Evidence Outcomes:

a. Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. (CCSS: 1.NBT.A.1)

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

The structure and pattern of a number provides meaning

Essential Understandings: In order to meet these transfer goals, the essential ideas and core process 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, odd/even, sequence, pennies nickels, dimes, hundreds chart

  • Significance of the quantity when represented with objects

  • Read numerals to 120

  • How to write numerals to 120 with correct formation

  • Identify patterns in number sequence

  • Skip Counting by 2s, 5s, and 10s (expose to real world connections: money, time, tally marks)

* 120 is the minimum number to meet the expectation of the standard

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

• Count to 120 beginning from any number less that 120

• Read up to 120

• Write numbers up to 120 with correct formation

• Represent numbers with objects

• Explain patterns in numbers

• Apply number pattern schema when counting or encountering unfamiliar numbers

• Count by 2s, 5s, 10s

Evidence Outcomes:

1. Understand that the two digits of a two- digit number represent amounts of tens and ones. Understand the following as special cases: (CCSS: 1.NBT.B.2)10 can be thought of as a bundle of ten ones; called a “ten.” (CCSS: 1.NBT.B.2.a) The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. (CCSS: 1.NBT.B.2.b) The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). (CCSS: 1.NBT.B.2.c)

2. Compare two two-digit numbers based on meanings of the tens and one's digits, recording the results of comparisons with the symbols >, =, and <. (CCSS: 1.NBT.B.3)

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 contexts and mathematical operations.

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

• The digit’s position in a number has a specific value

• There are multiple ways to compose and decompose numbers

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

• Numbers represent different values that can be greater than, equal to, or less than

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

Academic Vocabulary: digit, place value, base ten, ones, tens, greater than, less than, equal to, standard form, expanded form, unit form

• Numbers represent a quantity

• Two digits represent amounts of tens and ones

• 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

• Skip counting by tens (10, 20, 30…)

• 10, 20, 30 ...refers to 1, 2, 3 groups of tens

• Symbols for comparing >, <, =

• Exposure to the hundreds position in a 3 digit number

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

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

• Compose/decompose numbers to 100 into tens and ones and justify thinking

• Use objects, drawings, and equations to show compositions and decompositions

• Compare two 2 digit numbers based on meanings of the tens and ones

• Record comparisons using accurate symbols >, <, =

• Use reasoning to explain thinking

Evidence Outcomes:

1. Add within 100, including adding a two- digit number and a one-digit number, and adding a two-digit 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 and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. (CCSS: 1.NBT.C.4)

2. Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. (CCSS: 1.NBT.C.5)

3. Subtract multiples of 10 in the range 10– 90 from multiples of 10 in the range 10– 90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. (CCSS: 1.NBT.C.6)

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

• Operations can be used to solve problems

• 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 process students must understand are...

• You can add and subtract without counting by ones

• 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, compose, decompose, mental math, equation

• Addition and subtraction strategies

• The structure of place value

• Numbers up to 100 (written numerals and the quantity represented)

• The relationship between adding and subtracting

• Multiples of 10 (and the use of a hundredths chart)

• Number sentences (equation in written form)

• Correlation of skip counting and repeated addition

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

• Add and subtract with 100

• Add and subtract fluently within 10

• Model quantities with drawings and equations

• Use base ten structure to add and subtract

• Add and subtract multiples of 10

• Relate the strategies to their written forms

• Make thinking visible to demonstrate understanding

Evidence Outcomes:

1. 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. (CCSS: 1.OA.A.1)

2. 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. (CCSS: 1.OA.A.2)

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

• The ability to make sense of problems and persevere in solving them

• 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...

• Situations can be represented mathematically using addition and subtraction

• There is more than one way to solve a problem

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

Academic Vocabulary: part-part-whole, adding to, taking from, putting together, taking apart, compare

• How to monitor for meaning in math

• Identify key numbers and words that are relevant to solving the problem

• How to determine importance in a word problem

• Addition and subtraction strategies

• Relationship between addition and subtraction

• Tools and ways of modeling addition/subtraction (objects, drawings, and equations)

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

• Monitor for meaning to determine the operation of the word problem

• Determine importance in a word problem

• Use various addition and subtraction strategies to solve word problems

• Solve problems with unknowns in all positions

• Use objects and drawings to model thinking

• Relate strategies to their written form

• Attend to precision with another strategy

• Explain and justify thinking

Evidence Outcomes:

1. Apply properties of operations as strategies to add and subtract. (Students need not use formal terms for these properties.) 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.) (CCSS: 1.OA.B.3)

2. Understand subtraction as an unknown- addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8. (CCSS: 1.OA.B.4)

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

• Make sense of problems and persevere in solving them

• When and how to use the relationship between adding and subtracting

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

• Situations can be represented mathematically using addition or subtraction

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

Academic Vocabulary: operation, addend, commutative property, associative property.

• Concept of order of operations

• The properties of operations

• Understand subtraction as an unknown addend problem

• Commutative property of addition (8+3=11, and 3+8=11)

• Associative property of addition

• (2+6+4 = 2+10 = 12)

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

• Solve reciprocal math problems

• Use Associative Property when solving math problems

• Use Commutative Property when solving math problems

• Show more than one way to solve a problem

• Explain the understanding behind the commutative property

• Construct viable arguments and critique the reasoning of others

Evidence Outcomes:

1. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). (CCSS: 1.OA.C.5)

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). (CCSS: 1.OA.C.6)

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

• The ability to use a variety of strategies to solve addition and subtraction problems with automaticity

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

• There are multiple strategies to think about problems and see how the quantities involved support the use of some strategies over other

• The importance of and the strategies for mental math

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

Academic Vocabulary: mental math, equivalent, number line, fact family, double

• Addition and Subtraction strategies and tools

• Counting on (number line, charts…)

