## Formative Assessment and Bridging activities

Grade 2

These materials were co-designed by teachers, coaches and math teacher educators and are part of an iterative design process. We continue refine and enhance the resources for teachers. Feedback is welcome and accepted at the link below. ** ***

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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 2.1A

**S****tandard**** 2.1****a**** **Read, write, and identify the place and value of each digit in a three-digit numeral, with and without models.

**(Pull down for more)**

Understanding the Learning Trajectory

**Big Ideas:**

The value of each digit in a number depends on its position in that number.

Numbers are based on powers of ten. The value of each place is 10 times the value of the digit to the right.

The structure of numbers is based on unitizing amounts into groups of ones, tens, hundreds, etc.

Math Strengths Instructional Video 2.1a↗

**Important Assessment Look-fors***:* ** **

Student counts one hundred as a single unit.

Student composes and decomposes numbers into ones, tens, and hundreds.

Student knows the number of hundreds that can be made from any group of tens and the number of tens left over.

Student determines the total value of a group of hundreds, tens, and ones by reorganizing them into all possible hundreds, then all possible tens, with leftover ones.

Student describes any 3 digit number in terms of its value in hundreds, tens, and ones.

**Purposeful Questions:**

How many groups of ones, tens, and hundreds make this number?

How do the digits in this number relate to the groups of hundreds, tens, and ones in this number?

How can the hundreds, tens, and ones in this number be regrouped to represent an equivalent value?

**Student Strengths**

Students can organize objects into groups of tens and ones, and determine the total value without counting.**Student Strengths**

Students can read, write, and identify the place and value of each digit in a two-digit numeral, with and without models.

**Bridging Concepts**

The students can organize objects into groups of hundreds, tens, and ones, and determine the total value without counting all.**Bridging Concepts**

**Standard 2.1A**

The students can read, write, and identify the place and value of each digit in a three-digit numeral, with and without models.**Standard 2.1A**

**Full Module with Instructional Tips & Resources:**

**Full Module with Instructional Tips & Resources:**

**Formative Assessments: **

**Formative Assessments:**

**Routines: **

**Routines:**

**Rich Tasks: **

**Rich Tasks:**

**Games/Tech:**

## Standard 2.1B

**S****tandard**** 2.1b **Identify the number that is 10 more, 10 less, 100 more, and 100 less than a given number up to 999.

**(Pull down for more)**

Understanding the Learning Progression

**Big Ideas:**

The same value may be represented as 10 ones and 1 ten or 10 tens and 1 hundred.

Ones, tens, and hundreds can be grouped and counted as units.

The place value structure of hundreds, tens, and ones helps determine 10 more, 100 more, 10 less, and 100 less without counting by ones.

**Important Assessment Look-fors: **

Students moves vertically on a 120s chart to demonstrate 10 more/10 less/100 more/100 less than a number.

Student counts forward/backward by tens to determine 10 more/10 less than a given number.

Student adds or removes a ten rod to demonstrate 10 more/10 less of a number.

**Purposeful**** ****questions:**

Is there a way to show 10 more/10 less in one jump on the 120s chart? Is there a way to show 100 more/100 less in one jump on the 120s chart?

How can I represent 10 more/10 less, with base ten blocks?

Is there another model you can use to show 10 more/10 less? 100 more/100 less?

Explain to a friend how you would mentally solve 10 more/10 less/100 more/100 less questions.

**Student Strengths**

Students can count forward and backward by ten from a ten using the structure of numbers. **Student Strengths**

**Bridging Concepts**

Students can count forward and backward by ten from numbers other than tens using the structure of numbers.**Bridging Concepts**

**Standard 2.1****B**

Students can identify the number that is 10 more, 10 less, 100 more, and 100 less than a given number up to 999.**Standard 2.1**

**B**

**Full Module with Instructional Tips & Resources: **

**Full Module with Instructional Tips & Resources:**

- Bridging for Math Strength Standard 2.1B↗
**(START HERE)**

**Formative Assessments: **** **

**Formative Assessments:**

**Routines:**

**Routines:**

**Rich Tasks: **** **

**Rich Tasks:**

**Games/Tech:**

**Games/Tech:**

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## Standard 2.1C

**S****tandard**** 2.1****c**** **Compare and order whole numbers between 0 and 999.

**(Pull down for more)**

## Understanding the Learning Trajectory

**Big Ideas:**

According to the compare learning trajectory, students compare by counting, compare numbers with place value, use knowledge of number relationships and mental number line as well as benchmarks to determine relative size and position when comparing. (Clements & Sarama, 2019)↗

Whole numbers can be compared by analyzing corresponding place values (Charles, 2005, p.14).

