: Count in sequential order.
M.K.4.13: Mimic counting in sequential order.

Students:

• Answer questions regarding how many objects are in a set in various configurations.

Students know:

• how to use one-to-one correspondence when counting objects.
• how to demonstrate number word sequence.

Students are able to:

• count sequentially.
• Use one to one correspondence.
• Subitize.
• Represent a number of objects within 0 to 20.

Students understand that:

• numbers name quantities regardless of their arrangement.

Learning Objectives:
M.K.5.1: Define how many, all together, and in all.
M.K.5.2: Demonstrate one to one correspondence.
Example: Point to only one object when counting, and stop counting when all objects have been touched.
M.K.5.3: Count to 20 by ones.

Students:

• Explain and justify answers to questions such as "which group has more?" or "which group has less?".
• Answer questions such as which group has more or less by matching, recognizing without counting (subitizing), or counting up to 10 objects.

Students know:

• how to identify which number is larger and which number is smaller.
• number word sequence.

Students are able to:

• Count sequentially.

Students understand that:

• a set of objects is either greater than, less than, or equal to another set of objects.

Learning Objectives:
M.K.6.1: Define greater than, less than, and equal to.
M.K.6.2: Count to 20 by ones.
M.K.6.3: Count objects up to ten.

Students:

• Justify their identification of the larger or smaller pair of numerals using a variety of strategies such as referring to their order in the counting sequence, modeling the quantities, and using relational thinking.

Students know:

• how to identify which number is larger and which number is smaller with number 0 - 10.
• number word sequence.

Students are able to:

• count sequentially.
• Apply strategies for comparing numbers.

Students understand that:

• successive number names refer to quantities that are larger than the previous numbers in the counting sequence.

Learning Objectives:
M.K.7.1: Compare numbers 1 to 10 using objects.
M.K.7.2: Name numerals 1 to 10.
M.K.7.3: Identify numerals 1 to 10.
M.K.7.4: Count to 10 by ones.

Students:

• Create representations of the quantities and the actions in the situations using physical, pictorial, or symbolic representations.
• Explain the representations of the quantities and actions in the situations using physical, pictorial, or symbolic representations.

Students know:

• how to represent addition and subtraction using models, pictures or symbolic representations.
• how to explain representations of quantities.

Students are able to:

• Represent quantities and operations physically, pictorially, or symbolically.
• Use informational and mathematical language to communicate the connections among addition and subtraction.

Students understand that:

• both putting together and adding to can be viewed as addition.
• both taking apart and taking from can be viewed as subtraction.

Learning Objectives:
M.K.8.1: Define addition as combining groups of objects.
M.K.8.2: Define subtraction as separating groups of objects.
M.K.8.3: Represent numbers with objects or drawings.
M.K.8.4: Separate sets with nine or fewer objects.
M.K.8.5: Combine objects to form sets up to nine.

Students:

• Explain and justify solutions using connections among a variety of representations given oral addition and subtraction word problems within ten.

Students know:

• Characteristics of addition and subtraction contexts such as putting together, adding to, taking apart, and taking from.

Students are able to:

• represent quantities and operations physically, pictorially, or symbolically.
• Strategically use a variety of representations to solve addition and subtraction word problems.
• Use informal and mathematical language to communicate addition and subtraction representations.
• Accurately compute sums and differences.

Students understand that:

• both putting together and adding to can be viewed as addition.
• both taking apart and taking from can be viewed as subtraction.
• Mathematical problems can be solved using a variety of strategies and representations.

Learning Objectives:
M.K.9.1: Understand key words in addition and subtraction word problems.
Examples: all together, how many more, how many are left, in all.
M.K.9.2: Represent numbers with objects or drawings.
M.K.9.3: Separate sets with nine or fewer objects.
M.K.9.4: Combine objects to form sets up to nine.

Students:

• Use objects or drawings to decompose the given number into at least two pairs of smaller numbers.
• Record their solutions using pictures or equations.

Students know:

• "equal to" and the concept of equality meaning "the same as."
• Addition is putting together numbers and subtraction is taking apart numbers.

Students are able to:

• Represent quantities physically, pictorially, and symbolically.

Students understand that:

• quantities may be named in a variety of ways.

Learning Objectives:
M.K.10.1: Identify plus, minus, and equal signs.
M.K.10.2: Match numerals to objects or drawings.
M.K.10.3: Identify numerals 1 to 10.
M.K.10.4: Count 0 to 10.

Students:

• Given any number from 0 to 10 use a variety of representations and problem solving strategies to determine the number that when added to the given number equals 10.

Students know:

• Characteristics of addition and subtraction contexts such as putting together, adding to, taking apart, and taking from.

Students are able to:

• Represent quantities and operations physically, pictorially, or symbolically.

Students understand that:

• two smaller quantities join to create a larger target quantity.
• A quantity may be broken into smaller quantities.
• Mathematical tools and representations (ten frames and ten fingers) can be used to solve problems efficiently.

Learning Objectives:
M.K.11.1: Write numerals from 0 to 10.
M.K.11.2: Represent a given numeral 1 to 10 with objects or drawings.
M.K.11.3: Count forward from a given number 1 to 10.
M.K.11.4: Model joining sets of objects to total 10.

Students:

• Use an efficient strategy to accurately name the sums or differences within 5.

Students know:

• characteristics of addition and subtraction contexts such as putting together, adding to, taking apart, and taking from.
• Strategies for efficiently determining sums and differences within five.

Students are able to:

• Use addition strategies efficiently.

Students understand that:

• 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.

Learning Objectives:
M.K.12.1: Decompose numbers up to 5 using objects or drawings.
M.K.12.2: Compose numbers up to 5 using objects or drawings.
M.K.12.3: Count backward from 5.
M.K.12.4: Count forward to 5.

Students:

• Duplicate and extend the sequence when given a simple pattern.

Students know:

• how to sort and group objects before being able to duplicate and extend simple patterns.

Students are able to:

• Duplicate and extend simple patterns.

Students should understand that:

• looking for, describing, and extending patterns helps them develop the skills in all mathematical situations.

Learning Objectives:
M.K.13.1: Define ones and tens.
M.K.13.2: Match the number in the ones and tens position to a pictorial representation or manipulative of the value.
M.K.13.3: Add numbers 1-9 to ten to create teen numbers using manipulatives or place value blocks.
M.K.13.4: Count objects up to 10.

Students:

• Given any two-digit number from 11 and 19, use drawings or concrete objects to show and explain the decomposition of the number into one group of 10 and the correct number of ones.

Students know:

• the number sequence to 19.
• Strategies to decompose a number into tens and ones.

Students are able to:

• Use objects to compose and decompose numbers.

Students understand that:

• ten things can be represented as one ten or as ten ones.

Learning Objectives:
M.K.14.1: Define ones and tens.
M.K.14.2: Match the number in the ones and tens position to a pictorial representation or manipulative of the value.
M.K.14.3: Add numbers 1-9 to ten to create teen numbers using manipulatives or place value blocks.
M.K.14.4: Count objects up to 10.

Students:
Given a group of objects,

• sort the objects into categories (no more than ten objects in any category).
• Count the number of objects in each category.
• Order the categories by count.
• Justify their reasoning.
• Discuss information conveyed in analyzing graphs.

