 ## Formative Assessment and Bridging activities These materials are part of an iterative design process and will continue to be refined during the 2021-2022 school year. Feedback is being accepted at the link below.
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## Standard 1.1A

Standard 1.1a Count forward orally by ones to 110, starting at any number between 0 and 110.

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Understanding the Learning Trajectory

Big Ideas:

• Rote counting is a prerequisite skill for addition and subtraction (one more, one less). Each successive counting number describes a quantity that is one more than the quantity that the previous number describes. In a sense, then, counting is adding: Each counting number adds one more to the previous collection.[LT]2 Facilitator Guide: Counting

• Noticing patterns in numbers is helpful when counting. (Clements, D.H., & Sarama, J [2017/2019])

• Understanding groups of ten can help students stay on track when counting.

Important Assessment Look-fors:

• Student follows number patterns to count forward by 1s.

• Student moves through decade numbers with ease (e.g., 29, 30, 31).

• Student states next number when given a number out of order.

• Student corrects mistakes.

Purposeful Questions:

• What patterns do you notice with counting?

• What comes after 8? How can that help you get past 28? ### Student Strengths

Orally count to 100 by 1s, starting at any number.

The child will count with understanding and use numbers to tell how many, describe order, and compare.

### Bridging Concepts

Counts accurately beyond 100 [to 110], recognizing the patterns of ones, tens, and hundreds

### Standard 1.1A

Count forward orally by ones to 110, starting at any number between 0 and 110 .   Games:

## Standard 1.1B

Standard 1.1B Write numerals 0 to 110 in sequence/out-of-sequence.

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Understanding the Learning Trajectory

Big Ideas:

• Initially, students begin counting at 1, but eventually progress to counting on from any number and keeping track of their counting using patterns (Clements, D.H., & Sarama, J [2017/2019]).

• The patterns in the ones, tens, and hundreds help students count accurately (Clements, D.H., & Sarama, J [2017/2019]).

• Students progress from reading two-digit numbers as individual digits (ex: they read “23” as (two-three) to a beginning understanding of place value (ex: knowing the 2 in “23” represents 2 tens, or twenty, and read the number as “twenty-three”)

Important Assessment Look-fors:

• Student correctly continues the number pattern.

• Student generally forms numbers correctly and can read their own writing.

• Student uses number patterns to help write missing numbers in a sequence.

• Student recalls and writes a number when it is said orally.

Purposeful Questions:

• What do you notice about the pattern?

• Where might there be a decade/tens number to help get you on track? ### Student Strengths

Students can orally count to 100.

Students can write numbers to 20.

Students can identify one more and one less.

### Bridging Concepts

Students can Identify patterns in counting and writing number strings.

Student can start counting and writing in the middle of a string of numbers based on given information.

### Standard 1.1B

Students can write numerals 0 to 110 in sequence/out-of-sequence.    ## Standard 1.1d

Standard 1.1D Count forward orally by ones, twos, fives, and tens to determine the total number of objects to 110.

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Understanding the Learning Trajectory

Big Ideas:

• One-to-one correspondence is crucial to success with counting. Sometimes students can rote count without one-to-one correspondence.

• Skip counting is a way to count a group of objects quickly and efficiently; leads to algebraic thinking (Clements, D.H., & Sarama, J [2017/2019]).

• Skip counting can strengthen estimation skills by practicing repeated addition (Clements, D.H., & Sarama, J [2017/2019]).

Important Assessment Look-fors:

• Student uses and identifies a pattern to skip count.

• Student accurately skip counts.

• Student attempts a skip counting strategy before counting by ones.

• Student sees efficiency in skip counting and utilizes it in real world situations.

Purposeful Questions:

• What strategies do you know to help skip count?

• Can you get a running start to help you figure out what the next number might be? ### Student Strengths

Students can count forward to 100 by 1s.

Students can skip count by 10s to 100.

### Bridging Concepts

Students can skip count by 5s, connecting to 10s pattern.

Students can skip count by 2.

### Standard 1.1D

Students can count forward orally by ones, twos, fives, and tens to determine the total number of objects to 110 .   ## Standard 1.2a

Standard 1.2A Group a collection into tens/ones and write the corresponding numeral.

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Understanding the Learning Trajectory

Big Ideas:

• Each digit in our number systems has a place and a value.

• A collection can be grouped into tens and ones (Clements, D. H., & Sarama, J.[2017/2019]).

• A group of 10 can be counted as one unit of ten.

