Formative Assessment and Bridging activities

Kindergarten


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.
*
Share Feedback for Kindergarten Modules

Note: Links marked with will open in a new tab

Standard K.1A

Standard K.1a tell how many are in a given set of 20 or fewer objects by counting orally

(Pull down for more)

UNDERSTANDING THE LEARNING TRAJECTORY

Big Ideas:

  • Students use an indicating act like moving objects or pointing to them to pair each number word said with one object only. Counting objects in a line is easiest, and students later keep track of counting objects in more difficult arrangements.

  • Students connect counting to cardinality by understanding that the last number said in a counting sequence indicates the number of objects in the counted set.

  • Students initially consider the act of counting as the answer to a “How many ___?” question. With more experience students realize that the number of objects counted remains the same even if rearranged or if the objects are counted in a different order.

Important Assessment Look Fors:

  • Student uses the standard counting order when counting the animals.

  • Student touches and counts each animal only one time and says only one number when touching each animal.

  • Student moves animals or otherwise keeps track of which animals have been counted.

  • Student tells how many are in the set of animals by stating the last number counted.

Purposeful Questions:

  • How can you be sure you counted all of the animals?

  • How do you know that ___ is the total number of animals?

  • What strategy did you use to count the animals?

Bridging for Math Strength Logo

Student Strengths

Count with understanding and use numbers to tell how many, describe order, and compare.


Count a group (set/collection) of five to ten objects by touching each object as it is counted and saying the correct number (one-to-one correspondence)


Count the items in a collection of one to ten items and know the last counting word tells “how many.

Bridging Concepts

Count a group (set/collection) of greater than ten objects by touching each object as it is counted and saying the correct number (one-to-one correspondence)

Standard K.1a

Count orally to tell how many are in a given set up to 20 objects

Preview of formative assessment

Full Module with Instructional Tips & Resources:

Formative Assessments:

Routines:

Rich Task:

Games:

Back to top

Standard K.1B

Standard K.1B Read, write and represent numbers 0 to 20

(Pull down for more)

UNDERSTANDING THE LEARNING TRAJECTORY

Big Ideas:

  • The numerals 1, 2, 3,…, 9 and 0 are arbitrary markers for the first numbers in the counting sequence. Students learn that these numerals are used in different ways and in patterns in larger numbers.

  • Students explore the “teen” numbers, 11 through 19, through manipulatives, drawings, and equations to realize that these numbers represent ten ones and some more ones. Students group objects in the teen numbers to see the group of ten and the additional ones.

  • The teen numbers present challenges for children because they do not clearly indicate their base-ten meanings. “Eleven” and “twelve” do not sound like “ten and one” and “ten and two.” In the remaining teen numbers, the word “teen” must be interpreted as meaning “ten”, but the order is reversed because the number of ones is stated before the ten, as in “sixteen” meaning six ones and ten. Additionally, students may initially read 16 as “one, six” before they come to understand the meaning of the 1 as ten.


Important Assessment Look Fors:

  • Students count all numbers in the sequence without skipping or repeating numbers

  • Students count all objects by moving, grouping, or touching without skipping or repeating objects

  • Number reversals are developmentally appropriate and may require handwriting practice.

Purposeful Questions:

  • Are you sure that you counted all of the objects? How could you be sure?

  • What number comes before ____?

  • What number comes after _____?

Bridging for Math Strength Logo

Student Strengths

Count a group (set/collection) of five to ten objects by touching each object as it is counted and saying the correct number (one-to-one correspondence)


Trace or form numbers using various materials.

Bridging Concepts

Identify numbers 0-10 out of sequence.


Count the items in a collection of one to twenty items and know the last counting word tells “how many.


Copy or write numbers using various materials.

Standard K.1b

Read, write, and represent numbers 0 to 20

Preview of Formative Assessments

Full Module with Instructional Tips & Resources:

Formative Assessments:

Routines:

Rich Task:

Games:

Back to top

Standard K.2a

Standard K.2A Given no more than three sets, each set containing 10 or fewer concrete objects, compare and describe one set as having more, fewer, or the same number of objects as the other set(s).

(Pull down for more)

UNDERSTANDING THE LEARNING TRAJECTORY

Big Ideas:

  • Initially, students may use visual cues to decide which set is larger. They eventually learn to count or match objects in the sets to determine and compare the sizes of the sets. Students compare sets of objects by matching objects in each set and looking for any extra in one set to indicate that that set is larger than the other.