Students know:

• how to count.
• Sort objects.
• Category descriptors (e.g. triangles, rectangles, round, curved sides, color, etc).

Students are able to:

• sort objects.
• Effectively use strategies to count groups of objects.
• Read and understand graphs.

Students understand that:

• objects can be grouped into categories based on like characteristics.
• They can gain information from graphs.

Learning Objectives:
M.K.15.1: Identify more and less when given two groups of objects.
M.K.15.2: Identify object attributes.
Examples: color, shape, size, texture, use.
M.K.15.3: Count objects up to ten.
M.K.15.4: Count to 10 by ones.

Students:

• Given a variety of 2D and 3D objects, use informal language (short, tall, heavy, light, fat, skinny, etc.) to describe measurable attributes of objects such as length or weight.

Students know:

• how to describe similarities and differences in objects.

Students are able to:

• Describe measurable attributes of objects using informal language.

Students understand that:

• objects can be described by using measurable attributes.

Learning Objectives:
M.K.16.1: Define length and weight.
M.K.16.2: Explore objects in relationship to length and weight.

Students:

• Use direct comparisons of physical objects to determine and explain which object has more of or less of the attribute.

Students know:

• how to describe similarities and differences in objects.

Students are able to:

• Directly compare two objects and explain which object has more of or less of the attribute.

Students understand that:

• objects and geometric figures have measurable attributes that allow them to be compared.

Learning Objectives:
M.K.17.1: Use vocabulary related to length and weight.
Example: longer, shorter, heavier, lighter.
M.K.17.2: Identify objects by length and weight.
Example: shortest pencil, heaviest rock.
M.K.17.3: Sort objects according to measurable attributes.

Students:

• Describe objects in the environment using name of shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
• Describe the relative position of these objects using terms such as above, below, beside, in front of, behind, and next to.

Students know:

• 2D and 3D shapes.

Students are able to:

• Describe objects in the environment using names of shapes.
• Describe the relative position of objects.

Students understand that:

• the world is made up of geometric shapes.

Learning Objectives:
M.K.18.1: Recognize location and position.
Examples: above, below, beside, in front of, behind, next to.
M.K.18.2: Identify cubes, cones, cylinders, and spheres.
M.K.18.3: Imitate actions to place items.
Examples: in, on, under.
M.K.18.4: Match shapes.

Students:

• Use visual characteristics of shapes to orally justify naming 2D and 3D shapes in a variety of sizes and orientations.

Students know:

• 2D and 3D shapes.

Students are able to:

• Use geometric reasoning and visual characteristics of shapes to name shapes in a variety of sizes and orientations.

Students understand that:

• geometric shapes can be sorted based on like characteristics.

Learning Objectives:
M.K.19.1: Recognize shapes.
M.K.19.2: Sort shapes with different attributes.
Examples: sort different size or color squares, circles, triangles, rectangles or hexagons.

Students:

• Use visual characteristics of shapes (flat, fat, sticking out, solid, etc.) to justify categorizing shapes as 2D or 3D.

Students know:

• Characteristics of 2D and 3D shapes.

Students are able to:

• Use geometric reasoning and visual characteristics of shapes to designate shapes as 2D or 3D.

Students understand that:

• geometrics shapes can be grouped into classes of 2D or 3D shapes based on their physical characteristics.

Learning Objectives:
M.K.20.1: Define two-dimensional and three-dimensional.
Example: two-dimensional shapes are flat, three-dimensional figures are solid.
M.K.20.2: Sort flat and solid objects.
M.K.20.3: Explore two-dimensional shapes and three-dimensional figures.

Students:

• Use informal language to describe, compare, and contrast a variety of 2D and 3D shapes.

Students know:

• attributes of shapes (sides, corners, vertices, faces, edges, etc.).
• Informal language to describe these components.

Students are able to:

• Use geometric reasoning and attributes to compare and contrast a variety of shapes.

Students understand that:

• geometric shapes can be grouped into classes of shapes that all seem to be alike based on their visual characteristics.

Learning Objectives:
M.K.21.1: Define similar and different.
M.K.21.2: Use vocabulary related to two-dimensional shapes and three-dimensional figures.
Examples: vertices (corners), faces (flat surfaces), edges, sides, angles.
M.K.21.3: Recognize vocabulary related to two-dimensional shapes and three-dimensional figures.
M.K.21.4: Identify two-dimensional shapes and three-dimensional figures.
M.K.21.5: Identify shapes.

Students:

• Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.

Students know:

• 2D and 3D shapes (triangle, square, rectangle, hexagon, rhombus, circle, cube, cylinder, sphere, cone).

Students are able to:

• Compose shapes with known attributes using a variety of materials (pipe cleaners, marshmallows/toothpicks, etc.).

Students understand that:

• geometric shapes can be constructed and represented using a variety of physical materials.

Learning Objectives:
M.K.22.1: Recognize attributes of shapes.
M.K.22.2: Identify cubes, cones, cylinders, and spheres.
M.K.22.3: Identify squares, circles, triangles, rectangles, and hexagons.
M.K.22.4: Identify shapes in the environment.
M.K.22.5: Trace shapes.
M.K.22.6: Make purpose marks such as lines and circles.

Students:

• Combine simple shapes to construct known larger shapes.

Students know:

• 2D and 3D shapes (triangle, square, rectangle, hexagon, rhombus, circle, cube, cylinder, sphere, cone).

Students are able to:

• Combine simple shapes to form larger shapes.

Students understand that:

• geometric shapes can be composed of and decomposed into smaller shapes.

Learning Objectives:
M.K.23.1: Combine shapes to fill the area of a given shape.
M.K.23.2: Decompose pictures made of simple shapes.
M.K.23.3: Match shapes.
M.K.23.4: Match pieces by color, image, or shape to complete a puzzle.

Students:

• Use a variety of representations to solve word problems.
• Justify and explain answers using concrete objects and drawings.

Students know:

• addition and subtraction strategies and models.
• how to form an equation.

Students are able to:

• represent quantities and operations (addition & subtraction) with concrete objects, pictorially, or symbolically.
• Use informal and mathematical language to communicate the representations.
• Accurately compute sums and differences.

Students understand that:

• addition is both putting together and adding to. subtraction is taking apart, taking from, and comparisons.
• Mathematical problems can be solved using a variety of strategies. models, and representations.
• variables in the form of blanks, boxes, or letters, represent unknown quantities when representing mathematical situations algebraically.

Learning Objectives:
M.1.1.1: Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
M.1.1.2: Understand key words in addition and subtraction word problems.
Examples: sum, difference, all together, how many more, how many are left, in all.
M.1.1.3: Define subtraction as separating groups of objects, taking from, or taking apart.
M.1.1.4: Define addition as combining groups of objects, adding to, or putting together.
M.1.1.5: Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.
M.1.1.6: Represent numbers with objects or drawings.
M.1.1.7: Use objects to combine and separate groups.

Students:

• Compute the sum of three whole numbers using a variety of representations such as concrete objects, drawings, or equations.
• Explain and justify the answer using the representations.

Students know:

• how to solve for addition by using strategies and understanding the relationship between addition and subtraction.