Comparing the magnitude of two digit and three digit numbers uses the understanding that the tens place is greater than the ones place and the hundreds place is greater than the tens place (Common Core Standards Writing Team, 2019).

**Important Assessment Look Fors:**

Student chooses numbers that are very different from the original number when comparing quantities.

Student uses the place value structure of numbers to compare and order different amounts.

Student uses symbols to represent greater than, less than, and equal to relationships.

**Purposeful Questions: **

What determines whether a number is greater than, less than, or equal to another number?

How is understanding place value helpful when comparing and ordering numbers?

What words and symbols are used to compare and order numbers?

**Student Strengths**

Students can compare groups of objects that are lined up and tell which is greater than, is less than, and is equal to and tell how much more or less when the difference is 1 or 2.**Student Strengths**

**Bridging Concepts**

Students can compare and order groups of objects that are not lined up, and tell which is greater than, is less than, and is equal to up to 110 and then use symbols to express the relationship.**Bridging Concepts**

**Standard 2.1****C**

Students can compare and order whole numbers between 0 and 999.**Standard 2.1**

**C**

**Full Module with Instructional Tips & Resources: **

**Full Module with Instructional Tips & Resources:**

Bridging for Math Strength Standard 2.1C↗

**(START HERE)**

**Formative Assessments: **

**Formative Assessments:**

**Routines:**

**Routines:**

**Rich Tasks: **** **

**Rich Tasks:**

**Games:**

**Games:**

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## Standard 2.1d

**S****tandard**** 2.****1d **** **Round two-digit numbers to the nearest ten.

**(Pull down for more)**

Understanding the Learning Trajectory

**Big Ideas:**

An understanding of the structure of the base-ten number system is based upon a simple pattern of tens, where each place is ten times the value of the place to its right.

When rounding to the nearest 10, 100, or 1,000, the goal is to approximate the number by the closest number with no ones, no tens and ones, or no hundreds, tens, and ones. (Common Core Standards Writing Team, 2019)

Rounding should be conceptually understood to allow for flexibility in thinking about distance between numbers.

**Important Assessment Look Fors:**

Student can write the number accurately with the appropriate number of digits.

Student can identify the tens, hundreds, thousands place in order to round.

Student can identify the tens a number is between.

Student determines the closest multiple of ten for the given number.

**Purposeful Questions: **

How did you know to round ________ to ________? ( 37 to 40)

What digit is in the (tens, ones) place? Why did it round to _______?

Explain why you chose _________ to round to ______? (80)

What numbers would round to 60? How do you know?

**Student Strengths**

Students can count forward orally by ones, twos, fives, and tens to determine the total number ofobjects to 110.**Student Strengths**

Students can group a collection into tens and ones and write the corresponding numeral with objects up to 110

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; and

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

**Bridging Concepts**

Students can Identify the which two tens any given two digit number lies between**Bridging Concepts**

Students can place numbers on an open number line.

Students can count forward by twos, fives, and tens to 120, starting at various multiples of 2, 5, or 10;

The student can count backward by tens from 120

**Standard 2.****1d**

Students can round two-digit numbers to the nearest ten.**Standard 2.**

**1d**

**Full Module with Instructional Tips & Resources: **

**Full Module with Instructional Tips & Resources:**

Bridging for Math Strengths Standard 2.1d↗

**(START HERE)**

**Formative Assessments: **

**Formative Assessments:**

**Routines:**

**Routines:**

**Rich Tasks: **** **

**Rich Tasks:**

**Games:**

**Games:**

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## Standard 2.2A

**S****tandard**** 2.2A **** **Count forward by twos, fives, and tens to 120, starting at various multiples of 2, 5, or 10.

**(Pull down for more)**

Understanding the Learning Trajectory

**Big Ideas:**

Within the learning trajectory of counting forward and back, this level demonstrates students’ ability to count "counting words" (single sequence or skips counts) in either direction starting at any number. Recognizes that decades sequences mirror single-digit sequences (Clements & Sarama, 2019).