  • Students also use their knowledge of the counting sequence (ie. which number is farther along in the sequence) to determine which set is larger.

  • As students match objects in sets, they progress to understanding that objects matched in each set represent the same number in each set.


Important Assessment Look Fors:

  • Student builds a set with fewer than a given number.

  • Student builds a set with more than a given number.

  • Student justifies the number of counters in each set using a counting and matching method and/or their knowledge of the count sequence.

  • Student uses appropriate terminology (more, fewer, the same) to describe and compare the sets.


Purposeful Questions:

  • How do you know this set has fewer than 7 hearts?

  • How do you know this set has more than 7 hearts?

  • Which set has the most hearts? How do you know?

  • Which set has the fewest hearts? How do you know?

Bridging for Math Strength Logo

Student Strengths

Count concrete sets of up to 10 with one-to-one correspondence.


Build and match sets of up to 10 objects.


Identify a set that has more, fewer, or the same of a given set.


Bridging Concepts

Describe changes in groups (sets/collections) by using more when additional objects are added to a set.


Describe changes in groups (sets/collections) by using fewer when objects from a group have been removed.


Standard K.2a

Compare and describe one set as having more, fewer, or the same number of objects as the other set(s), when given no more than three sets, each set containing 10 or fewer concrete objects


Preview of Formative Assessments

Full Module with Instructional Tips & Resources:

Formative Assessments:

Routines:

Rich Task:

Games:

Back to top

Standard K.2B

Standard K.2B Given no more than three sets, each set containing 10 or fewer concrete objects, compare and order sets from least to greatest and greatest to least.

(Pull down for more)

UNDERSTANDING THE LEARNING TRAJECTORY

Big Ideas:

  • Initially students may use visual cues to decide which set is greatest or least. They eventually learn to count or match objects in the sets to determine and compare the sizes of the sets. Students compare sets of objects by matching objects in each set and looking for any extra in one set to indicate that that set is larger than the other.

  • Students also use their knowledge of the counting sequence (ie. which number is farther along in the sequence) to determine which set is greater.

  • As students match objects in sets, they progress to understanding that objects matched in each set represent the same number in each set.


Important Assessment Look Fors:

  • Students will use a method to count and match up the objects in each set.

  • Students will justify the order of their sets of objects using their counting and matching method and/or their knowledge of the count sequence.

  • Student will use appropriate terminology (least, greatest) to describe the ordered sets of objects.


Purposeful Questions:

  • Why did you put the sets of fish in this order?

  • Why does this set of fish come before/after this set?

  • How can you describe the order of the sets of fish?

  • When ordering from greatest to least/least to greatest, how did you know which number to put first?

Bridging for Math Strength Logo

Student Strengths

Match the objects in the two groups to see if there are any extra.


Count the objects in each group and use knowledge of the counting sequence to decide which number is greater (the number farther along in the count sequence).

Bridging Concepts

Count with understanding and use numbers to tell how many, describe order, and compare.


Compare two sets of matched objects (zero through ten in each set) and describe the groups using the terms more, fewer, or same.


Standard K.2b

Compare and describe three sets using words like more, fewer and same.


Compare and order three sets from least to greatest and greatest to least (zero through ten in each set).


Preview of Formative Assessments

Full Module with Instructional Tips & Resources:

Formative Assessments:

Routines:

Rich Task:

Games:

Back to top

Bridging Standard K.3A

Standard K.3A Count forward orally by ones from 0 to 100.

(Pull down for more)

UNDERSTANDING THE LEARNING TRAJECTORY

Big Ideas:

  • Students progress from initially chanting and stringing together multiple number words, to articulating each individual number with distinct words. This indicates their understanding of the uniqueness of each spoken number. In particular, they progress in articulating similar-sounding numbers, such as “fourteen” and “forty.”

  • Students learn that teen numbers name the number of ones before “teen,” meaning 10, unlike the numbers in the decades from 20 to 100 in which there is agreement between the written and spoken word, with the number of tens written and spoken first. Students develop an understanding that the decade words indicate the number of tens, such as 2 tens (20), 3 tens (30), 4 tens (40), etc. and that the suffix “-ty” means ten.

