Evidence Outcomes:

1. Count to 100 by ones and by tens. (CCSS: K.CC.A.1)

2. Count forward beginning from a given number within the known sequence (instead of having to begin at 1). (CCSS: K.CC.A.2)

3. Write numbers from 0 to 20. Represent a number of objects with a written numeral 0–20 (with 0 representing a count of no objects). (CCSS: K.CC.A.3)

Transfer Goals: Based on the Evidence Outcomes, what will students transfer to new contexts/situations?

The structure and patterns of a number provide meaning

Essential Understandings: In order to meet these transfer goals, the essential ideas and core processes students must understand are...

• Numbers follow a sequence and the sequence from 1-9 repeats

• Numbers follow a predictable pattern

In order to meet these essential understandings, students must know...

Academic Vocabulary: pattern, skip counting, sequence, hundreds chart

• Count to 100 (minimum understanding)

• How to write numbers to 20 with correct formation (minimum understanding)

• Count on from any number

• Represent a number with objects

• Identify patterns in numbers

• Skip counting by 5s and 10s (expose to real world connections: money, time, tally marks)

In order to meet these essential understandings, students must be able to...

• Count to 100

• Write numbers to 20 with correct formation

• Explain patterns in numbers

• Use objects to represent quantities

• Apply number pattern schema when counting or encountering unfamiliar numbers

• Skip count by 5s and 10s

Evidence Outcomes:

1. Apply the relationship between numbers and quantities and connect counting to cardinality. (CCSS: K.CC.B.4)

   • When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. (CCSS: K.CC.B.4.a)

   • Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. (CCSS: K.CC.B.4.b)

   • Understand that each successive number name refers to a quantity that is one larger. (CCSS: K.CC.B.4.c)

2. Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects. (CCSS: K.CC.5)

Transfer Goals: Based on the Evidence Outcomes, what will students transfer to new contexts/situations?

The relationship between a numeral to a quantity of objects

Essential Understandings: In order to meet these transfer goals, the essential ideas and core processes students must understand are...

• A quantity can be represented by a numeral

• The cardinality and sequence of numbers

• Organizing objects strategically can help us count more efficiently

In order to meet these essential understandings, students must know...

Academic Vocabulary: sequence, numeral

• The sequence of numbers (one less, one more)

• Count a number of objects to 20 (minimum understanding)

• One to one correspondence

• A quantity can be arranged in many different ways

In order to meet these essential understandings, students must be able to...

• Apply counting schema to count a given number of objects

• Organize objects in a strategic way to aid counting

• Subitize to (a minimum) of 5

• Use reasoning to justify thinking

Evidence Outcomes:

1. Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. (Include groups with up to 10 objects.) (CCSS: K.CC.6)

2. Compare two numbers between 1 and 10 presented as written numerals. (CCSS: K.CC.7)

Transfer Goals: Based on the Evidence Outcomes, what will students transfer to new contexts/situations?

Compare and relate different objects or concepts and justify thinking

Essential Understandings: In order to meet these transfer goals, the essential ideas and core processes students must understand are...

• Precise language can help us when comparing objects or concepts

In order to meet these essential understandings, students must know...

Academic Vocabulary: greater than, less than, equal to, one more, one less

• The sequence of numbers

• Amount of objects a numeral represents

• How to describe a number in comparison to another number (minimum understanding 0-10)

• Strategies for comparing numbers (matching or counting)

• Exposure to >, <, and = symbols when comparing numbers

In order to meet these essential understandings, students must be able to...

• Analyze two numbers and compare them using academic vocabulary

• Use strategies to compare numbers and explain thinking

Evidence Outcomes:

1. Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. (CCSS: K.NBT.A.1)

Transfer Goals: Based on the Evidence Outcomes, what will students transfer to new contexts/situations?

Recognize patterns of the base ten system to make sense of unfamiliar numbers, and apply it to new situations

Essential Understandings: In order to meet these transfer goals, the essential ideas and core processes students must understand are...

• Patterns of the base ten system

• A digit’s position in a number has a specific value (14 represents 1 ten and 4 ones)

• We can compose and decompose numbers using base ten models/manipulatives

In order to meet these essential understandings, students must know...

Academic Vocabulary: digit, place value, base ten, ones, tens, standard form (number), expanded form (addition equation of tens and ones), unit form (place value), composing, decomposing

• Two digits represent amounts of tens and ones based on their position in the number

• 10 can be thought of as a bundle of ten ones - also known as a “ten”

• 11-19 are composed of a ten and ones

• How base ten models/manipulatives can be used to represent numbers

In order to meet these essential understandings, students must be able to...

• Understand and explain that a 2 digit number represents tens and ones

• Use objects, drawings, and equations to show compositions and decompositions of numbers (minimum understanding 11 to 19)

• Demonstrate understanding of base ten models/manipulatives

Evidence Outcomes:

1. Represent addition and subtraction with objects, fingers, mental images, drawings (drawings need not show details, but should show the mathematics in the problem), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. (CCSS: K.OA.A.1)

2. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. (CCSS: K.OA.A.2)

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). (CCSS: K.OA.A.3)

4. For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. (CCSS: K.OA.A.4)

5. Fluently add and subtract within 5. (CCSS: K.OA.A.5)

Transfer Goals: Based on the Evidence Outcomes, what will students transfer to new contexts/situations?

Examine and apply a variety of strategies to accurately and effectively solve problems

Essential Understandings: In order to meet these transfer goals, the essential ideas and core processes students must understand are...

