Elementary FALs

Elementary Formative Assessment Lessons

Created by Kentucky Department of Education Mathematics Specialists and field tested by Kentucky teachers participating in the Mathematics Leadership Network.
These versions have been through at least one revision.

>> Formative Assessment Lesson Outline slide <<

Elementary Formative Assessment Lessons
KDE website: https://education.ky.gov/curriculum/conpro/Math/Pages/ElemFormAssessLessons.aspx
Inside Mathematics websites: https://www.insidemathematics.org/classroom-videos/formative-re-engaging-lessons
www.insidemathematics.org/classroom-videos/public-lessons

Concept Development Lessons
Kindergarten
Counting Dots - Counting and Cardinality
Decomposing Numbers - Operations & Algebraic Thinking
Operations and Algebraic Thinking - Greater Than, Less Than, Equal To in Range up to 10
Kindergarten measurement draft FAL

Grade 1
Number Relationships - Equal or Not - Operations & Algebraic Thinking
Pieces of Hundred Chart - Number & Operations in Base Ten
Operations and Algebraic Thinking - Greater Than, Less Than, Equal To in Range up to 10
1st grade measurement draft FAL
From Inside Mathematics Base 10 Menu Lesson
From Inside Mathematics Measurement Lesson

Grade 2
Place Value What's the Value of Place? - Number & Operations in Base Ten
Two-Digit Computation Mental Math - Number & Operations in Base Ten
Geometry - Partitioning the Whole into Equal Shares
2nd grade measurement draft FAL

Grade 3
Multiplication - Operations & Algebraic Thinking Version 1
Multiplication - Operations & Algebraic Thinking Version 2
Fractions on a Number Line - Number & Operations - Fractions
Attributes of Shapes - Geometry
Multiplication/Geometry - Distributive Property
From Inside Mathematics Interpreting Multiplication and Division Lesson

Grade 4
Relating Fraction Equivalencies to Decimal Fractions - Number & Operations - Fractions
Multi-Digit Multiplication Strategies - Number & Operations Base Ten
Factors and Multiples Number Puzzles - Operations & Algebraic Thinking
Geometry - Two-Dimensional Shapes, Angles and Symmetry
From Inside Mathematics Understanding Fractions Lesson

Grade 5
Multiplication and Division with Decimals - Number & Operations in Base Ten
Division and Interpreting Remainders - Number & Operations in Base Ten
Pizza with Friends - Number & Operations in Base Ten
Measurement - Metric Comparisons and Conversions
Measurement and Data: Volume
From Inside Mathematics Interpreting Fractions Lesson
From Inside Mathematics Decimal Place Value Lesson
From Inside Mathematics Fraction Multiplication Lesson
From Inside Mathematics Add & Subtract Fractions on a Line Plot Lesson

Problem Solving Lessons
Grades K-3Caterpillars and Leaves – Number & Operations in Base Ten

Grades 1-4
Snail in the Well – Operations & Algebraic ThinkingGrades 4-6
Where are the Cookies? - Number & Operations – Fractions

Grades 4-8
Beads under the Blanket – Patterns from Operations & Algebraic Thinking to Functions

Descriptions of Formative Assessment Lesson below:

Kindergarten: Counting Dots – Counting & Cardinality

This lesson unit is intended to help you assess how well students are able to count objects up to 10 no matter how they are arranged and also how well they are able to represent their counts with written numerals. It will help you to identify students who have the following difficulties: Not being able to track where they start/stop counting, Arranging objects to be counted, One-to-one correspondence.This lesson involves mathematical content in the standards from across the grade, with emphasis on: Counting and Cardinality K.CC Know number names and the count sequence. Count to tell the number of objects. This lesson involves a range of Standards for Mathematical Practice, with emphasis on:
2. Reason abstractly and quantitatively. 7. Look at and make use of structure.

Kindergarten: Decomposing Numbers – Operations & Algebraic Thinking

This lesson is intended to help you assess how well students are able to decompose numbers less than or equal to 10 into pairs in more than one way. It will help you to identify students who have difficulty anchoring to 5 and 10, identifing different representations of a number sentence, one- to-one correspondence, structuring numbers, and/or addition. This lesson involves mathematical content in the standards from across the grade, with emphasis on Operations and Algebraic Thinking K.OA: Understanding addition as putting together and adding to, and understanding subtraction as taking apart and taking from. This lesson involves a range of Standards for Mathematical Practice, with emphasis on: 2. Reason abstractly and quantitatively. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

1st grade: Pieces of Hundred Chart – Number & Operations in Base Ten

This lesson unit is intended to help you assess how well students are able to count to count from any number and recognize patterns on the 100 chart that will help them to count on or back. It will also help you to assess how well they write numbers between 1 and 100. It will help you to identify students who have the following difficulties: Recognizing patterns on the hundred chart. Counting on or back from a given number This lesson involves mathematical content in the standards from across the grade, with emphasis on: Number and Operations in Base Ten 1.NBT Extend the counting sequence. Understand place value. This lesson involves a range of Standards for Mathematical Practice, with emphasis on: 2. Reason abstractly and quantitatively. 7. Look at and make use of structure.