  • Students initially make mistakes such as “twenty-nine, twenty-ten, twenty-eleven, twenty-twelve…” until they develop an understanding of the relationship between written and spoken number words. They eventually learn to make decade transitions, and they come to recognize that the decade sequence mirrors the single-digit sequence.


Important Assessment Look Fors:

  • Student says each number in sequence from 0 to 100.

  • Student differentiates between similar sounding numbers, such as fourteen/forty and fifteen/fifty.

  • Student applies patterns in their count sequence.

  • Student transitions from one decade to the next (nineteen, twenty, twenty-onetwenty-nine, thirty, thirty-onethirty-nine, forty, forty-one).

Purposeful Questions:

  • What patterns do you notice when counting to 100?

  • What do you notice whenever you get to a number that ends in 9 (i.,e., 9, 19, 29, 39 etc.)? Why does the next number you say end in zero (i.e., 10, 20, 30, etc.)?

Bridging for Math Strength Logo

Student Strengths

Count forward orally to 20 or more

Bridging Concepts

Students count forward orally to 50

Standard K.3a

Count forward orally by ones from 0 to 100

Preview of Formative Assessments

Full Module with Instructional Tips & Resources:

Formative Assessments:

Routines:

Rich Task:


Games:

Back to top

Bridging Standard K.3c

Standard K.3c Identify the number after within 100, and the number before, within 10.

(Pull down for more)

UNDERSTANDING THE LEARNING TRAJECTORY

Big Ideas:

  • Students can count by ones through 100, including the decade transitions from 39 to 40, 49 to 50, and so on, starting at any number. (Clements)

  • Students recognize that each counting number identifies a quantity that is one more than the previous number. (van de Walle, pg. 128)

  • Students begin to count on, counting verbally and with objects from numbers other than 1. Students can determine immediately the number just before or just after another number without having to start back at 1. (Clements)


Important Assessment Look Fors:

  • Student uses patterns and structure in numbers to identify the number before a given number.

  • Student uses patterns and structure in numbers to identify the number after a given number.

  • Student provides reasoning for why a number comes after.

  • Student provides reasoning for why a number comes before.


Purposeful Questions:

  • What comes before 7? How do you know?

  • Why does 6 come before 7?

  • What comes after 69? How do you know?

  • Why do we say 70 after 69?

Bridging for Math Strength Logo

Student Strengths

Identify the number after within 20, and the number before, within 5.

Bridging Concepts

Identify the number after within 50, and the number before, within 10.

Standard K.3c

Identify the number after within 100, and the number before, within 10.

Preview of Formative Assessments

Full Module with Instructional Tips & Resources:

Formative Assessments:

Routines:

Rich Task:


Games:

Back to top

Bridging Standard K.4a

Standard K.4a Recognize and describe with fluency part-whole relationships for numbers to 5.

(Pull down for more)

UNDERSTANDING THE LEARNING TRAJECTORY

Big Ideas:

  • Students come to understand that a whole is larger than its parts (ie. 5 is larger than 2 and 3).

  • Students understand that numbers are nested inside of each other when counting and the next number is one more (ex. 9 is nested inside of 10, 9+1 = 10). (Clements, D.H., & Sarama, J. 2009)

  • Students learn to identify the size of a whole by composing its smaller parts. They develop intuitive understandings of commutativity (ie. 2 and 3 is the same as 3 and 2) and associativity (ie. 1 and 1 and 3 is the same as 2 and 3 and 1 and 4).

  • Students subitize, or visually recognize the number of items in a collection, using spatial and numeric structures, such as common dot patterns (ie. 2x2 array).


Important Assessment Look Fors:

  • Student uses their knowledge of visual patterns (subitizes) to identify an unknown part of a set up to 5.

  • Student uses a counting strategy to determine the unknown part of a set up to 5.


Purposeful Questions:

  • What are all the ways you can make 5? Which combination could this be? How do you know?

  • How can you figure out the unknown part?

  • How can you show (with drawings, manipulatives, tens frame, number beads/board, etc.) this part-whole relationship?

Bridging for Math Strength Logo

Student Strengths

Recognize that a number is made up of parts, which equal the whole.

Bridging Concepts

Recognize and describe the part-whole relationship for numbers up to 3.

Standard K.4a

Recognize and describe the part-whole relationship for numbers up to 5.

Preview of Formative Assessments

Full Module with Instructional Tips & Resources:

Formative Assessments:

Routines:

Rich Task:

Games:

Back to top

Bridging Standard K.4b

Standard K.4b Investigate and describe part-whole relationships for numbers to 10.