• Making ten (8+2+4 instead of 8+6)

• Decomposing a number leading to a ten

• Using the relationship between addition and subtraction

• Creating equivalent but easier or known sums (instead of 6+7, 6+6+1)

• Doubles (2+2)

• Tens frame/ hundreds chart/ place value chart

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

• Use mental math to fluently compute operations within 10

• Use structure of numbers to make tens

• Relate counting to addition and subtraction

• Evaluate the problem and determine importance to choose the most efficient strategy

• Use multiple strategies when adding and subtracting

• Make thinking visible and use academic vocabulary to explain your process

Evidence Outcomes:

1. 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. (CCSS: 1.OA.D.7)

2. 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 =_ . (CCSS: 1.OA.D.8)

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

• Make sense of quantities and their relationships with the use of an equal sign

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

• The significance and purpose of an equal sign

• The associative property (2+6+3 = 5+6 …)

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

• The parts of a ‘number sentence’ (written equation)

  • Equal Sign

  • Operation signs

• Understanding the concept of greater than and less than (to evaluate each side of the equation)

• The concept of the equal sign

• Schema relating to addition and subtraction

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

• Determine if equations involving addition/subtraction are true or false

• Determine the unknown whole number in any position of the equation (relating up to 3 whole numbers)

Evidence Outcomes:

1. Order three objects by length; compare the lengths of two objects indirectly by using a third object. (CCSS: 1.MD.A.1)

2. Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps. (CCSS: 1.MD.A.2)

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

• The spacial awareness to compare measurable attributes

• Abstract comparisons between lengths

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

Students will understand…

• That length measurement is the number of same-sized length units that span it with no gaps or overlaps.

• While the size of the item is constant, the measurement tool can change, and will then change the measurement of the item.

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

Academic Vocabulary: horizontal, vertical, unit, length, standard nonstandard

• Unit of measurement

• Greater than/ less than (in size and numerically)

• Spacial awareness in the lens of comparison

• Concept of length

• Conceptions of comparison:

  • conservation (no matter how you organize 5 toys, they will still be a group of 5),

  • seriation (positioning, ordering a sequence),

  • iteration (repetition of a process).

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

• Measure objects without gaps or overlaps

  • Using nonstandard tools of measurement

  • Direct comparisons of objects

• Measure 2 objects indirectly by using a third object

• Compare lengths of objects

• Order objects by length

• Express the length of an object as a whole number of length units

Evidence Outcomes:

1. Tell and write time in hours and half- hours using analog and digital clocks. (CCSS: 1.MD.B.3)

2. 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. (CCSS: 1.MD.C.4)

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

• Tell and manage time to be both personally responsible and responsible to the needs of others

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

• The relationship between hours, half hours, and minutes, and relate that understanding to analog and digital clock faces.

• Recognize that time is a quantity that can be measured with different degrees of precision

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

Academic Vocabulary: analog, digital, AM/PM, noon, midnight

• • Format of an analog clock

  • Format of a digital clock

  • Hour hand

  • Minute hand

  • Clockwise direction and how it correlates to numbers

  • Exposure to AM/PM

  • Purpose for telling time

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

• Identify hour and minute hand

• Distinguish difference between digital and analog

• Tell time in hours and half hours using analog and digital clocks

• Write time in hours and half hours using digital and analog clocks.

• Record time on a blank clock face

• Explain the relationship between a time and the clock face.

Evidence Outcomes:

1. 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. (CCSS: 1.MD.C.4)

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

• The ability to organize, represent, and interpret data in different situations

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

• Data can be represented and categorized in a variety of ways to deepen understanding

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

Academic Vocabulary: data, categorize/category, table, picture graph, bar graph, tally marks, line plot

• • Multiple ways to categorize

  • Attributes

  • Similarities and differences

  • Concept of greater than/less than

  • Skills to compare different categories and data sets

  • Exposure to different representational formats for data

  • Object attributes can determine the grouping of data

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

• Categorize objects based on attributes

• Abstract similar objects into new conceptual groups

• Organize data

• Use appropriate labels

• Ask questions about represented data

• Answer questions about represented data

• Justify how you categorized

• Explain the purpose for gathering and representing data

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

Evidence Outcomes:

1. Distinguish between defining attributes (e.g., triangles are closed and three- sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. (CCSS: 1.G.A.1)

2. Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. (Students do not need to learn formal names, such as “right rectangular prisms.”) (CCSS: 1.G.A.2)

3. Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. (CCSS: 1.G.A.3)

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

Students will transfer...

• Describe the physical world from geometric perspectives

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

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

• Shapes exist in the world, and they can help us make meaning of our surroundings

• A whole shape can be broken apart, and we can use 2D and 3D shapes to create composite shapes.

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

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

Academic Vocabulary: attributes, defining attributes, non-defining attributes, two-dimensional, three-dimensional, corner/vertex, side/edge, face, halves/half of, fourths/quarters/quarter of

• • Attributes of shapes

  • Difference between defining attributes and non-defining attributes

  • Two-dimensional shapes

    • Rectangles

    • Squares

    • Trapezoids

    • Triangles

    • Half circles

    • Quarter circles

  • Three-dimensional shapes

    • Cubes

    • Prisms

    • Cones

    • cylinders

  • Schema of composing and decomposing shapes and pieces of shapes (equal shares)

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

• Identify names of shapes

• Sort shapes by defining attributes

• Compose shapes using their defining attributes

• Distinguish defining attributes vs. non-defining attributes

• Justify whether shapes belong in the non-defining or defining attributes category

• Compose 2D and 3D shapes to create a composite shape (i.e. build a structure using three-dimensional shapes)

• Compose new shapes from the composite shape

• Partition whole shapes into two or four equal shares