Students are able to skip counting by saying a sequence of numbers represents a grouping of objects. Organizing objects into groups while skip counting by that quantity is more efficient than skip counting by ones (Richardson, 2012).

Skip counting can occur at various places in the sequence of numbers. Skip counting by tens forward leads to place value strategies for addition (Richardson, 2012).

**Important Assessment Look Fors:**

Student counts by two or fives rather than by ones when objects are presented in groups of 2 or 5, respectively.

Student skip counts by 10s to continue a counting sequence.

Student recognizes that a zero in the ones place signals counting by tens.

Student applies the pattern of 5s and 0s in the ones place when counting by fives beginning at a multiple of 5.

**Purposeful Questions: **

How are the objects grouped in the pictures?

How does the way objects are grouped determine the skip counting pattern?

How do the numbers you say while skip counting help you determine the pattern?

What are some patterns noticed in the specific numbers said when skip counting by a specific amount?

**Student Strengths**

Students can create groups of objects of twos, fives, and tens while they skip count to 120. **Student Strengths**

**Bridging Concepts**

Students can count forward by twos, fives, and tens, starting at 0.**Bridging Concepts**

**Standard 2.2A**

Students can count forward by twos, fives, and tens to 120, starting at various multiples of 2, 5, or 10.**Standard 2.2A**

**Full Module with Instructional Tips & Resources: **

**Full Module with Instructional Tips & Resources:**

Bridging for Math Strength Standard 2.2A↗

**(START HERE)**

**Formative Assessments: **

**Formative Assessments:**

**Routines:**

**Routines:**

**Rich Tasks: **** **

**Rich Tasks:**

**Games:**

**Games:**

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## Standard 2.2B

**S****tandard**** 2.****2B **Count backward by tens from 120.

**(Pull down for more)**

## Understanding the Learning Trajectory

**Big Ideas:**

Within the learning trajectory of counting forward and back, this level demonstrates students’ ability to count "counting words" (single sequence or skips counts) in either direction starting at any number. Recognizes that decades sequences mirror single-digit sequences (Clements & Sarama, 2019).

Organizing objects into groups of ten while skip counting backward is more efficient than skip counting backward by ones.

Skip counting backwards by tens is “ ten less” than a number. Skip counting backwards by tens supports place value strategies for subtraction.

**Important Assessment Look Fors:**

Student skip counts backward by tens without counting backwards by ones.

Student determines “10 less” than a number.

Student uses a number line or hundreds chart to facilitate their skip counting.

**Purposeful Questions: **

How is skip counting backwards by ten more efficient than skip counting backwards by one?

How is skip counting backwards by ten the same as “10 less” than a number?

How is skip counting backwards by ten similar and different than skip counting forward by ten?

**Student Strengths**

Students can count forward by tens to 120. **Student Strengths**

**Bridging Concepts**

**Bridging Concepts**

Students can identify 10 more and 10 less than any ten between 10 and 110.

Students can describe the pattern when skip counting by tens forward and backward.

**Standard 2.****2B**

Students can count backward by tens from 120.**Standard 2.**

**2B**

**Full Module with Instructional Tips & Resources:**

**Full Module with Instructional Tips & Resources:**

Bridging for Math Strength Standard 2.2B↗

**(START HERE)**

**Formative Assessments: **

**Formative Assessments:**

**Routines:**

**Routines:**

**Rich Tasks: **** **

**Rich Tasks:**

**Games:**

**Games:**

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## Standard 2.2c

**S****tandard**** ****2.****2c**** **Use objects to determine whether a number is even or odd.

**(Pull down for more)**

## Understanding the Learning Trajectory

**Big Ideas:**

Building on their own intuitive mathematical knowledge, students display a natural need to organize things by sorting, comparing, ordering, and labeling objects in a variety of collections. (VDOE Curriculum Framework, VDOE, grade 2)

Odd and even numbers can be explored in different ways (e.g., dividing collections of objects into two equal groups or pairing objects). When pairing objects, the number of objects is even when each object has a pair or partner. When an object is left over, or does not have a pair, then the number is odd. (VDOE Curriculum Framework, Grade 2)

Determine if a number is even or odd by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. (corestandards.org)

**Important Assessment Look Fors:**

Students can organize marbles into two equal groups or group into groups of two

Students can apply rote counting by twos to coordinate with groups of two

Students can write an equation to express an even number as a sum of two equal addends or an odd number of two equal addends plus 1.

