Formative Assessment and Bridging activities

Kindergarten


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*These standards are bridging standards. Standards are considered a bridge when they: function as a bridge to which other content within the grade level/course is connected; serve as prerequisite knowledge for content to be addressed in future grade levels/courses; or possess endurance beyond a single unit of instruction within a grade level/course.

Standard K.1A

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

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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

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Standard K.1B

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

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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 _____?

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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

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).

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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?

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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

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.

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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?

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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

Bridging Standard K.3A

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

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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.)?

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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

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Bridging Standard K.3b

Standard K.3b Count backward orally by ones when given any number between 1 and 10

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UNDERSTANDING THE LEARNING TRAJECTORY

Big Ideas:

  • Numbers follow predictable patterns. You can count up and you can count down from any given number.

  • Humans have 10 fingers. These can be used as an aid no matter the circumstance.

  • 0 comes before 1.

  • Rote counting sets a base for subtraction.


Important Assessment Look Fors:

  • Student says 0 after they say 1.

  • Each number is said in sequence.


Purposeful Questions:

  • What number comes before 1? What does 0 mean?

  • Can you count backward from 3? What about 5?

  • Why is it important to count backward?

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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).


Zero represents no objects.


Numbers happen in a sequence.

Bridging Concepts

Student understands the concept of the number that comes before.


Student understands that 0 comes before 1.


Student recognizes the directionality of numbers.

Standard K.3b

Students can count backward orally by ones when given any number between 1 and 10

Preview of Formative Assessments

Bridging Standard K.3c

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

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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?

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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

Bridging Standard K.3d

Standard K.3d Count forward by tens to determine the total number of objects to 100

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UNDERSTANDING THE LEARNING TRAJECTORY

Big Ideas:

  • Student “sees” groups of ten within a quantity and counts those groups by 10 (relating to algebraic thinking and multiplication) (Clements, D. H., & Sarama, J. (2019)).

  • Understanding 10 as an important building block of large numbers sets students up for success in understanding place value.

  • Having one-to-one correspondence is crucial to being able to skip count. Students must trust that each group holds the amount they’re skip counting by, and this needs to be able to be confirmed.


Important Assessment Look Fors:

  • When creating groups of 10, student has strong one-to-one correspondence.

  • When creating groups, once student gets to 10, they start over with a new group of 10 instead of saying “11, 12,...” etc.

  • When skip counting, student touches each group and counts in order, not skipping any decade number.


Purposeful Questions:

  • How many counters are in this group? (Point to a random group, answer should always be 10). How do you know?

  • When you count by 10s, how do you know what number comes next?

  • Why is it important to know how to skip count?

  • What skip count comes after 100 when counting by 10?

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Student Strengths

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


Student can rote count to 100.

Bridging Concepts

Student can take a large group of objects and break it into groups of 10.


Multiple sets of the same object can be skip counted to find the total.

Standard K.3d

Students can count forward by tens to determine the total number of objects to 100

Bridging Standard K.4a

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

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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?

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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

Bridging Standard K.4b

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

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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?

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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.

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Bridging Standard K.5

Standard K.5 Investigate fractions by representing and solving practical problems involving equal sharing with two sharers

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UNDERSTANDING THE LEARNING TRAJECTORY

Big Ideas:

  • Teachers should be using language like “half” and “halves” to describe two equal shares of an object or set.

  • Fair shares are equal. Equal means the same.

  • Shapes can be proportioned in different ways. You can divide a rectangle horizontally OR vertically and still maintain halves.


Important Assessment Look Fors:

  • Use concrete representation if necessary.

  • Equal parts are the same.

  • Describe the equal part as “one half”.


Purposeful Questions:

  • Are these pieces the same size? How do you know?

  • How much of the whole brownie do we each get?

  • (When using the set of “cookies”) What is a fair way to make sure we both get the same number of cookies?

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Student Strengths

Children understand that fair shares happen in equal parts.


Intuitively and visually combines regions that are a part of a whole, showing initial foundations for addition.

Bridging Concepts

Share a whole equally with two sharers, when given a practical (real life) situation.


Represent fair shares concretely or pictorially, when given a practical situation.


Describe shares as equal pieces or parts of the whole (e.g., halves), when given a practical situation.

Standard K.5

Students can Investigate fractions by representing and solving practical problems involving equal sharing with two sharers.

Bridging Standard K.6

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

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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?

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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.

Bridging Standard K.7

Standard K.7 Recognize the attributes of a penny, nickel, dime, and quarter and identify the number of pennies equivalent to a nickel, a dime, and a quarter

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UNDERSTANDING THE LEARNING TRAJECTORY

Big Ideas:

  • The value of a coin changes what it is worth. One dime has the value of ten cents. It is the equivalent of ten pennies.

  • The value of a coin can make it worth more than another coin. One dime is worth more than one nickel.