Students are able to:

• efficiently apply strategies for solving multiple addend problems.
• Use symbols to represent unknown quantities in equations.
• Accurately compute sums.

Students understand that:

• more than two quantities can be combined in a problem.

Learning Objectives:
M.1.2.1: Solve addition word problems with sums less than or equal to 10, e.g., by using objects or drawings to represent the problem.
M.1.2.2: Understand key words in addition word problems.
Examples: sum, all together, how many more, in all.
M.1.2.3: Define addition as combining groups of objects, adding to, or putting together.
M.1.2.4: Represent addition with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.
M.1.2.5: Represent numbers with objects or drawings.
M.1.2.6: Use objects to combine groups.

Students:

• Use informal language of properties to justify their sums and differences ("I already figured out that 8 + 3 = 11, and 3 + 8 is just the turn around of that so it must be 11, too.").

Students know:

• addition and subtraction strategies.
• how to form an equation.
li>how the commutative property works.

Students are able to:

• Strategically apply properties of addition in order to find sums.

Students understand that:

• the order in which addends are joined doesn't change the sum.
• numbers may be composed or decomposed in a variety of ways.

Learning Objectives:
M.1.3.1: Define addition and subtraction.
M.1.3.2: Recognize properties of operations.
M.1.3.3: Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
M.1.3.4: Apply signs +, -, = to actions of joining and separating sets. M 1.3.5: Identify fact families to ten.
M.1.3.6: Recognize the value of zero.

Students:

• Use a pictorial or physical model to explain the connection between subtraction and addition.

Students know:

• The relationship between addition and subtraction.
• how to explain subtraction as an unknown addend.

Students are able to:

• use symbols such as blanks, boxes, or letters to represent unknown quantities in equations.
• Communicate the connections between subtraction and addition.
• Use the inverse relationship between addition and subtraction to find differences.
• Choose and apply addition and subtraction strategies to accurately determine sums and differences within 20.

Students understand that:

• addition and subtraction have an inverse relationship that can be used to solve problems.

Learning Objectives:
M.1.4.1: Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
M.1.4.2: Identify fact families to ten.
M.1.4.3: Recall basic addition facts to ten.
M.1.4.4: Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.

Students:

• Use modeling strategies (number paths, counting objects) to justify solutions (both counting on and counting back) and to show the relationship between counting, addition, and subtraction.

Students know:

• how to count on or count back from a given number within 20.

Students are able to:

• Explain counting strategies for addition and subtraction.

Students understand that:

• counting patterns can be used to find solutions in addition and subtraction situations.
• A variety of models and tools can be used to communicate justifications for mathematical ideas and solutions.

Learning Objectives:
M.1.5.1: Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.
M.1.5.2: Count forward and backward from a given number.
M.1.5.3: Count to 20 by ones.

Students:

• Use an efficient strategy (e.g., recall, doubles, counting on 1 or 2, close to doubles) to add numbers within 20.
• Fluently add and subtract within 10.

Students know:

• Strategies for finding sums and differences within 20.

Students are able to:

• Use addition and subtraction strategies.

Students understand that:

• Addition and subtraction strategies can be used to compute sums and differences, and how.

Learning Objectives:
M.1.6.1: Decompose numbers less than or equal to 10.
M.1.6.2: Add and subtract within 5.
M.1.6.3: Count forward and backward from a given number.
M.1.6.4: Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.

Students:

• Justify the truth of the statement on each side of the equal sign.

Students know:

• strategies for finding the value of simple addition and subtraction equations.
• Strategies for comparing quantities between 0 and 20.
• Strategies to show equality or inequality.

Students are able to:

• efficiently apply strategies for determining the value of simple addition and subtraction equations.
• Justify and explain their thinking.

Students understand that:

• the equal sign represents a relationship of balance between numerical expressions rather than performing an operation.

Learning Objectives:
M.1.7.1: Define true, false, and equal.
M.1.7.2: Demonstrate equal using manipulatives or object drawings.
M.1.7.3: Recall basic addition facts to ten.
M.1.7.4: Recognize equation symbols in vertical and horizontal addition and subtraction problems.
M.1.7.5: Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.

Students:

• Solve single operation addition/subtraction equations containing a single unknown.

Students know:

• Strategies for solving simple addition or subtraction equations with one unknown.

Students are able to:

• solve simple addition and subtraction equations.
• Justify and explain their thinking.

Students understand that:

• equalities contain expressions that name the same amount on each side of the equal sign, even with quantities unknown.

Learning Objectives:
M.1.8.1: Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
M.1.8.2: Identify fact families as a relationship between addition and subtraction.
M.1.8.3: Recall basic addition and subtraction facts to ten.
M.1.8.4: Identify plus, minus, and equal signs.
M.1.8.5: Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.

Students:

• Reproduce a pattern.
• Extend a pattern.
• Create patterns.
• Create sequences of numbers.

Students know:

• how to duplicate simple patterns.
• how to extend simple patterns.

Students are able to:

• reproduce given patterns.
• Extend given patterns.
• Create patterns.
• Create sequences of numbers.

Students should understand that:

• looking for, describing, and extending patterns can be used to help them develop skills in all mathematical situations.

Learning Objectives:
M.1.9.1: Duplicate and extend simple patterns by using concrete objects.
M.1.9.2: Identify simple patterns.
M.1.9.3: Mimic simple patterns.
M.1.9.4: Match a simple object.

Students:

• Use the pattern and regularity in the counting sequence to recognize the position of any number between 0 and 120 and then continue counting in sequence from the given number.
• Count backwards by ones from any given number 0 to 120.
• Write the corresponding numeral when given a number orally or given a quantity of objects from 0 to 120.

Students know:

• number/numeral correspondence (from 0-120).
• Strategies for counting sets of objects.
• how to read numbrs from 0 - 120.
• how to write numbers from 0 - 120.

Students are able to:

• strategically apply counting strategies.
• Write numerals 0-20.

Students understand that:

• there are patterns in our base ten number system.
• quantities can be represented both physically and symbolically (numerals).

Learning Objectives:
M.1.10.1: Write numerals from 0 to 20.
M.1.10.2: Recognize numerals to 100.
M.1.10.3: Match the numeral to the number objects or picture of objects.
M.1.10.4: Count to 100 by ones.
M.1.10.5: Count to 20 by ones.
M.1.10.6: Identify and name numerals 0-9.
M.1.10.7: Trace numerals 0-9.

Students:

• Use a variety of representations (symbolic: 10+8. pictorial: one line and 8 dots. physical: place value blocks, bundles of sticks, or groups of fingers, etc.) to show and explain the decomposition of the number into groups of 10 and ones.

Students know:

• how to decompose numbers 11-19.

Students are able to:

• Use place value models or mental strategies to decompose numbers.

Students understand that:

• a two-digit number represents amounts of tens and ones.
• Ten things can be represented as one ten or as ten ones.

Learning Objectives:
M.1.11.1: Match the number in the ones and tens position to a pictorial representation or manipulative of the value.
M.1.11.2: Represent numbers with multiple models.
Examples: models—base ten blocks, number lines, linking cubes, straw bundles.
M.1.11.3: Count to 100 by tens.
M.1.11.4: Count 10 objects.
M.1.11.5: Count to 10 by ones.
M.1.11.6: Name numerals 0 to 19.