(Pull down for more)

UNDERSTANDING THE LEARNING TRAJECTORY

Big Ideas:

  • Students build on their subitizing skills and visual recognition of numbers up to 5 to learn combinations up to 10.

  • Students first learn familiar combinations, such as common doubles facts (ie. 5 and 5).

  • The use of a ten-frame structure supports students’ recognition of combinations up to 10 and beyond.


Important Assessment Look Fors:

  • Student uses their knowledge of visual patterns (subitize) to identify an unknown part of a set of up to 10.

  • Student uses a counting strategy to determine the unknown part of a set up to 10.


Purposeful Questions:

  • What combinations make 9? Which combination could this be? Why?

  • How can you figure out the unknown part?

  • How can you show (with drawings, manipulatives, tens frame, rekenrek, etc.) this part-whole relationship?

Bridging for Math Strength Logo

Student Strengths

Describe the part-whole relationship for numbers up to 5.

Bridging Concepts

Recognize and describe the part-whole relationship for numbers up to 5.

Standard K.4b

Investigate and describe part-whole relationships for numbers to 10.

Preview of Formative Assessments

Full Module with Instructional Tips & Resources:

Formative Assessments:

Routines:

Rich Task:

Games:

Back to top

Bridging Standard K.6

Standard K.6 Model and solve story problems with sums to 10 and differences within 10, using concrete objects.

(Pull down for more)

UNDERSTANDING THE LEARNING TRAJECTORY

Big Ideas:

  • Students use objects, fingers, and math drawings to act out addition and subtraction situations, allowing them to “mathematize the real world” (Common Core Progression, 2019, p. 17).

  • Students need experience acting out problems of each different addition and subtraction type, including join, separate, part-part-whole contexts.

  • Students should be presented with problems in picture and word format.


Important Assessment Look Fors:

  • Student uses standard counting order when counting objects.

  • Student uses a counting strategy to count each object only one time and says only one number when counting each object.

  • Student solution aligns to the numbers and action they used.

  • Student describes, draws, or models the action in the problem.


Purposeful Questions:

  • How can you be sure you counted all of the animals?

  • How can you be sure you counted each animal only once?

  • How do you know that ___ is the total number of animals?

  • How can you show what happened in the problem?

Bridging for Math Strength Logo

Student Strengths

Tell stories with words like more and less.


Describe changes in groups (sets/collections) using words such as more and fewer.

Bridging Concepts

Describe part/whole relationships up to 5.


Model and solve story problems within 5.

Standard K.6

Model and solve story problems with sums to 10 and differences within 10, using concrete objects.

Preview of Formative Assessments

Full Module with Instructional Tips & Resources:

Formative Assessments:

Routines:

Rich Task:

Games:

Back to top

Bridging Standard K.12

Standard K.12 Sort and classify objects according to one attribute.

(Pull down for more)

UNDERSTANDING THE LEARNING TRAJECTORY

Big Ideas:

  • Children intuitively recognize similarities between objects or situations, leading to the ability to group similar and dissimilar objects.

  • Students may begin by grouping objects by general resemblance, and later by formal attributes (size, color, shape, etc.) but may switch attributes during a sort.

  • Students learn to follow verbal instructions for sorting objects and fixing a sorted set. Early on they make mistakes in these sorting activities, but eventually they consistently and accurately sort by a single attribute and re-classify a sorted set by a different attribute.


Important Assessment Look Fors:

  • Student can articulate their rationale for sorting the objects.

  • Student classifies the objects into piles based on a single attribute (ie. color OR shape OR size).

  • Student name the attribute used to sort the objects.


Purposeful Questions:

  • Why did you put these shapes in a set together?

  • What do these shapes have in common?

  • How do you know where this shape should go?

  • What other ways might you sort these shapes?

Bridging for Math Strength Logo

Student Strengths

Group and sort like concepts together by various attributes/properties.

Bridging Concepts

Match and sort shapes (circle, triangle, rectangle, and square).


Describe how shapes are similar and different.


Recognize and name shapes (circle, triangle, rectangle, and square).

Standard K.12

Sort and classify objects according to one attribute.

Preview of Formative Assessments

Full Module with Instructional Tips & Resources:

Formative Assessments:

Routines:

Rich Task:

Games:

Back to top