  • Coins have different attributes. That’s how you can tell them apart.


Important Assessment Look Fors:

  • Pennies are easily differentiated from the rest of the coins.

  • Both nickels and quarters look like “big” coins. Notice how student differentiates them based on other characteristics.

  • Student identifies the coin and creates a correct collection of pennies to match the value of the coin


Purposeful Questions:

  • What clues tell you that that coin is a (penny/nickel/dime/quarter)?

  • How can you tell the difference between (nickel & quarter/ penny & dime)?

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Student Strengths

Student can count up to 25 objects with one-to-one correspondence.


Student can group objects into 5s and 10s.


Student can describe attributes like shape, size, color, and thickness.

Bridging Concepts

Student can identify the different coins based off of attributes (size, shape, thickness, color, and imagery).


Coins are worth different values.

Standard K.7

Students can recognize the attributes of a penny, nickel, dime, and quarter and identify the number of pennies equivalent to a nickel, a dime, and a quarter.

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Bridging Standard K.8

Standard K.8 Investigate the passage of time by reading and interpreting a calendar.

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UNDERSTANDING THE LEARNING TRAJECTORY

Big Ideas:

  • A calendar organizes time into days, weeks, months, and years.

  • Time never stops.

  • Calendars have patterns that follow rules.


Important Assessment Look Fors:

  • Student is appropriately differentiating between days and months.

  • Student is appropriately differentiating between yesterday, today, and tomorrow.


Purposeful Questions:

  • Is “yesterday” about the past, present, or the future?

  • What day of the week is after Saturday?

  • Can you always tell what tomorrow will be if you know what day it is today? How?

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Student Strengths

Student can count to 31 by 1s.


Student recognizes patterns around them and that events happen in a logical sequence.

Bridging Concepts

A calendar is used to organize time.


Name the twelve months of the year. Name the seven days in a week. Determine the day before and after a given day (e.g., yesterday, today, tomorrow).

Standard K.8

Students can investigate the passage of time by reading and interpreting a calendar.

Bridging Standard K.9

Standard K.9 Compare two objects or events, using direct comparisons, according to one or more of the following attributes: length (longer, shorter), height (taller, shorter), weight (heavier, lighter), temperature (hotter, colder), volume (more, less), and time (longer, shorter).

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UNDERSTANDING THE LEARNING TRAJECTORY

Big Ideas:

  • This standard is heavy in vocabulary. Be especially mindful of students with limited vocabulary as you teach this standard. Use explicit vocabulary teaching strategies, giving students hands-on experiences with each term. Explicit definitions can be found in the Curriculum Framework.

  • Volume, length, height, and weight are attributes that can be separated from size (big/small).

  • There are strategies and tools used to compare objects to one another.


Important Assessment Look Fors:

  • Physically aligns two objects to determine which is longer or if they are the same length.

  • Student is using appropriate vocabulary to describe the comparison (The cow is heavier than the milk carton).

  • Comparing time may be challenging for students, as it is an abstract concept. Student may act out the events in order to make a conjecture about which is longer or shorter.


Purposeful Questions:

  • How were you able to tell that one object is (longer/shorter/heavier/lighter/more/less)?

  • What do you know about that object that helps you compare it?

  • Can you act out the event to try to figure out how to compare?

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Student Strengths

Student can compare objects using a variety of attributes such as length, height, weight, temperature, or time.


Student can count using one-to-one correspondence.

Bridging Concepts

Student can choose one object that is longer/shorter, taller/shorter, heavier/lighter, hotter/colder, more/less, or longer/shorter when given two objects.

Standard K.9

Students can compare two objects or events, using direct comparisons, according to one or more of the following attributes: length (longer, shorter), height (taller, shorter), weight (heavier, lighter), temperature (hotter, colder), volume (more, less), and time (longer, shorter).

Bridging Standard K.10

Standard K.10 The student will

a) identify and describe plane figures (circle, triangle, square, and rectangle);

b) compare the size (smaller, larger) and shape of plane figures (circle, triangle, square, and rectangle);

c) describe the location of one object relative to another (above, below, next to) and identify representations of plane figures (circle, triangle, square, and rectangle) regardless of their positions and orientations in space.

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UNDERSTANDING THE LEARNING TRAJECTORY

Big Ideas:

  • Presentation of triangles, rectangles, and squares should be made in a variety of spatial orientations so that students are less likely to develop common misconception that triangles, rectangles, and squares must have one side parallel to the bottom of the page on which they are printed.

  • Children should have experiences with different types of triangles (e.g., equilateral, isosceles, scalene, right, acute, obtuse); however, at this level, they are not expected to name the various types.

  • A common misconception students have when a figure such as a square is rotated is they will frequently refer to the rotated square as a diamond. Clarification needs to be ongoing (e.g., a square is a square regardless of its location in space; there is no plane figure called a diamond).