Important Assessment Look-fors:

• Student makes groups of ten.

• Student uses groups of ten to determine the value of a collection rather than counting by ones.

• Student writes the number corresponding to a collection of objects.

• Student demonstrates understanding of the value of the digit in the tens place as meaning that many groups of ten, and the value of the digit in the ones place as being that many ones.

Purposeful Questions:

• Did you make groups? Can you tell me how you grouped your cubes?

• What do these leftover cubes represent?

• How does the number that you counted connects to the number of cubes you have?

• How do you know the value of __ based on the place that it’s in? ### Student Strengths

Students can tell how many are in a set of 20 or fewer by counting orally.

Students read, write, and represent numbers 0-20.

Students can count forward orally by ones 0 to 100.

Students can count forward orally by tens, starting at 0, to determine a total number of objects to 100.

### Bridging Concepts

Students can make a group of ten that represents one set of ten.

Students can write the corresponding numeral for collections of tens.

Students can identify the place and value for each digit in a two digit number.

Students can identify the number of tens and ones that can be made from any number up to 100.

### Standard 1.2A

Students can group a collection into tens and ones and write the corresponding numeral.    ## Standard 1.2B

Standard 1.2B Compare two numbers between 0 and 110 represented pictorially or with concrete objects, using the words greater than, less than or equal to.

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Understanding the Learning Trajectory

Big Ideas:

• Greater than is more, less than is fewer, and equal to means the same as.

• Concrete models, pictorial models, and written numbers can be compared by deciding which has a higher value.

• The digit in the tens place is more important when determining the size of a two digit number (Common Core Writing Team, 2019, pg 6).

Important Assessment Look-fors:

• Student understands and can use the terms less than, greater than, and equal to.

• Student uses the model to determine how many are in each set.

• Student recognizes each tens block as a unit of ten when counting.

• Student determines that the tens place is more important than the ones place when determining which value is greater.

Purposeful Questions:

• What do you notice about the two sets of blocks?

• How can you decide which set has more?

• Which numbers helped you decide how to compare the two? ### Student Strengths

Students can compare and describe a set as having more, fewer, or the same number of objects as another set.

### Bridging Concepts

Students can represent two digit numbers pictorially.

Students can count and represent numbers from 100-110.

Students can correctly use the words greater than, less than, and equal to.

### Standard 1.2B

Students can compare two numbers between 0 and 110 represented pictorially or with concrete objects, using the words greater than, less than or equal to.   ## Standard 1.2c

Standard 1.2C Order three or fewer sets from least to greatest and greatest to least.

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Understanding the Learning Trajectory

Big Ideas:

• The digit in the tens place is more important when determining the size of a two digit number (Common Core Core Progressions, 2019).

• Least to greatest means smallest to largest, and greatest to least means largest to smallest.

• Conceptual subitizing by place value and multiplicative thinking allow students to use the base-10 system to describe quantities and order them. Learning Trajectory Information

Important Assessment Look-fors:

• Student determines the value of two images and compares them.

• Student represents numbers with pictures using groups of tens and ones.

• Student uses the tens place to compare and determine the larger or smaller of two numbers.

• Student sees the groups of ten and the group of ones in any number up to 110.

Purposeful Questions:

• What do you notice about these two pictures?

• How did you decide which order you wanted to write the numbers? ### Student Strengths

Students can compare and order three or fewer sets, each set containing 10 or fewer concrete objects, from least to greatest and greatest to least.

### Bridging Concepts

Students can compare sets up to 110 objects.

Students can understand and use the terms least to greatest and greatest to least.

### Standard 1.2C

Students can order three or fewer sets from least to greatest and greatest to least.  ## Standard 1.6

Standard 1.6 Create and solve single-step story and picture problems using addition and subtraction within 20.

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Understanding the Learning Trajectory

Big Ideas:

• Story problems provide an opportunity to act out and reason through what is happening and what needs to be determined (i.e., which part is unknown).

• There are numerous strategies that work together to develop fluency with operations and efficiency in problem solving (i.e., one more/one less, doubles, make ten, using related facts, etc.)

• Various representations may be used to model and solve the same problem: spoken words (act it out), moving objects and manipulatives, drawing pictorial models, and writing number sentences.

• A number sentence is one way of representing the action (or operation) used to solve a problem. Every problem has an action that translates to an operation (Van de Walle et. al., 2018).

Important Assessment Look-fors:

• Student represents a story problem with an appropriate number sentence.