Students:

• Use place value terminology and concepts to explain and justify the use of <, =, > to compare the numbers and create true equalities and inequalities.

Students know:

• how to compare quantities using the terminology "greater than", "equal to", and "less than".

Students are able to:

• compare 2-digit numbers.

Students understand that:

• numbers can be decomposed to determine if the amount is greater than, equal to, or less than, how that can be done.

Learning Objectives:
M.1.12.1: Define greater than, less than and equal to.
M.1.12.2: Demonstrate greater than, less than, and equal to using manipulatives, object drawings or numbers 0 to 10.
M.1.12.3: Use comparison vocabulary.
Examples: greater than, equal to, and less than.
M.1.12.4: Recognize symbols for greater than, less than and equal to.
M.1.12.5: Determine the value of the digits in the ones and tens place.
M.1.12.6: Identify sets with more, less or equal objects.
M.1.12.7: Imitate creating sets of a given size.

Students:

• Add within 100.
• Explain their reasoning using concrete models or drawings, or using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
• Relate the strategy used to a written method (symbolic and numeric recording of the steps used).

Students know:

• how to add within 100 using place vaue strategies.
• how to identify tens and ones.
• how to compose two digit numbers.
• how to decompose two digit numbers.

Students are able to:

• add within 100.
• Model addition problems using visual models.
• Record strategies for solving addition problems.
• Communicate the relationship between models and symbolic (numeric) representations.

Students understand that:

• relationships between models of addition problems and written strategies of those models can be used to justify solutions.

Learning Objectives:
M.1.13.1: Demonstrate regrouping, total sum, and solve using drawings and concrete models.
M.1.13.2: Model written method for recording horizontal addition problems.
M.1.13.3: Determine the value of the number in the ones and tens place.
M.1.13.4: Match the number in the ones, tens, and hundreds position to a pictorial representation or manipulative of the value.
M.1.13.5: Represent numbers with multiple models.
Examples: models—base ten blocks, number lines, linking cubes, straw bundles.
M.1.13.6: Recall single-digit addition facts.

Students:

• Can efficiently find 10 more or 10 less than the given number.
• Explain their mental strategies.

Students know:

• how to mentally find 10 more or 10 less of a two digit number and explain reasoning.
• place value vocabulary: tens, ones.

Students are able to:

• mentally add or subtract 10 from a number in the range from 1-100.
• Explain their reasoning using place value understanding and patterns.

Students understand that:

• patterns in the place value system can be used to mentally compute sums and differences.

Learning Objectives:
M.1.14.1: Define more and less.
M.1.14.2: Demonstrate conceptual understanding of adding or subtracting 10 using concrete models.
M.1.14.3: Count backward from 100 by tens.
M.1.14.4: Count forward to 100 by tens.
M.1.14.5: Count to 100 by ones.

Students:

• subtract multiples of 10 from more tens using concrete models, drawings, and written equations.
• look for and describe patterns they find.
• explain their reasoning using place value and patterns.

Students know:

• place value models for adding and subtracting numbers less than 100.
• strategies for adding and subtracting multiples of 10.

Students are able to:

• use models and strategies to find and record solutions to problems where a multiple of 10 is subtracted.
• explain their strategies.

Students understand that:

• patterns in the place value system can be used to mentally compute sums and differences.

Learning Objectives:
M.1.15.1: Demonstrate conceptual understanding of subtraction using concrete models.
M.1.15.2: Model written method for recording problems involving subtraction of 10 from multiples of 10.
M.1.15.3: Count backward from 100 by tens.
M.1.15.4: Count forward to 100 by tens. M 1.15.5: Mimic counting to 100 by tens.

Students:

• will create a table or chart to organize and represent data with up to three categories using physical objects, tally mark graphs, pictographs, Venn diagrams, yes/no charts, or bar graphs.
• analyze and interpret the data verbally and in writing by asking and answering questions about the total number of data points, how many in each category, or how many more or less are in one category than in another.
• use measurement vocabulary such as most, least, more than, less than, and similar comparison words.

Students know:

• objects can be grouped into categories based on like characteristics.
• they can gain information from graphs.

Students are able to:

• create, analyze, and interpret data.

Students understand that:

• questions concerning mathematical contexts can be answered by collecting and organizing data.

Learning Objectives:
M.1.16.1: Define more and less.
M.1.16.2: Describe methods for representing data.
Examples: pictographs, tally charts, bar graphs, and Venn Diagrams.
M.1.16.3: Locate information on data displays.
M.1.16.4: Classify objects into given categories; count the number of objects in each category, and sort the categories by count.
M.1.16.5: Recognize different types of data displays.

Students:

• use measurement vocabulary to first estimate, describe, and then compare the measurable attributes.

Students know:

• how to correctly align the objects.

Students are able to:

• use direct and indirect comparison to order objects by length.

Students understand that:

• measurable attributes of objects can be used to describe and compare the objects.

Learning Objectives:
M.1.17.1: Define length.
M.1.17.2: Use vocabulary related to length.
Examples: longer, shorter, longest, shortest, taller.
M.1.17.3: Identify objects by length.
Examples: shortest pencil, tallest boy.
M.1.17.4: Sort objects according to length.
Example: sort short pencils from long pencils.
M.1.17.5: Explore objects in relationship to length.

Students:

• accurately measure length using non-standard units (e.g., paper clips, Cuisenaire rods).
• understand that units must be laid end to end with no gaps or overlaps when measuring.

Students know:

• measurable attributes of objects, specifically length.

Students are able to:

• accurately measure length using non-standard units (to the nearest whole unit).

Students understand that:

• the smaller the unit, the more units will be needed to measure the object.
• the larger the unit, the fewer units needed to measure an object.

Learning Objectives:
M.1.18.1: Describe gap and overlap.
M.1.18.2: Describe what it means to measure using non-standard units.
M.1.18.3: Model measuring using non-standard units.

Students:

• tell and write time in hours and half-hours using analog and digital clocks.

Students know:

• how to tell time to the hour and half hour using analog and digital clocks.
• how to tell time to the hour and half hour using analog and digitial clocks.

Students are able to:

• accurately read and write time to the hour and half hour from analog and digital clocks.

Students understand that:

• analog and digital clocks represent the time at any particular moment and show the passage of time with the movement of the hands or the changing of the digits.

Learning Objectives:
M.1.19.1: Describe the short hand as the hour hand and the long hand as the minute hand on an analog clock.
M.1.19.2: Describe the first number as the hour, and the numbers after the colon as the minutes on a digital clock.
M.1.19.3: Count to 30 by fives.
M.1.19.4: Recognize numbers 1 to 12, and 30.
M.1.19.5: Trace numerals 1 to 12, and 30.
M.1.19.6: Associate digital and analog clocks with the measurement of time.

Students:

• identify pennies by name and value.
• identify dimes by name and value.

Students know:

• how to count by ones and identify a penny.
• how to count by tens and identify a dime.

Students are able to:

• identify a penny by name and its value as 1 cent.
• identify a dime by name and its value as 10 cents.

Students understand that:

• pennies represents counting by ones.
• a dime represents counting by tens.