**Purposeful Questions: **

How did you use the marbles to help determine if 25 is even or odd?

How do you know 25 is even or odd?

How might you write an equation to prove 25 is even or odd?

**Student Strengths**

**Student Strengths**

Students can count forward orally by ones to 110, starting at any number between 0 and 110;

Students can count forward orally by ones and twos to determine the total number of objects to 110.

**Bridging Concepts**

**Bridging Concepts**

Students can divide a group of objects into two equal groups

Students can group objects in groups of two

**Standard 2.****2c**

**Standard 2.**

**2c**

Students can use objects to determine whether a number is even or odd.

**Full Module with Instructional Tips & Resources:**

**Full Module with Instructional Tips & Resources:**

Bridging for Math Strength Standard 2.2c↗

**(START HERE)**

**Formative Assessments: **

**Formative Assessments:**

**Routines:**

**Routines:**

**Rich Tasks: **** **

**Rich Tasks:**

**Games:**

**Games:**

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## Standard 2.3ab

**S****tandard**** ****2.****3ab**** **The student will,

a) count and identify the ordinal positions first through twentieth, using an ordered set of objects; and

b) write the ordinal numbers 1st through 20th.

**(Pull down for more)**

## Understanding the Learning Trajectory

**Big Ideas:**

An understanding of the cardinal and ordinal meanings of numbers is necessary to quantify, measure, and identify the order of objects.

The ordinal meaning of numbers is developed by identifying and verbalizing the place or position of objects in a set or sequence (VDOE curriculum framework)

An ordinal counter is someone who can identify and use ordinal numbers from first to tenth. Ordinal counters can also make connections to counting words. For example, if you are fifth in line, you are number 5 in line. (Clements, D. H., & Sarama, J.)

**Important Assessment Look Fors:**

Student can identify where to start when counting, indicating they know left, right, top, and bottom.

Student can match the correct ordinal position with the cardinal numbers.

Student can place the correct drawing or notation in the correct spot indicating they understand ordinal number placement.

**Purposeful Questions: **

How did you know which shape is fifth from the right? How did you know which shape to put an “x” on?

How did you know the order of ice cream colors? How did you know to start from the top? bottom?

How did you know where to find the twelfth shape? Fourteenth?

**Student Strengths**

**Student Strengths**

Given an ordered set of ten objects and/or pictures, Students can indicate the ordinal position of each object, first through tenth.

Students can describe the location of one object relative to another (above, below, next to)

**Bridging Concepts**

**Bridging Concepts**

Students can orally match the ordinal terms (first, second, third, fourth, etc) to the cardinal counterpart.

Students understand and can use the vocabulary words left, right, top, and bottom.

**Standard 2.****3ab**

**Standard 2.**

**3ab**

Students can

a) count and identify the ordinal positions first through twentieth, using an ordered set of objects; and

b) write the ordinal numbers 1st through 20th.

**Full Module with Instructional Tips & Resources:**

**Full Module with Instructional Tips & Resources:**

Bridging for Math Strength Standard 2.3ab↗

**(START HERE)**

**Formative Assessments: **

**Formative Assessments:**

**Routines:**

**Routines:**

**Rich Tasks: **** **

**Rich Tasks:**

**Games:**

**Games:**

Back to top ↗

## Standard 2.4a

**S****tandard**** ****2.****4a**** **Name and write fractions represented by a set, region, or length model for halves, fourths, eighths, thirds, and sixths

**(Pull down for more)**

## Understanding the Learning Trajectory

**Big Ideas:**

Fractions are equal shares of a whole or a unit. Therefore, fraction instruction should begin with equal sharing activities that build on whole number knowledge to introduce fraction as quantities(i.e., 2 sandwiches shared with 4 friends). SOL K.5 and 1.4 focus on equal shares and the number of sharers of 2 and 4 and move to other fractional parts like thirds, sixths, eighths, etc. in support of the learning trajectory.

A fraction is a numerical way of representing equal parts of a whole region (i.e., an area model), parts of a group (i.e., a set model), or parts of a length (i.e., a measurement model).

Parts of a region model may not be congruent but maintain an equal value (area).

The numerator represents the equal parts being considered and the denominator represents the equal parts that create the whole.

