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Formative Assessment and Bridging activities

Grade 2


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Standard 2.1A

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

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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.

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?

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Student Strengths

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

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 2.1B

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

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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.

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Student Strengths

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

Bridging Concepts

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

Standard 2.1A

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

Standard 2.1C

Standard 2.1c Compare and order whole numbers between 0 and 999.

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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?

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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.

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.

Standard 2.1C

Students can compare and order whole numbers between 0 and 999.
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Full Module with Instructional Tips & Resources: Bridging for Math Strength Standard 2.1C


Formative Assessments:

Routines:

Rich Tasks:

Games:


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Standard 2.2A

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

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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?

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Student Strengths

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

Bridging Concepts

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

Standard 2.2A

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

Standard 2.2B

Standard 2.2B Count backward by tens from 120.

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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?

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Student Strengths

Students can count forward by tens to 120.

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 2.4a

Standard 2.4a Name and write fractions represented by a set, region, or length model for halves, fourths, eighths, thirds, and sixths

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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)

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Student Strengths

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

Bridging Concepts

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


Standard 2.4a

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


Standard 2.4b

Standard 2.4b Represent fractional parts with models and with symbols.

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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?

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Student Strengths

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

Bridging Concepts

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

Standard 2.6c

Students can represent fractional parts with models and with symbols.

Standard 2.4c

Standard 2.4c Compare the unit fractions for halves, fourths, eighths, thirds, and sixths, with models

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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?

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Student Strengths

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

Bridging Concepts

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

Standard 2.4c

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


Standard 2.5A

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

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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?

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Student Strengths

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

Bridging Concepts

Students can use related facts to help solve practical problems.

Standard 2.5a

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

Standard 2.5B

Standard 2.5B Demonstrate fluency with addition and subtraction within 20.

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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?

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Student Strengths

Students can recognize and describe part whole relationships within 10.

Bridging Concepts

Students can demonstrate fluency with addition and subtraction within 10.

Standard 2.5b

Students can demonstrate fluency with addition and subtraction within 20.


Full Module with Instructional Tips & Resources:

  • Bridging for Math Strength Standard 2.


Formative Assessments:


Routines:


Rich Tasks:


Games:


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Standard 2.6A

Standard 2.6a Estimate sums and differences.

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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?

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Student Strengths

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

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

Students can estimate sums and differences.


Standard 2.6B

Standard 2.6b Determine sums and differences, using various methods.

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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?

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Student Strengths

Students can recognize and describe part whole relationships within 10.

Bridging Concepts

Students can demonstrate fluency with addition and subtraction within 20.

Standard 2.

Students can determine sums and differences, using various methods.

Standard 2.6c

Standard 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?

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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

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


Standard 2.6c

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


Standard 2.7A

Standard 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?

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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

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 2.7B

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

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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?

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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.

Bridging Concepts

Students recognize the symbols associated with recording values of money.

Standard 2.7b

Students can use the cent symbol, dollar symbol, and decimal point to write a value of money.


Standard 2.8A

Standard 2.8A Estimate and measure length to the nearest inch.

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Understanding the Learning Trajectory

Big Ideas:

  • Measurement is a process of comparing a unit to the object being measured.

  • Objects can be described, compared and ordered by length.

  • Same size units must be used when measuring with nonstandard units (i.e., same size paperclips, etc.).

  • There are standard measurement tools for measuring length.


Important Assessment Look Fors:

  • Student describes, compares, and orders objects by length.

  • Student demonstrates the appropriate use of nonstandard measurement tools (i.e., same size paperclips).

  • Student identifies and chooses the appropriate measuring tool when measuring length.


Purposeful Questions:

  • How would you describe and compare the lengths of these two objects? (longer or shorter)

  • What nonstandard measuring tool could be used to measure the length of this object?

  • Which measuring tool would be the most effective to measure the length of this object?

  • Is the measurement closer to __ inches or __ inches?

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Student Strengths

Students can compare the lengths of two objects, using direct comparisons (longer, shorter).

Bridging Concepts

Students can measure and compare length using nonstandard units.


Students choose an appropriate measuring tool (ruler, tape measure) to measure length.

Standard 2.8a

Students can estimate and measure length to the nearest inch.