Learning Objectives:
M.1.20.1: Identify that a penny has a value of one cent and demonstrate that 10 pennies has the same value as 1 dime.
M.1.20.2: Recognize the value of 1 and 10.
M.1.20.3: Sort pennies and dimes.
M.1.20.4: Count 10 objects.

Students:

• build and draw two dimensional shapes.
• define attributes such as number of sides and the name of the shape.

Students know:

• defining characteristics of basic shapes (triangles, rectangles, squares, circles).

Students are able to:

• use defining characteristics to build/draw and identify basic shapes.

Students understand that:

• shapes may be sorted by many sets of attributes, but their geometric classification is based on certain defining attributes.

Learning Objectives:
M.1.21.1: Define side, angle, closed and open.
M.1.21.2: Describe attributes of shapes.
Examples: number of sides, number of angles.
M.1.21.3: Identify two-dimensional shapes.
M.1.21.4: Sort two-dimensional shapes.
M.1.21.5: Identify basic attributes.
Examples: color, shape, size.

Students:

• compose 2D shapes from smaller 2D shapes (e.g., use two right triangles to make a square or two squares to make a rectangle).
• compose 3D shapes from smaller 3D shapes (e.g., use two cubes to make a rectangular prism or two triangular prisms to make a rectangular prism).

Students know:

• attributes of basic shapes (rectangles, squares, trapezoids, triangles, half-circles, quarter-circles, cubes, right rectangular prisms, right circular cones, and right circular cylinders).

Students are able to:

• use shape manipulatives to create composite shapes.

Students understand that:

• composite shapes and figures are created by joining two or more geometric shapes together to create a different shape.

Learning Objectives:
M.1.22.1: Combine shapes to fill in the area of a given shape.
M.1.22.2: Replicate composite shapes.
M.1.22.3: Decompose pictures made of simple shapes.
M.1.22.4: Name shapes.
Examples: square, circle, triangle, rectangle, and hexagon.
M.1.22.5: Recognize shapes.

Students:

• divide shapes into two and four equal shares.
• describe the whole as cut into halves, fourths, and quarters.
• describe a set of like pieces as halves, fourths, quarters.
• describes a single piece as half of, fourth of, or quarter of when compared to the whole.
• describe the whole as two of, or four of the shares.
• explain that cutting the shape into more shares creates smaller pieces.

Students know:

• how to patition shapes into halves or fourths describe the shares using academic vocabulary.

Students are able to:

• decompose circles and rectangles into halves and fourths.
• explain the size of pieces using the appropriate fraction terminology.
• explain the relative size of halves and fourths by reasoning about the number of shares created.

Students understand that:

• fractional parts of a whole are equal-sized portions of that whole.
• decomposing into more equal shares creates smaller shares.

Learning Objectives:
M.1.23.1: Define halves, fourths, quarters, whole, parts (shares) and equal.
M.1.23.2: Demonstrate sharing situations to show equal smaller shares.
M.1.23.3: Distinguish between equal and non-equal parts.
M.1.23.4: Decompose pictures made of simple shapes.
M.1.23.5: Identify squares, circles, triangles and rectangles.

Students:

• solve a variety of addition and subtraction problems, using concrete and pictorial representations.
• explain and justify solutions using connections among a variety of representations (e.g., manipulatives, drawings, and equations with a symbol for the unknown number).
• write equations that represent the work they have shown.

Students know:

• addition and subtraction strategies to solve one- and two-step word problems within a 100.

Students are able to:

• represent quantities and operations (addition & subtraction) physically, pictorially, or symbolically.
• strategically use a variety of representations to solve addition and subtraction word problem.
• use informal and mathematical language to communicate the connections among addition and subtraction.
• accurately compute sums and differences.
• use symbols to represent unknown quantities in equations.

Students understand that:

• addition is both putting together and adding to.
• subtraction is taking apart, taking from, and comparisons.
• mathematical problems can be solved using a variety of strategies, models, representations.
• variables represent unknown quantities when representing mathematical situations algebraically.

Learning Objectives:
M.2.1.1: Solve one-step addition and subtraction word problems with an unknown by using drawings and equations with a symbol for the unknown number to represent the problem.
M.2.1.2: Understand key words in addition and subtraction word problems.
Examples: adding to, taking from, putting together, taking apart, sum, difference, all together, how many more, how many are left, in all.
M.2.1.3: Locate the unknown regardless of position.
Examples: start unknown, change unknown, and result unknown.
M.2.1.4: Apply signs +, -, = to actions of joining and separating sets.
M.2.1.5: Add and subtract within 50, e.g., by using objects or drawings to represent the problem.
M.2.1.6: Solve 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 or drawings to represent the problem.
M.2.1.7: Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.
M.2.1.8: Represent numbers with objects or drawings.

Students:

• find sums and differences of basic facts through sums of 20.
• use an efficient mental strategy (recall, inverse to addition, derived facts) to find the difference (large minus small) of two numbers less than twenty.
• show fluency (efficiency and accuracy based on understanding) with sums of 20.
• when given two one-digit numbers can state their sum with minimal hesitation (by the end of 2nd grade).

Students know:

• how to use mental strategies to add and subtract within 20.

Students are able to:

• use addition and subtraction strategies efficiently.

Students understand that:

• 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.

Learning Objectives:
M.2.2.1: Recall single-digit subtraction facts with minuends of 10 or less.
M.2.2.2: Recall single-digit addition facts with sums up to 10.
M.2.2.3: Apply addition and subtraction strategies.
Examples: doubles, doubles plus one, doubles minus one.
M.2.2.4: Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

Students:

• determine whether the set has an odd or even number of objects.
• explain odd + odd = odd, even + even = even, odd + even = odd.

Students know:

• how to make equal groups and determine if that group has an odd or even amount of objects.

Students are able to:

• use strategies to determine whether numbers are odd or even.
• communicate reasoning for a label of odd or even.

Students understand that:

• numbers are classified as odd or even based on their characteristics.
• the term even describes numbers that can be divided into groups of 2 with no leftovers.
• the term odd describes numbers that when divided into groups of 2 will have one item leftover.

Learning Objectives:
M.2.3.1: Define pair, odd and even.
M.2.3.2: Recall doubles addition facts with sums to 20.
M.2.3.3: Apply signs + and = to actions of joining sets.
M.2.3.4: Model written method for composing equations.
M.2.3.5: Skip count by 2s.

Students:

• use rectangular arrays to determine the total number of objects.
• use repeated addition to determine the total number of objects.
• write equations expressing the total number of objects with repeated addition.

Students know:

• how to use arrays and repeated addition as multiplication strategies.

Students are able to:

• represent the total number of objects in a rectangular array as the sum of repeated addition.
• choose and apply addition strategies to accurately compute sums for multiple addend problems.

Students understand that:

• repeated addition determines the total number of items in a rectangular array.

Learning Objectives:
M.2.4.1: Distinguish between rows and columns.
M.2.4.2: Use repeated addition to solve problems with multiple addends.
M.2.4.3: Count forward in multiples from a given number.
Examples: 3, 6, 9, 12; 4, 8, 12, 16.
M.2.4.4: Recall doubles addition facts.
M.2.4.5: Model written method for composing equations.