**Important Assessment Look Fors:**

Student identifies the shaded parts of a region model as the numerator and the total number of parts as the whole or denominator.

Student identifies that the total number of objects in a set represent the whole or denominator, and that the shaded objects represent the identified part, or numerator.

Student compares lengths of sections and their positions relative to whole numbers on a number line to name fractional marks on a number line.

Student compares sizes and shapes of fractional parts to determine whether or not a region model is divided into equal parts.

**Purposeful Questions: **

How do we name fractions? What does the numerator represent? What does the denominator represent?

How does a fraction represent a part to whole relationship?

What does a fraction on a number line represent? What makes the whole on the number lines? What is the part being considered?

How do you find a fraction of a set? (Set model - discrete objects)

How must a shape be divided to represent a fraction? (region or area model- continuous)

**Student Strengths**

**Student Strengths**

Students can name fractions represented by drawings or concrete materials for halves and fourths.

**Bridging Concepts**

**Bridging Concepts**

Students can name fractions represented by drawings or concrete materials for halves and fourths, eighths, thirds, and sixths.

Students can share items of a set or area equally between halves and fourths.

**Standard 2.4a**

**Standard 2.4a**

Students can name and write fractions represented by a set, region, or length model for halves, fourths, eighths, thirds, and sixths.

**Full Module with Instructional Tips & Resources: **

**Full Module with Instructional Tips & Resources:**

Bridging for Math Strength Standard 2.4a↗

**(START HERE)**

**Formative Assessments: **

**Formative Assessments:**

**Routines:**

**Routines:**

**Rich Tasks: **** **

**Rich Tasks:**

**Games/Tech:**

**Games/Tech:**

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## Standard 2.4b

**S****tandard**** ****2.****4b**** **Represent fractional parts with models and with symbols.

**(Pull down for more)**

## Understanding the Learning Trajectory

**Big Ideas:**

The whole must be defined when working with fractions.

In a region/area model, the parts must have the same area.

In a set model, the set represents the whole and each item represents an equivalent part of the set.

In a length model, each length represents an equal part of the whole.

**Important Assessment Look Fors:**

Student divides a whole region into the appropriate number of equal parts to represent the denominator of a fraction.

Student uses the appropriate number of shapes to represent the identified numerator of the fraction.

Student folds the paper strip (or other model) into equal parts, as represented by the denominator, and shades the parts identified by the numerator.

**Purposeful Questions: **

When creating a model to represent a fraction, what does the numerator represent and what does the denominator represent?

When making a model to represent a fraction, what must all the pieces have in common?

**Student Strengths**

**Student Strengths**

Students can represent fractional parts for halves and fourths with area/region models.

**Bridging Concepts**

**Bridging Concepts**

Students can represent fractional parts for halves and fourths with area/region, length/measurement, and set models.

**Standard 2.6c**

**Standard 2.6c**

Students can represent fractional parts with models and with symbols.

**Full Module with Instructional Tips & Resources: **

**Full Module with Instructional Tips & Resources:**

Bridging for Math Strength Standard 2.4b↗

**(START HERE)**

**Formative Assessments: **

**Formative Assessments:**

**Routines:**

**Routines:**

**Rich Tasks: **** **

**Rich Tasks:**

**Games****/Tech****:**

**Games**

**/Tech**

**:**

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## Standard 2.4c

**S****tandard**** ****2.****4****c **Compare the unit fractions for halves, fourths, eighths, thirds, and sixths, with models

**(Pull down for more)**

## Understanding the Learning Trajectory

**Big Ideas:**

A whole is composed of equal parts and each part is considered a unit fraction.

A unit fraction is represented symbolically with a one as the numerator.

The more equal parts a whole is divided into, the smaller each part becomes.

The value of a fraction depends on the number of equivalent parts making up the whole and how many parts are being considered.

**Important Assessment Look Fors:**

Student creates equal sized parts when representing a fraction in a region model.

Student compares sizes of unit fractions, of the same size whole, to determine which unit fraction is larger/smaller.

Student recognizes that parts get smaller as a region is divided into more equal parts, and that a larger denominator indicates a smaller unit fraction.

Student identifies that the total number of parts in a region is indicated by the denominator and the shaded parts are indicated by the numerator.

**Purposeful Questions: **

Why is a unit fraction smaller with a larger number in the denominator?