Standard 2.8B

Standard 2.8B Estimate and measure weight to the nearest pound.

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Understanding the Learning Trajectory

Big Ideas:

  • Measurement is a process of comparing a unit to the object being measured.

  • Objects can be described, compared and ordered by weight.

  • Same size units must be used when measuring with nonstandard units (Example: same blocks, cubes, etc.).

  • There are standard measurement tools for measuring weight.


Important Assessment Look Fors:

  • Student describes, compares, and orders objects by weight.

  • Student demonstrates the appropriate use of nonstandard measurement tools (i.e., same blocks, cubes, etc.).

  • Student identifies and chooses the appropriate measuring tool when measuring weight.


Purposeful Questions:

  • How would you describe and compare the weights of these two objects? (lighter or heavier)

  • What nonstandard measuring tool could you use to measure the weight of this object?

  • Which measuring tool would be the most effective to measure the weight of this object?

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Student Strengths

Students can compare the weights of two objects, using direct comparisons (heavier, lighter).

Bridging Concepts

Students can use nonstandard units to measure and compare weight.

Standard 2.8b

Students can estimate and measure weight to the nearest pound.


Standard 2.9

Standard 2.9 Tell time and write time to the nearest five minutes, using analog and digital clocks.

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Understanding the Learning Trajectory

Big Ideas:

  • Telling time is the ability to read instruments (analog and digital clocks). (Van de Walle, 2019, p 493.)

  • Clocks are instruments used to measure time.

  • Units of hours and minutes are used for telling time.

  • Skip counting by fives and tens supports the skill of reading analog clocks.


Important Assessment Look Fors:

  • Student compares and describes the amount of time spent on two events (as longer or shorter), using direct comparison.

  • Student identifies different types of clocks (analog and digital).

  • Student skip counts by fives.

  • Student tells and matches time to the hour, half hour and nearest 5 minutes on an analog and digital clock (and vice versa).

  • Student demonstrates an understanding of hours and minutes when writing time to the hour, half hour and nearest five minutes.


Purposeful Questions:

  • What would take longer, riding in your car or riding your bike to school?

  • Why are clocks needed?

  • How are digital and analog clocks the same? different?

  • What time does this clock represent?

  • Can you show the time _____ on this clock?

  • Can you write the time represented on this clock?

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Student Strengths

Students can compare the duration of two events, using direct comparisons (longer, shorter).


Students can skip count by fives.

Bridging Concepts

Students can tell time to the hour and half-hour, using analog and digital clocks.


Students can distinguish between the hour hand and the minute hand.

Standard 2.9

Students can tell time and write time to the nearest five minutes, using analog and digital clocks.


Standard 2.15B

Standard 2.15B Read and interpret data represented in pictographs and bar graphs.

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Understanding the Learning Trajectory

Big Ideas:

  • Some questions can be answered by collecting and analyzing data.

  • Categorical data are displayed in pictographs and bar graphs (Common Core Progressions, p. 2)

  • Pictographs and bar graphs are labeled with accurate titles, key or scale, and appropriate categories (Common Core Progressions, p. 7).

  • Data can be represented visually using objects, tables, charts, and graphs. The type of data to be collected often determines the best choice of visual representation.

  • Data can be read and interpreted using categorically (number of categories)and numerically (more, fewer, less than, etc…) relationships.


Important Assessment Look Fors:

  • Student reads a table and picture graph correctly.

  • Student identifies and makes comparisons based on data in a table or graph.

  • Student interprets data that represents categorical and numerical relationships.

  • Student uses the data represented on a table or graph to make predictions and generalizations.


Purposeful Questions:

  • What information does the table or graph represent (show)?

  • What do you notice or wonder about the data?

  • Looking at the (pictograph or bar graph), which category has the least amount? The largest amount?

  • Looking at the (pictograph or bar graph), are there any options with the “zero” as the amount? If so, what does that mean?

  • What is the key of the pictograph? What is the scale of the bar graph? Explain how you know.

Bridging for Math Strength Logo

Student Strengths

Students can read and interpret data in object graphs, picture graphs, and tables.


Students can count and compare numbers to 25 or more.

Bridging Concepts

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


Students can use the key to determine total numbers for data representations.

Standard 2.15b

Students can read and interpret data represented in pictographs and bar graphs.

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