Students:

• reproduce a pattern.
• extend a pattern.
• create patterns.
• describe number patterns and sequences.

Students know:

• how to duplicate simple patterns.
• how to extend simple patterns.
• how to create simple patterns.

Students are able to:

• reproduce given patterns.
• extend given patterns.
• create patterns.
• describe patterns.
• describe numbers patterns.

Students should be engaged in looking for, describing, and extending patterns to help them develop the skills in all mathematical situations.

Learning Objectives:
M.2.5.1: Describe a pattern of colors, shapes, and/or numbers using a variety of materials.
M.2.5.2: Create a pattern of colors, shapes, and/or numbers using a variety of materials.
M.2.5.3: Extend a pattern of colors, shapes, and/or numbers.
M.2.5.4: Mimic a simple pattern of colors, shapes, and/or numbers.
M.2.5.5: Match a simple pattern of colors, shapes, and/or numbers.

Students:

• use concrete materials to bundle groups of 10 to represent numbers (including 100, 200, 300) as bundles of one hundred with no tens and no ones.
• describe multiples of 100 using words that include the number of groups of a hundred as a unit.
• recognize and explain a variety of names for a single quantity up to 1,000 (706 as 706 ones, 70 tens and 6 ones, and 7 hundreds and 6 ones).

Students know:

• vocabulary of the structure of numbers (place value: ones, tens, hundreds, etc.).
• patterns and regularities that exist in the place value system (ten ones make a ten, ten tens make a hundred, etc.).

Students are able to:

• represent numbers using a variety of models (physical, visual, and symbolic).
• explain the relationships among various representations and models of three-digit numbers.

Students understand that:

• three digit numbers are made up of a variety of base ten representations.
• one hundred can be thought of as one group of 100, ten groups of 10, or 100 ones.

Learning Objectives:
M.2.6.1: Match the number in the ones, tens, and hundreds position to a pictorial representation or manipulative of the value.
M.2.6.2: Represent numbers with multiple concrete models.
Examples: concrete models—base ten blocks, number lines, linking cubes, straw bundles.
M.2.6.3: Count to 1000 by hundreds.
M.2.6.4: Count to 100 by tens.
M.2.6.5: Create groups of 10.
M.2.6.6: Match the numeral in the ones and tens position to a pictorial representation or manipulative of the value.
M.2.6.7: Match the numeral to the number of objects or picture of objects.

Students:

• use the pattern and regularity in the counting sequence to recognize the position of any number between 1 and 1000 and then continue counting in sequence from the given number.
• given any multiple of 5, 10, or 100, continue counting by the corresponding base (count by 5s from any multiple of 5, count by 10s from any multiple of 10, etc.).

Students know:

• how to count from 0 to 1,000 by ones, fives, tens, and hundreds.

Students are able to:

• use patterns and regularity in counting sequences to count by 1s, 5s, 10s, & 100s to 1000.

Students understand that:

• patterns and regularities in the counting sequence are useful in reasoning about numbers and solving problems.
• there are patterns in our base ten number system.
• quantities can be represented both physically and symbolically (numerals).

Learning Objectives:
M.2.7.1: Create a number pattern.
M.2.7.2: Count backward from 100 by fives and tens.
M.2.7.3: Count forward to 100 by fives and tens.
M.2.7.4: Count to 100 by ones.

Students:

• read and write numbers represented in expanded form.
• read the number name the physical model represents.
• read number names without physical models.

Students know:

• how to read and write numbers up to 1,000.
• how to read and write numbers in expanded form up to 1,000.

Students are able to:

• represent quantities in a variety of forms including words, base-ten numerals, and expanded form.

Students understand that:

• there are patterns and regularities in the counting sequence.
• the same quantity can be represented with words, base-ten numerals, or expanded form, and all forms are useful in different situations.

Learning Objectives:
M.2.8.1: Identify zero as a place holder in two-digit and three–digit numbers.
M.2.8.2: Match the number in the ones, tens, and hundreds position to a pictorial representation or manipulative of the value.
M.2.8.3: Identify the value of number in the ones, tens and hundreds place.
M.2.8.4: Identify place value for ones, tens and hundreds.
M.2.8.5: Read number names one through one hundred.
M.2.8.6: Write numerals 1 to 100.
M.2.8.7: Recognize number names one through twenty.
M.2.8.8: Trace numerals 0 to 100.

Students:

• use place value terminology and concepts to explain and justify the placement of <, =, > to compare two 3-digit numbers and create true equalities and inequalities.

Students know:

• how to compare 3-digit numbers using the terminology "greater than," "equal to," and "less than".

Students are able to:

• compare 3-digit numbers using place value concepts.
• justify their reasoning as they compare numbers.

Students understand that:

• the three digits of a 3-digit number represent groups of hundreds, tens, and ones.

Learning Objectives:
M.2.9.1: Define greater than, less than and equal to.
M.2.9.2: Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.
M.2.9.3: Arrange two-digit numbers in order from greatest to least or least to greatest.
M.2.9.4: Identify zero as a place holder in two-digit and three-digit numbers.
M.2.9.5: Model using >, =, and < symbols to record the results of comparisons of two two-digit numbers.
M.2.9.6: Select numbers on a number line that are more than, less than or equal to a specified number.
M.2.9.7: Match the words greater than, equal to and less than to the symbols >, =, and <.
M.2.9.8: Determine the value of the digits in the ones and tens place.
M.2.9.9: Identify sets with more, less or equal objects.

Students:

• solve addition examples with sums to 100 using a variety of strategies.
• solve subtraction examples with differences within 100 using a variety of strategies.
• justify solutions and explain the reasoning for the strategy chosen.

Students know:

• strategies and methods for symbolically (numerically) recording strategies for fluently solving addition and subtraction problems.

Students are able to:

• record strategies for solving addition and subtraction problems.
• communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems.

Students understand that:

• models/strategies can be used to justify their answers.

Learning Objectives:
M.2.10.1: Add within 100, including adding a two-digit number and a one-digit number and adding two two-digit numbers, 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.
M.2.10.2: Add within 20, demonstrating fluency for addition within 10. Use strategies such as counting on; making ten; decomposing a number leading to a ten; and creating equivalent but easier or known sums.
M.2.10.3: Determine the value of the number in the ones, tens and hundreds place.
M.2.10.4: Model written method for recording horizontal and vertical addition problems.
M.2.10.5: Understand that the two digits of a two-digit number represent amounts of tens and ones.
M.2.10.6: Match the number in the ones and tens position to a pictorial representation or manipulative of the value.

Students:

• add up to four 2-digit numbers using strategies based on place value and/or properties of operations.
• justify solutions and explain the reasoning for the strategy chosen.

Students know:

• to use place value strategies to add up tp four 2-digit numbers and justify their thinking.

Students are able to:

• strategically choose and then record methods for efficiently and accurately solving addition problems with multiple addends.

Students understand that:

• choosing efficient strategies for finding sums of multiple addends depends on the numbers in the problem.