What happens to the parts of a whole as they are divided into more parts?

What does the numerator represent in a fraction? What does the denominator represent in a fraction?

How can skip counting by unit fractions help determine the fraction represented by a model?

What symbol represents “greater than”, “less than”, and “equal to”? How can we use the symbol to compare two fractions?

**Student Strengths**

**Student Strengths**

Students can count unit fractions as they create the unit fractions for halves, fourths, eighths, thirds, and sixths, with models.

**Bridging Concepts**

**Bridging Concepts**

Students can represent and identify the unit fractions for halves, fourths, eighths, thirds, and sixths, with models.

**Standard 2.****4****c**

**Standard 2.**

**4**

**c**

Students can compare the unit fractions for halves, fourths, eighths, thirds, and sixths, with models.

## Standard 2.5A

**S****tandard**** ****2.5****a **Recognize and use the relationships between addition and subtraction to solve single-step practical problems, with whole numbers to 20

**(Pull down for more)**

## Understanding the Learning Trajectory

**Big Ideas:**

According to the learning trajectories, children around age 7-8 move from being a “deriver” to a “problem solver”. At the level, deriver, a child can use flexible strategies and related facts/derived combinations (for example, “7 1 7 is 14, so 7 1 8 is 15”) to solve all types of problems. As children develop their addition and subtraction problem solving abilities, they can solve all types of problems by using flexible strategies and many known combinations. For example, when asked, “If I have 13 and you have 9, how could we have the same number?” this child says, “9 and 1 is 10, then 3 more to make 13. 1 and 3 is 4. I need 4 more!” (For more information, go to learning trajectories levels at https://www.learningtrajectories.org/.)

Addition and subtraction are related and have an inverse relationship.

Number relationships provide the foundation for strategies that help students remember basic facts.

The patterns formed by related facts facilitate the solution of problems involving a missing addend in an addition sentence or a missing part in a subtraction sentence.

**Important Assessment Look Fors:**

Student has an understanding of the word “related.”

Student models an addition story problem with manipulatives.

Student creates a number sentence to model the practical problem.

Student models and writes equations to match various types of word problems.

**Purposeful Questions: **

Is there a way to use a different operation to solve this number story?

Does the number sentence you wrote match the number story? What could be used to represent what information we are looking for?

How can using the inverse operation help us?

**Student Strengths**

**Student Strengths**

Students can understand that addition is combining and subtraction is separating.

**Bridging Concepts**

**Bridging Concepts**

Students can use related facts to help solve practical problems.

**Standard 2.5a**

**Standard 2.5a**

Students can recognize and use relationships between addition and subtraction to solve single-step practical problems, with whole numbers to 20.

**Full Module with Instructional Tips & Resources: **

**Full Module with Instructional Tips & Resources:**

Bridging for Math Strength Standard 2.5a↗

**(START HERE)**

**Formative Assessments: **

**Formative Assessments:**

**Routines:**

**Routines:**

**Rich Tasks: **** **

**Rich Tasks:**

**Games/Tech:**

**Games/Tech:**

Desmos 2.5abAddition Strategies↗

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## Standard 2.5B

**S****tandard**** ****2.5****B **** **Demonstrate fluency with addition and subtraction within 20.

**(Pull down for more)**

## Understanding the Learning Trajectory

**Big Ideas:**

Flexible methods for computing build computational fluency.

Composing and decomposing numbers build understanding and flexibility with number.

Part-whole relationships are foundational to understanding computation.

**Important Assessment Look Fors:**

Student identifies the symbols for representing computation and understands the meaning of the symbols for addition and subtraction.

Student uses one or more strategies to solve addition and subtraction facts/problems.

Student uses a manipulative to model a strategy to solve addition and subtraction facts/problems.

**Purposeful Questions: **

What strategy did you use? Why did you choose that strategy?

Is there another strategy you can use?

Is there another fact you used to help you solve?

How can you use a different operation to check your answer?

**Student Strengths**

**Student Strengths**

Students can recognize and describe part whole relationships within 10.

**Bridging Concepts**

**Bridging Concepts**

Students can demonstrate fluency with addition and subtraction within 10.

**Standard 2.5b**

**Standard 2.5b**

Students can demonstrate fluency with addition and subtraction within 20.