• Student uses an appropriate strategy (i.e., picture, number sentence, talk-aloud, fingers, etc.) to make sense of the problem.

• Student identifies and uses an appropriate action to solve the problem.

• Student identifies the unknown part (i.e., start, change, result).

Purposeful Questions:

• What strategy did you use to solve? What are some strategies you know?

• What’s the action in the story? What is happening?

• What part of the story is missing? What are we trying to find out? ### Student Strengths

Students can represent addition and subtraction story problems within 10.

Students can recognize, describe, and utilize part/whole relationships through 10 to solve single-step problems.

Students can count to 20 and beyond.

### Bridging Concepts

Students can recognize, describe, and utilize part/whole relationships through 20.

Students can select, utilize, and explain strategies to solve various types of problems.

### Standard 1.6

Students can create and solve single-step story and picture problems using addition and subtraction within 20.    ## Standard 1.7a

Standard 1.7a Recognize and describe with fluency part-whole relationships for numbers to 10.

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Understanding the Learning Trajectory

Big Ideas:

• Subitizing skills and visual recognition of numbers up to 5 facilitate learning combinations to 10.

• A quantity (whole) can be decomposed into equal or unequal parts; the parts can be composed to form the whole (Erikson Institute’s Early Math Collaborative).

• Quantities represented by numbers can be decomposed (or composed) into part-whole relationships (NCTM Number and Numeration, p.25).

Important Assessment Look-fors:

• Student demonstrates conservation of number by “holding onto” the original number of objects.

• Student uses a strategy (i.e., fingers, counting backwards, adding up, doubles, etc.) to figure out how many counters are hidden.

• Student recognizes with ease the quantity of small groups of objects (up to five).

• Student shows beginning understanding of the inverse relationship between addition and subtraction (i.e., 6-2=4, 4+2=6).

Purposeful Questions:

• What strategy can you use to find the missing number?

• What small group do you see? How is that related to the total? ### Student Strengths

Students can recognize and describe part-whole relationships to 5.

Students easily recognize (subitize) sets up to 5.

### Bridging Concepts

Students can recognize partners (complements) of 10, and patterns within partners of 10.

### Standard 1.7a

Students can recognize and describe with fluency part-whole relationships for numbers to 10.          ## Standard 1.7b

Standard 1.7B Demonstrate fluency with addition and subtraction within 10.

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Understanding the Learning Trajectory

Big Ideas:

• Flexible methods can be used when adding and subtracting.

• Composing and decomposing numbers build understanding and flexibility with number.

• Part-whole relationships are foundational to developing computational fluency.

• Fluency leads to efficiency by allowing students to recall basic facts when solving more complex problems (Common Core Progressions, p. 4).

Important Assessment Look-fors:

• Student sees a total of 10, broken into two parts.

• Student uses flexible strategies to determine the number of dots/counters (5 and 3 more makes 8, counts backward from 10 to make 8).Student writes a complete number sentence to represent a problem.

• Student composes and decomposes numbers to 10 with ease.

Purposeful Questions:

• Tell me about the strategy you are using. How did it help you to solve the problem?

• When you first look at this card/ten frame, how many do you see? How do you see it?

• Can you represent that with a number sentence? What would it look like? ### Student Strengths

Represent addition and subtraction story problems within 10.

Recognize, describe, and utilize part/whole relationships through 10 to solve single-step problems.

Count to 20 and beyond.

### Bridging Concepts

Recognize, describe, and utilize part/whole relationships through 20.

Select, utilize, and explain strategies to solve various types of problems.

### Standard 1.6

Create and solve single-step story and picture problems using addition and subtraction within 20.    ## Standard 1.9a

Standard 1.9a Tell time to hour and half-hour, using analog and digital clocks.

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Understanding the Learning Trajectory

Big Ideas:

• Time cannot be seen, but it can still be measured. Time is the duration of an event from its beginning to its end. (Van De Walle, Teaching Student Centered Mathematics, K-3)

• Telling time is related to reading the instrument of a clock rather than measuring time. The numbers on a clock represent the time in that moment.

• We can communicate our measures of time in units of hours and half hours.

Important Assessment Look-fors:

• Student recognizes analog and digital clocks as instruments to tell the current time.

• Student distinguishes between the hour hand and the minute hand on the analog clock and between the two sides of the digital clock.

• Student uses the vocabulary words “hours” and “o’clock”.

• Student is able to read the time on the clock to the nearest hour and half-hour.

Purposeful Questions:

• What does it mean to “tell time?”