Learning Objectives:
M.2.11.1: Add within 100, including adding a two-digit number and a one-digit number and adding two two-digit numbers, 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.
M.2.11.2: Add within 20, demonstrating fluency for addition within 10. Use strategies such as counting on; making ten; decomposing a number leading to a ten; and creating equivalent but easier or known sums.
M.2.11.3: Determine the value of the number in the ones, tens and hundreds place.
M.2.11.4: Model written method for recording horizontal and vertical addition problems.
M.2.11.5: Understand that the two digits of a two-digit number represent amounts of tens and ones.
M.2.11.6: Match the number in the ones and tens position to a pictorial representation or manipulative of the value.

Students:

• add and subtract within 1000.
• explain their reasoning using concrete models or drawings, or using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
• relate the strategy used to a written method (symbolic and numeric recording of the steps used).

Students know:

• how to count to 1,000.
• how to identify hundreds, tens, and ones.
• how to compose numbers.
• how to decompose two digit numbers.
• how to record strategies for solving addition and subtraction problems.

Students are able to:

• add and subtract within 1000.
• model addition problems using visual models.
• record strategies for solving addition problems.
• communicate the relationship between models and symbolic (numeric) representations.

Students understand that:

• relationships between models of addition/subtraction problems and written strategies of those models can be used to justify solutions.

Learning Objectives:
M.2.12.1: Define regrouping, total, sum, difference and solve.
M.2.12.2: Add and subtract two two-digit numbers with and without regrouping.
M.2.12.3: Determine the value of the number in the ones, tens, hundreds and thousands place using concrete models or drawings and strategies based on place value.
M.2.12.4: Match the number in the ones, tens, hundreds and thousands position to a pictorial representation or manipulative of the value.
M.2.12.5: Model written method for recording horizontal and vertical addition and subtraction problems.
M.2.12.6: Represent two- and three-digit numbers with multiple models.
Examples: models—base ten blocks, number lines, linking cubes, straw bundles.
M.2.12.7: Recall single-digit addition and subtraction facts.
M.2.12.8: Add and subtract within 20, e.g., by using objects or drawings to represent the problem.

Students:

• Use a variety of materials and strategies to add or subtract 10 or 100 from a three-digit number in the range of 100 to 900.

Students know:

• use place value models for adding and subtracting numbers from 1 to 1000.
• use strategies for mentally adding and subtracting multiples of 10 and 100.

Students are able to:

• use patterns and regularity in counting sequences and understandings of place value to add or subtract a "ten" or a "hundred".
• communicate reasoning and solution strategies.

Students understand that:

• the digits of a 3-digit number represent amounts of hundreds, tens and ones.
• patterns in the place value system can be used to mentally compute sums and differences.

Learning Objectives:
M. 2.13.1: Demonstrate conceptual understanding of adding or subtracting 10 using concrete models.
M.2.13.2: Recognize the place value of ones, tens and hundreds.
M.2.13.3: Count forward and backward by 100.
M.2.13.4: Count forward and backward by 10.
M.2.13.5: Recall single-digit subtraction facts.
M.2.13.6: Recall single-digit addition facts.

Students:

• solve addition and subtraction problems using objects, pictures, words and numbers. Explain and justify strategies for adding and subtracting.

Students know:

• strategies for finding sums and differences.
• physical (manipulative) models and pictorial models (place value blocks, lines and dots, bundles and sticks, etc.) for representing numbers using place value concepts.

Students are able to:

• use logical reasoning, place value concepts and vocabulary, and properties of numbers and operations to justify strategies for finding sums and differences.

Students understand that:

• relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and strategies.

Learning Objectives:
M.2.14.1: Explain addition and subtraction problems using concrete objects, pictures.
M.2.14.2: Use multiple strategies to add and subtract including counting on, counting back and using doubles.
M.2.14.3: Recall single-digit subtraction facts.
M.2.14.4: Recall single-digit addition facts.
M.2.14.5: Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

Students:

• use line plots (whole number scale) to display the data generated by measuring lengths of several objects.
• communicate questions and descriptions related to the data display.

Students know:

• to use graphs to make observations about the data.

Students are able to:

• use standard units and the related tools to measure length to the nearest whole unit.
• organize and represent length measurement data on a line plot.
• analyze data.

Students understand that:

• questions concerning mathematical contexts can be answered by collecting and organizing data and displaying the data in line plots.

Learning Objectives:
M.2.15.1: Define length and line plot.
M.2.15.2: Use vocabulary related to comparison of length.
Examples: longer, shorter, longest, shortest, taller.
M.2.15.3: Demonstrate rounding up to the nearest whole unit on measurement tools.
M.2.15.4: Demonstrate measuring length using standard units.
M.2.15.5: Describe a line plot.
M.2.15.6: Model measuring length using standard units.
M.2.15.7: Identify objects by length.
M.2.15.8: Sort objects according to length.
M.2.15.9: Explore objects in relationship to length.

Students:

• collect data.
• represent data in picture graph or bar graph format.
• share a summary of that data.
• share conclusions.

Students know:

• strategies for collecting, organizing, and recording data.
• strategies for counting and comparing quantities.
• strategies for solving addition and subtraction problems.

Students are able to:

• choose and apply appropriate strategies for organizing and recording data.
• read and interpret graphical representations (pictographs and bar graphs) of data.
• communicate and defend solutions and solution paths.

Students understand that:

• questions concerning mathematical contexts can be answered by collecting and organizing data on pictographs and bar graphs.

Learning Objectives:
M.2.16.1: Use addition and subtraction within 20 to solve addition and subtraction word problems with an unknown number.
M.2.16.2: Describe picture graph and bar graph.
M.2.16.3: Demonstrate conceptual understanding of adding or subtracting using a variety of materials.
M.2.16.4: Use vocabulary related to comparing data.
Examples: more than, less than, most, least, equal.
M.2.16.5: Recognize attributes of data displays.
M.2.16.6: Locate information on data displays.
M.2.16.7: Classify objects into given categories.
M.2.16.8: Sort the categories by count.
M.2.16.9: Recognize different types of data displays.
M.2.16.10: Count objects up to 50.

Students:

• choose appropriate tools and units of measurement based on size of object.
• measure objects correctly.

Students know:

• standard units of length measure (inches, feet, yards, centimeters and meters) and the related tools.

Students are able to:

• measure length in standard units (inches, feet, yards, centimeters and meters).
• choose and accurately use appropriate measurement tools and units of measure.

Students understand that:

• without overlaps or gaps.
• the length of the object is expressed as the number of unit lengths needed to cover the same distance.

Learning Objectives:
M.2.17.1: Identify units of measurement for length.
Examples: inches, feet, yard; centimeter, meters.
M.2.17.2: Demonstrate how to use measurement tools.
Example: avoiding gaps and overlaps.
M.2.17.3: Identify measurement tools.
M.2.17.4: Model measuring using non-standard units.
M.2.17.5: Order three objects by length.
M.2.17.6: Compare the lengths of two objects indirectly by using a third object.
M.2.17.7: Describe measurable attributes of objects such as length or weight.

Students:

• accurately measure the length of objects using two different standard units.
• describe how the two measurements relate to each other.

Students know:

• standard units of length measure (inches, feet, yards, centimeters and meters) and the related tools.

Students are able to:

• measure length in standard units.
• choose and accurately use appropriate measurement tools and units of measure.

Students understand that:

• the smaller the unit of measure the more of that unit it takes to measure a length.