**Full Module with Instructional Tips & Resources: **

**Full Module with Instructional Tips & Resources:**

Bridging for Math Strength Standard 2.5b↗

**(START HERE)**

**Formative Assessments: **

**Formative Assessments:**

**Routines:**

**Routines:**

**Rich Tasks: **** **

**Rich Tasks:**

**Games/Tech:**

**Games/Tech:**

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## Standard 2.6A

**S****tandard**** ****2.6a **Estimate sums and differences.

**(Pull down for more)**

## Understanding the Learning Trajectory

**Big Ideas:**

Estimation is a valuable time saving skill in practical situations when an exact answer is not needed.

Estimation helps students complete computations with larger numbers.

Composing and decomposing numbers can build estimation skills.

**Important Assessment Look Fors:**

Student identifies which two tens a number falls between.

Student breaks apart numbers and finds friendly combinations to solve.

Student understands when an estimate is needed and not an exact answer.

**Purposeful Questions: **

What strategy did you use to find an estimate? Why did you choose that strategy?

How did estimation help you determine the solution?

How can estimation help you decide if your answer is correct?

**Student Strengths**

**Student Strengths**

Students can determine if a number is closer to 0, 10, 100.

**Bridging Concepts**

**Bridging Concepts**

Students can identify which two tens a number falls between (nesting) and identify the number then count on or back from there.

**Standard 2.6a**

**Standard 2.6a**

Students can estimate sums and differences.

**Full Module with Instructional Tips & Resources: **

**Full Module with Instructional Tips & Resources:**

Bridging for Math Strength Standard 2.6a↗

**(START HERE)**

**Formative Assessments: **

**Formative Assessments:**

**Routines:**

**Routines:**

**Rich Tasks: **** **

**Rich Tasks:**

**Games:**

**Games:**

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## Standard 2.6B

**S****tandard**** ****2.6b** Determine sums and differences, using various methods.

**(Pull down for more)**

## Understanding the Learning Trajectory

**Big Ideas:**

Flexible methods of addition and subtraction involve composing and decomposing numbers in a variety of ways.

Flexible methods for computation require a strong understanding of the operations including the properties of operations.

**Important Assessment Look Fors:**

Student uses estimation strategies before and after solving addition and subtraction problems.

Student illustrates or acts out a story problems to determine the operation needed to solve.

Student uses various methods for computing and describes how the method works.

**Purposeful Questions: **

What strategy did you use to find an answer? Why did you choose that strategy?

Is there another strategy you could try?

Will your strategy work for other numbers? How do you know?

How can estimation help you decide if your answer is correct?

**Student Strengths**

**Student Strengths**

Students can recognize and describe part whole relationships within 10.

**Bridging Concepts**

**Bridging Concepts**

Students can demonstrate fluency with addition and subtraction within 20.

**Standard 2.**

**Standard 2.**

Students can determine sums and differences, using various methods.

**Full Module with Instructional Tips & Resources: **

**Full Module with Instructional Tips & Resources:**

Bridging for Math Strength Standard 2.6b↗

**(START HERE)**

**Formative Assessments: **

**Formative Assessments:**

**Routines:**

**Routines:**

**Rich Tasks: **** **

**Rich Tasks:**

**Games:**

**Games:**

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## Standard 2.6c

**S****tandard**** ****2.6c **Create and solve single-step and two-step practical problems involving addition and subtraction.

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## Understanding the Learning Trajectory

**Big Ideas:**

Addition and subtraction are used to solve problems that arise in everyday life.

Addition and subtraction have an inverse relationship.

Different representations can be used to model a variety of problem types.

Flexible methods of computation involve taking apart (decomposing) and combining (composing) numbers in a variety of ways (Van de Walle et al, 2018).

Using related combinations can be helpful in solving problems that contain larger numbers (i.e., 9 + 7 can be thought of as 9 broken up into 2 and 7; using doubles, 7 + 7 = 14; 14 + 2 = 16 or 7 broken up into 1 and 6; making a ten, 1 + 9 = 10; 10 + 6 = 16).

**Important Assessment Look Fors:**

Student creates a representation that models the problem and supports their understanding.

Student interprets the context described in the problem and is able to solve for different unknowns (i.e., problem types).

Student chooses an efficient strategy that makes sense to them and can be used to solve the problem.

Student records the problem and their answer(s) using pictures, words, and/or symbols.