• The relationship between addition and subtraction

• Situations can be represented mathematically using addition and subtraction

In order to meet these essential understandings, students must know...

Academic Vocabulary: sum, difference, mental math, equation

• Number combinations that equal 10

• Strategies to represent addition and subtraction (minimum to 10)

  • Objects

  • Fingers

  • Mental images

  • Drawings

  • Sounds (claps, taps)

  • Acting out

  • Oral explanation

• The relationship between adding and subtracting

• How to monitor for meaning in word problems

• How skip counting correlates to repeated addition

In order to meet these essential understandings, students must be able to...

• Solve addition and subtraction problems using various strategies

• Fluently add and subtract (minimum within 5)

• Monitor for meaning and determine importance in word problems to accurately solve

• Connect strategies to written equations

• Make thinking visible to justify reasoning

• Attend to precision

Evidence Outcomes:

1. Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. (CCSS: K.MD.A.1)

2. Directly compare two objects with a measurable attribute in common, to see which object has “more of”/”less of” the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter. (CCSS: K.MD.A.2)

Transfer Goals: Based on the Evidence Outcomes, what will students transfer to new contexts/situations?

• Make sense of the world by comparing and ordering objects by their attributes

• Be precise about meanings when describing measurable attributes

Essential Understandings: In order to meet these transfer goals, the essential ideas and core processes students must understand are...

• The world around us can be described and compared in measurable ways

In order to meet these essential understandings, students must know...

Academic Vocabulary: length (longer, shorter), weight (heavier, lighter), height (taller, shorter)

• Shapes can be described and compared in measurable ways

• Begin to understand we can use repeating units to measure (non-standard and standard units)

In order to meet these essential understandings, students must be able to...

• Use descriptive attributes to compare objects

• Begin to relate measurable attributes to units of measurements and the tools used

• Use reasoning to justify thinking

Evidence Outcomes:

1. Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. (Limit category counts to be less than or equal to 10.) (CCSS: K.MD.B.3)

Transfer Goals: Based on the Evidence Outcomes, what will students transfer to new contexts/situations?

• Group objects into categories to help make sense of problems

Essential Understandings: In order to meet these transfer goals, the essential ideas and core processes students must understand are...

• Objects and concepts can be categorized to deepen our understanding of them

In order to meet these essential understandings, students must know...

Academic Vocabulary: similarities, differences, categories, sort, classify

• How to identify similarities and differences between objects

• How to group objects by similarities

• There are multiple ways to sort objects/concepts

• Counting with one to one correspondence

In order to meet these essential understandings, students must be able to...

• Categorize objects in various ways

• Name how you categorized and use reasoning to justify thinking

• Engage in respectful discourse with peers to understand another point of view

Evidence Outcomes:

1. Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. (CCSS: K.G.A.1)

2. Correctly name shapes regardless of their orientations or overall size. (CCSS: K.G.A.2)

3. Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). (CCSS: K.G.A.3)

Transfer Goals: Based on the Evidence Outcomes, what will students transfer to new contexts/situations?

• Describe the physical world from geometric perspectives

• Recognize similarities and differences between shapes using precise descriptions

Essential Understandings: In order to meet these transfer goals, the essential ideas and core processes students must understand are...

• The world around us is composed of shapes

• We can apply our understanding of shapes to make meaning of our surroundings

• A shape’s attributes stay consistent no matter the orientation

In order to meet these essential understandings, students must know...

Academic Vocabulary: two-dimensional, three-dimensional, positional words (above, below, beside, in front of, behind, next to), attributes (side/edge, corner/vertex, face)

• Two-dimensional shapes:

  • Square

  • Circle

  • Triangle

  • Rectangle

  • Hexagon

• Three-dimensional shapes:

  • Cube

  • Cone

  • Cylinder

  • Sphere

• Names of shapes regardless of orientation or size

• Difference between two- and three-dimensional shapes

In order to meet these essential understandings, students must be able to...

• Name and describe shapes by their attributes

• Use positional vocabulary when describing objects

• Describe the physical world using shapes

• Sort shapes into categories based on attributes

• Distinguish difference of two- and three-dimensional shapes

• Use reasoning to justify thinking

Evidence Outcomes:

1. Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/”corners”) and other attributes (e.g., having sides of equal length). (CCSS: K.G.B.4)

2. Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. (CCSS: K.G.B.5)

3. Compose simple shapes to form larger shapes. For example, “Can you join these two triangles with full sides touching to make a rectangle?” (CCSS: K.G.B.6)

Transfer Goals: Based on the Evidence Outcomes, what will students transfer to new contexts/situations?

• The imagination, flexibility, and inventiveness to compose and compare two- and three-dimensional shapes

Essential Understandings: In order to meet these transfer goals, the essential ideas and core processes students must understand are...

• The world around us is composed of shapes

• We can apply our understanding of shapes to analyze, compare, create, and compose shapes

In order to meet these essential understandings, students must know...

Academic Vocabulary: two-dimensional, three-dimensional, attributes (side/edge, corner/vertex, face)

• Names of two- and three-dimensional shapes (found in previous standard MA.K.G.A)

• Difference between two- and three-dimensional shape

In order to meet these essential understandings, students must be able to...

• Analyze, compare, create, and compose two- and three-dimensional shapes

• Compose simple shapes to form larger shapes (join two triangles to make a rectangle)

• Use specific attributes to explain thinking

• Engage in respectful discourse with peers to understand another point of view