  • This standard is heavy in vocabulary. Be especially mindful of students with limited vocabulary as you teach this standard. Use explicit vocabulary teaching strategies, giving students hands-on experiences with each term. Explicit definitions can be found in the Curriculum Framework.


Important Assessment Look Fors:

  • Squares and rectangles are differentiated.


Purposeful Questions:

  • What clues tell you that shape is a (square/rectangle/triangle/circle)?

  • Do (squares/triangles) always have a side that sits on the bottom?

  • What’s another way to describe where the shape is?

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Student Strengths

Early experiences with comparing, sorting, combining, and subdividing figures assist students in analyzing the characteristics of plane figures.


A plane figure is any closed, two-dimensional shape.

Bridging Concepts

Student matches familiar shapes (circle, square, typical triangle) that have the same size and orientation. In specific congruence tasks, may think that two shapes are the same if they are more visually similar than different.


Student matches familiar shapes with different orientations.


Student matches familiar shapes with different sizes.

Standard K.10

Students can


-identify and describe plane figures (circle, triangle, square, and rectangle);


-compare the size (smaller, larger) and shape of plane figures (circle, triangle, square, and rectangle); and


-describe the location of one object relative to another (above, below, next to) and identify representations of plane figures (circle, triangle, square, and rectangle) regardless of their positions and orientations in space.

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Bridging Standard K.11

Standard K.11 The student will

a) collect, organize, and represent data; and

b) read and interpret data in object graphs, picture graphs, and tables.

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UNDERSTANDING THE LEARNING TRAJECTORY

Big Ideas:

  • Data are pieces of information collected about people or things. The primary purpose of collecting data is to answer questions. The primary purpose of interpreting data is to inform decisions.

  • When data are presented in an organized manner, students can interpret and discuss the results and implications of their investigation.

  • Data is collected all around us. Draw attention to the lunch count, the weather graph, or the “How Many Days in School?” chart for a glimpse into data.

  • Data can be represented in multiple ways, yet draw the same conclusion (bar graph vs. picture graph).


Important Assessment Look Fors:

  • The first image in the graph is the anchor, NOT a part of the data collection. Children may count it in their data set.

  • Student may confuse the words “greatest” and “least”.

  • Students may count all of the data points, not just the ones you’ve asked them too.


Purposeful Questions:

  • How do you know that category has the (greatest/least) votes?

  • How many (more/fewer) votes does ___ have than ___?

  • What do you think is the best way to show data?

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Student Strengths

Comfort in asking and answering questions.


Use background knowledge and knowledge of the world around them to draw logical conclusions (The grass is wet because it rained last night).


Student can sort and organize items into categories.

Bridging Concepts

When given precise answers to a question, those answers can be categorized and analyzed.


When students begin to collect data, they recognize the need to categorize, which helps develop the understanding of “things that go together.”


Students understand and can use “least” and “greatest” to describe sets of data.

Standard K.11

Students can


-collect, organize, and represent data; and


-read and interpret data in object graphs, picture graphs, and tables.

Full Module with Instructional Tips & Resources:

Formative Assessments:

Routines:

Rich Task:

Games/Tech:

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Bridging Standard K.12

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

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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.

Bridging Standard K.13

Standard K.13 Identify, describe, extend, create, and transfer repeating patterns.

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UNDERSTANDING THE LEARNING TRAJECTORY

Big Ideas:

  • Patterning is a fundamental cornerstone of mathematics, particularly algebra. The process of generalization leads to the foundation of algebraic reasoning.

  • Eventually, students learn to find patterns in numbers, such as skip counting, which leads to understanding multiplication and division.

  • A variety of patterns are introduced. Examples include:

    • ABABABAB

    • ABCABC

    • ABBAABBA

    • AABBAABBAABB

    • AABAAB.

  • Translates patterns into new media or using new materials; that is, abstract and generalize the pattern.


Important Assessment Look Fors:

  • Student extends the pattern by two repetitions of the core, not just by a few shapes.

  • Student translates the given pattern using two different manipulatives/shapes/colors/numbers/etc.

  • Student is able to create a repeating (not growing!) pattern.


Purposeful Questions:

  • How can you identify the core of the pattern?

  • How is your pattern like the pattern you see above?

  • What is the core of your pattern? How many times will it repeat?

Bridging for Math Strength Logo

Student Strengths

Student is able to identify shapes, numbers, letters, and colors.


Student can participate in a call-and-repeat type of activity such as repeating a clapping pattern.

Bridging Concepts

Student identifies repeating patterns in the world around them such as on the calendar, in a movement/ sound/ clapping way, or in colors.


Student identifies the part of the pattern that repeats called the core.

Standard K.13

Students can identify, describe, extend, create, and transfer repeating patterns.