• Can you explain how to use the arrows/hands on an analog clock to tell time?

• How does the time change if the hour hand is moved?

• What do the numbers on a digital clock mean? How do you know? ### Student Strengths

Students can recognize the numbers 1-12.

### Bridging Concepts

Students can recognize the number 30.

Students recognize the role of each of the hands on an analog clock.

Students understand that half an hour means one of two parts has passed.

### Standard 1.9a

Students can tell time to hour and half-hour, using analog and digital clocks.        ## Standard 1.12b

Standard 1.12b Read and interpret data displayed in tables, picture graphs, and object graphs, using the vocabulary more, less, fewer, greater than, less than, and equal to.

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Understanding the Learning Trajectory

Big Ideas:

• Graphs are read and interpreted in order to compare information that has been gathered.

• Categorical data comes from sorting information into categories.

Important Assessment Look-fors:

• Student identifies the categories on a graph.

• Student identifies the whole set total.

• Student makes comparisons using the data.

Purposeful Questions:

• Using the lunch orders graph, tell me what you can learn from this graph.

• How do you know which juice is liked the most?

• How can we use the graph to make a comparison? ### Student Strengths

Students can read a graph to determine the categories, the whole set, and its parts.

Students can compare data using the terms greatest, least, and same.

Students are familiar with object graphs, pictographs, and tables.

### Bridging Concepts

Students can use terms more, less, fewer, greater than, less than, and equal to accurately.

Students can compare data with comparison statements.

### Standard 1.12b

Students can read and interpret data displayed in tables, picture graphs, and object graphs, using the vocabulary more, less, fewer, greater than, less than, and equal to.      ## Standard 1.13

Standard 1.13 Sort and classify concrete objects according to one or two attributes.

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Understanding the Learning Trajectory

Big Ideas:

• Shapes can be defined and classified according to their attributes (Early Math Collaborative)

• Geometrically defining attributes (i.e., squares have 4 straight equal sizes) are differentiated from non-geometric attributes (i.e., color, size, orientation).

• Non-examples can help students explain the attributes of shapes.

Important Assessment Look-fors:

• Student groups objects by at least one attribute.

• Student describes the attribute used to sort the shapes (i.e., shape, size, color, pattern, thickness, etc.).

• Student groups objects in another way.

Purposeful Questions:

• How did you sort these objects?

• What attributes do the shapes in this pile have? How are they alike?

• Which group does ‘this’ shape (object) belong in? Why?

• What do you know about shapes? ### Student Strengths

Students can recognize and describes objects based on shapes, colors, and size.

Students can describe how objects are similar and different.

### Bridging Concepts

Students can understand thickness as an attribute of objects.

Students can sorts objects based on two attributes (eg: color and shape = red triangles in one pile).

Students begin to understand non-examples.

### Standard 1.13

Students can sort and classify concrete objects according to one or two attributes.  ## Standard 1.15

Standard 1.15 Demonstrate an understanding of equality through the use of the equal symbol.

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Understanding the Learning Trajectory

Big Ideas:

• Quantities can be represented in multiple ways (i.e., 7 can be represented as 4 + 3, 2 + 5, or 0 +7, etc.)

• Equations can be used to represent the relationship between two expressions of equal value (4+2=3+3)(VDOE).

• Child accepts number sentences not in the form of 3 +4 = 7 (i.e., 7 = 3 + 4 or 3 + 4 = 2 + 5) (Clements, D.HH., & Sarama, J)

• The equal symbol represents equality not the common misconception that the answer comes next.

Important Assessment Look-fors:

• Student represents equivalent quantities

• Student understands the purpose of the equal sign and uses it appropriately.

• Student solves equation correctly.

• Student uses a strategy for equation solving.

Purposeful Questions:

• Notice where the equal sign is. What does that tell you?

• How can you make both sides equal? ### Student Strengths

Students understand and use the terms “more/greater”, “less/fewer”, and “same” to compare quantities.

Students demonstrate a basic understanding of addition and subtraction.

Students combine smaller groups together to make a larger whole using models.

### Bridging Concepts

Students understand that two quantities or representations can be equal to each other (i.e., one stick of 10 and 10 unit cubes or 6 blue cubes and 5 green cubes plus 1 red cube).

Students read and use the equal sign (=) to represent equality (quantities of equal value).

Students identify and describe two sets (quantities) that are not equal.

### Standard 1.15

Students demonstrate an understanding of equality through the use of the equal symbol.          ### Routines: 