Student estimates to check the reasonableness of each solution.

**Purposeful Questions: **

Describe your problem solving process. Tell me what you know and what you did.

Is there another way you can represent/model your thinking?

What strategies are most efficient for this problem and how do you know?

Is your answer reasonable? How do you know?

**Student Strengths**

**Student Strengths**

Students can model and solve single-step story and picture problems with sums to 10 and differences within 10, using concrete objects.

Students use related combinations to combine parts contained in larger numbers (i.e., using doubles, making tens, etc.).

**Bridging Concepts**

**Bridging Concepts**

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

**Standard 2.6c**

**Standard 2.6c**

Students can create and solve single-step and two-step practical problems involving addition and subtraction.

**Full Module with Instructional Tips & Resources: **

**Full Module with Instructional Tips & Resources:**

Bridging for Math Strength Standard 2.6c↗

**(START HERE)**

**Formative Assessments: **** **

**Formative Assessments:**

**Routines:**

**Routines:**

**Rich Tasks: **** **

**Rich Tasks:**

**Games:**

**Games:**

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## Standard 2.7A

**S****tandard**** ****2.7a **Count and compare a collection of pennies, nickels, dimes, and quarters whose total value is $2.00 or less.

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## Understanding the Learning Trajectory

**Big Ideas:**

Coins have unique values and physical attributes. The size of a coin does not indicate its value. The value of some coins and bills can be represented as a combination of other coins.

Skip counting can be used to determine the value of a set of like coins and can serve to build the foundation for multiplication.

The ability to switch between different types of skip counting (i.e., 1, 5, 10, and 25) allows students to see patterns in numbers.

**Important Assessment Look Fors:**

Student identifies and describes attributes of a penny, nickel, dime and quarter.

Student identifies the number of pennies equivalent to a nickel, dime and quarter.

Student determines the value of a collection of coins using the skill of skip counting.

Student determines the value of a collection of coins by counting the highest valued coin first, adding the values of the individual coins, or other efficient strategies (i.e., combining two or more coins by utilizing benchmark numbers).

Student compares the values of two sets of coins and a dollar bill using the terms greater than, less than or equal to.

**Purposeful Questions: **

Can you tell me what coins you have?

What’s the value of each coin? Of this collection of coins?

Are there any coins that you can use to make 25? Are there other ways to make that same amount?

What would be an effective way to count a combination of coins?

Can you use skip counting to help you could these coins?

Which combination of coins has the greatest value/least value?

**Student Strengths**

**Student Strengths**

Students can recognize the attributes of a penny, nickel, dime, and quarter.

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

**Bridging Concepts**

**Bridging Concepts**

Students can determine the value of a collection of like coins (pennies, nickels, or dimes) whose total value is 100 cents or less.

Students can compare number up to three digits.

**Standard 2.7a**

Students can count and compare a collection of pennies, nickels, dimes, and quarters whose total value is $2.00 or less.**Standard 2.7a**

**Full Module with Instructional Tips & Resources: **

**Full Module with Instructional Tips & Resources:**

Bridging for Math Strength Standard 2.7a↗

**(START HERE)**

**Formative Assessments: **

**Formative Assessments:**

**Routines:**

**Routines:**

**Rich Tasks: **** **

**Rich Tasks:**

**Games/Tech:**

**Games/Tech:**

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## Standard 2.7B

**S****tandard**** ****2.7B **Use the cent symbol, dollar symbol, and decimal point to write a value of money.

**(Pull down for more)**

## Understanding the Learning Trajectory

**Big Ideas:**

The value of some coins and bills can be represented as a combination of other coins.

Combinations of coins and bills can be represented in different ways without changing the value.

The cent symbol, dollar symbol, and decimal point are used to write a value of money.

**Important Assessment Look Fors:**

Student can use two or more sets of coins to make the same value.

Student uses the cent symbol to write the value of a combination of coins.

Student uses the cent, dollar symbol and decimal point to write the value of a combination of coins and one dollar bill.

**Purposeful Questions: **

How many ways could you receive change at the store if change is given in pennies or other coins.

How many ways could you show this same amount with like coins?

Can you write the value of this money combination using the cent and dollar symbol?

**Student Strengths**

**Student Strengths**

Students can determine the value of a collection of like coins (pennies, nickels, or dimes) whose total value is 100 cents or less.