Learning Objectives:
M.2.18.1: Identify units of measurement for length.
Examples: inches, feet, yard; centimeter, meters.
M.2.18.2: Demonstrate how to use measurement tools.
Example: avoiding gaps and overlaps.
M.2.18.3: Identify units of measure on measurement tools.
M.2.18.4: Use vocabulary related to comparison of length.
Examples: longer, shorter, longest, shortest, taller.
M.2.18.5: Identify numerals one to 50.

Students:

• estimate lengths using the standard units of inches, feet, centimeters, and meters.

Students know:

• personal benchmarks (e.g. fingernail for centimeter, door knob to floor for meter) for the length of standard units.

Students are able to:

• use strategies for using personal benchmarks for estimating lengths in standard units.
• explain and justify length estimates.

Students understand that:

• estimating before measuring helps them develop a benchmark for the length of an object.

Learning Objectives:
M.2.19.1: Define estimate.
M.2.19.2: Measure objects using standard and non-standard units.
M.2.19.3: Identify units of measure on measurement tools.
M.2.19.4: Model measuring using non-standard units.
M.2.19.5: Use vocabulary related to comparison of length.
Examples: longer, shorter, longest, shortest, and taller.

Students:

• select appropriate tools for measuring.
• measure lengths of two objects.
• determine how much longer one object is than another.
• express the length differences for the two objects using centimeters, inches, meters, or yards.

Students know:

• strategies for comparing the length of objects.
• standard units of length.
• related tools.

Students are able to:

• choose and accurately use appropriate measurement tools and units of measure.
• explain and justify procedures for determining the difference between the lengths of two objects.

Students understand that:

• comparisons of objects are determined using attributes that are measurable.

Learning Objectives:
M.2.20.1: Measure objects using standard units.
M.2.20.2: Record lengths with appropriate units.
M.2.20.3: Use subtraction within 20 to solve problems.
M.2.20.4: Compare length using non-standard units to determine which is longer.
M.2.20.5: Use vocabulary related to comparison of length.
Examples: longer, shorter, longest, shortest, and taller.

Students:

• use concrete models and/or pictures to make sense of a word problem.
• write an equation with a symbol for the unknown in the problem.
• explain verbally how the problem was solved.

Students know:

• Students know strategies for solving addition and subtraction word problems involving length.

Students are able to:

• represent quantities and operations physically, pictorially, or symbolically.
• strategically use a variety of representations to solve problems with all addition and subtraction contexts.
• use symbols to represent unknown quantities in equations.

Students understand that:

• that they can apply the concept of length to solve addition and subtraction word problems for numbers within 100.

Learning Objectives:
M.2.21.1: Solve one-step addition and subtraction word problems with an unknown by using drawings and equations with a symbol for the unknown number to represent the problem.
Examples: question mark, blank, box, or letter.
M.2.21.2: Demonstrate the understanding of terms in addition and subtraction word problems involving length.
Examples: adding to, taking from, putting together, taking apart, sum, difference, all together, how many more, how many are left, in all, inches, feet, yards, longer, shorter, nearer, farther, closer.
M.2.21.3: Locate the unknown number regardless of position.
M.2.21.4: Add and subtract within 50, e.g., by using objects or drawings to represent the problem.
M.2.21.5: Model writing equations from word problems.
M.2.21.6: Apply signs +, -, = to actions of joining and separating sets.
M.2.21.7: Identify units of measurement for length.
Examples: inches, feet, yard; centimeter, meters.

Students:

• create number line(s) with equally spaced points and a scale of one.
• represent the quantities as lengths from 0.
• explain and justify the solutions using representations on number lines (may include open number lines).

Students know:

• how to create a number line.
• how to count forwards and backwards on a number line.
• how to use addition and subtraction to solve equations using the number line.

Students are able to:

• represent quantities and addition/subtraction on number line diagrams.
• create and use number line models to represent, solve, and justify solutions to addition and subtraction problems within 100.

Students understand that:

• quantities can be represented as distances from zero on a number line.
• a variety of models, including number lines, can be used to represent and solve addition and subtraction problems.

Learning Objectives:
M.2.22.1: Recognize that each successive number name refers to a quantity that is one larger; and each previous number name refers to a quantity that is one less.
M.2.22.2: Use a number line to add and subtract within 10.
M.2.22.3: Write numerals 0 to 100.
M.2.22.4: Trace numerals 0 to 100.

Students:

• tell time to the nearest five minutes using analog and digital clocks.
• write time to the nearest five minutes using analog and digital clocks.
• use descriptive terms such as five after, half past, quarter past, and quarter to.
• delineate between a.m. and p.m.

Students know:

• how tell and write time to the nearest 5 minutes using analog and digital clocks.
• how to explain the difference between a.m. and p.m.

Students are able to:

• accurately read and write time to the nearest five minutes from analog and digital clocks.

Students understand that:

• analog and digital clocks represent the time at any particular moment.
• clocks show the passage of time with the movement of the hands or the changing of the digits.
• time is an attribute that can be measured.

Learning Objectives:
M.2.23.1: Tell and write time in hours and half-hours using analog and digital clocks.
M.2.23.2: Recognize vocabulary terms related to time measurements.
Examples: minute, hour, half hour, o'clock, morning, evening, a.m., p.m.
M.2.23.3: Illustrate time to hour and half hour.
Example: Given the time 3:00, illustrate long hand and short hand positions on a clock.
M.2.23.4: Identify the short hand as the hour hand, and the long hand as the minute hand on an analog clock.
M.2.23.5: Identify the first number as the hour, and the numbers after the colon as the minutes on a digital clock.
M.2.23.6: Write numerals 0 to 59.
M.2.23.7: Recognize numerals 0 to 59.
M.2.23.8: Count to 60 by fives.
M.2.23.9: Distinguish between analog and digital clocks.

Students:

• identify nickels and quarters.
• find the value of a combination of coins.
• solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using dollar and cent symbols appropriately.

Students know:

• the value of pennies, nickels, dimes, and quarters.
• ccounting sequence and skip counting by 1s, 5s, and 10s.
• strategies for solving word problems.

Students are able to:

• use problem solving strategies to solve word problems involving a variety of coins.

Students understand that:

• a variety of strategies can be used to model and solve problems involving money.
• mathematics procedures can be used to answer questions involving daily life situations.

Learning Objectives:
M.2.24.1: Determine the monetary value of a set of like and unlike bills.
M.2.24.2: Determine the monetary value of a set of like and unlike coins.
M.2.24.3: Apply addition and subtraction strategies.
M.2.24.4: Understand key words in addition and subtraction word problems involving money.
Examples: adding to, taking from, putting together, taking apart, sum, difference, all together, how much more, how much is left, in all, cents, dollar, change, paid, total.
M.2.24.5: Count forward from a given number by ones, fives, tens, and twenty-fives.
M.2.24.6: Identify coins and bills and their value.
M.2.24.7: Identify symbols for dollar ($), cent (¢).
M.2.24.8: Identify coins by name including penny, nickel, dime and quarter.
M.2.24.9: Sort pennies, nickels, dimes, and quarters.
M.2.24.10: Count 10 objects.
Examples: pennies and dollar bills.