1st grade: Number Relationships – Equal or Not - Operations & Algebraic Thinking

This lesson is intended to help you assess how well students are able to use various strategies to add and subtract within 20 using various strategies. It will help you to identify students who have difficulty recognizing equivalent equations and expressions, and or using strategies to determine related equations and expressions. This lesson involves mathematical content in the standards from across the grade, with emphasis on: Operations and Algebraic Thinking 1.OA: Understand and apply properties of operations and the relationship between addition and subtraction, add and subtract within 20, and work with addition and subtraction equations. This lesson involves a range of Standards for Mathematical Practice, with emphasis on: 2. Reason abstractly and quantitatively. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

2nd grade: Place Value What's the Value of Place? – Number & Operations in Base Ten

This lesson unit is intended to help you assess how well students are able to recognize the value of the place in a number. It will help you to identify students who have the following difficulties: Recognizing place value of ones, tens, hundreds. Use correct mathematical vocabulary to explain place value to a partner. Make connections of place value to previously taught lessons. This lesson involves mathematical content in the standards from across the grades, with emphasis on: Number and Operations in Base Ten 2.NBT Understand Place Value. This lesson involves a range of Standards for Mathematical Practices, with emphasis on: 2. Reason abstractly and quantitatively. 7. Look for and make use of structure.

2nd grade: Two-digit Computation Mental Math – Number & Operations in Base Ten

This lesson is intended to help you assess how well students are able to fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or relationships between adding and subtracting. It will help you to identify students who have difficulty recognizing place value of ones, tens, and hundreds, understanding the commutative and associative properties as they relate to the numbers used in addition and subtraction equations, and applying efficient strategies (especially strategies based on place-value, properties of operations, and the relationship between addition and subtraction) to add and subtract fluently. This lesson involves mathematical content in the standards from across the grades, with emphasis on: Number and Operations in Base Ten 2.NBT: Use place value understanding and properties of operations to add and subtract. This lesson involves a range of Standards for Mathematical Practice, with emphasis on: 2. Reason abstractly and quantitatively. 7. Look for and make use of structure.

3rd grade: Multiplication – Operations & Algebraic Thinking

This lesson is intended to evaluate the understanding of your students in multiplication and how well students are able to interpret various representations of multiplication facts. It will help you to identify students who have a lack of conceptual understanding of the properties of numbers, do not see connections from addition to multiplication, or have multiplication facts memorized, but lack conceptual understanding. This lesson involves mathematical content in the standards from across the grades, with emphasis on: Operations and Algebraic Thinking 3.OA: Represent and solve problems involving multiplication and division, multiply and divide within 100. This lesson involves a range of Standards for Mathematical Practices, with emphasis on: 1. Make sense of problems and persevere in solving them. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

3rd grade: Fractions on a Number Line – Number & Operations – Fractions

This lesson is intended to help you assess how well students are able to understand a fraction as the quantity formed by 1 part when a whole is partitioned into equal parts, represent a fraction on a number line diagram, understand two fractions are equivalent (equal) if they are the same point on a number line, and solve fraction word problems using the number line to represent solutions. This lesson asks students to select and apply Standards for Mathematical Content from across the grades, with the emphasis on: Number and Operations – Fractions 3.NF (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)Developing understanding of fractions as numbers. 3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts: understand a fraction a/b as the quantity formed by a parts of 1/b. 3.NF.2a.b. Understand a fraction as a number on the number line; represent fractions on a number line diagram. 3. NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

3rd grade: Attributes of Shapes – Geometry

This lesson unit is intended to help you assess how well students are able to: Identify defining attributes of shapes, Think abstractly and concretely, Defend mathematical decisions. In this unit, students use the attributes of shapes to view shapes as members of both specific sub-categories and larger, more general, categories. This lesson involves a range of mathematical practices from the standards, with emphasis on: Reason abstractly and quantitatively, Construct viable arguments and critique the reasoning of others, Attend to precision, Look for and make use of structure. This lesson asks students to apply mathematical content from: 3.G – Reason with shapes and their attributes

4th grade: Multi-Digit Multiplication Strategies – Number & Operations Base Ten

with REVISED card sort pages This concept-based lesson is intended to help you assess how well students are able to use a variety of strategies to multiply. In particular, this unit aims to identify and help students who have difficulties with the traditional multiplication algorithm and representing multiplication in multiple ways. Common Core State Standards: This lesson involves a range of mathematical practices from the standards, with emphasis on: 2. Reason abstractly and quantitatively, 7. Look for and make use of structure, 8. Look for and make use of repeated reasoning. This lesson asks students to select and apply mathematical content from across the grades, including the content standards: Number and Operations in Base Ten: 4-NBT: Use place value understanding and properties of operations to perform multi-digit arithmetic and 5-NBT: Perform operations with multi-digit whole numbers. CLICK HERE FOR REVISED CARD SORT.

4th grade: Factors and Multiples Number Puzzles – Operations & Algebraic Thinking

This lesson is intended to help you assess how well students are able to use "clues" about numbers including: factors, multiples, prime, composite, square, even, odd, etc. In particular, this unit aims to identify and help students who have difficulties with: understanding the difference between primes and composites. understanding the difference between factors and multiples. This lesson involves mathematical content in the standards from across the grade, with emphasis on: Operations and Algebraic Thinking 4.OA Gain familiarity with factors and multiples This lesson involves a range of mathematical practices from the standards, with emphasis on: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 6. Attend to precision. 7. Look for and make use of structure.

4th grade: Relating Fraction Equivalencies to Decimal Fractions – Number & Operations – Fractions

This lesson unit is intended to help you assess how well students are able identify equivalent decimal fractions. Students will: Recognize and generate equivalent fractions. Use Equivalent fractions to add and subtract fractions with like denominators. Use decimal notation for fractions with denominators 10 and 100. Use words to indicate the value of the decimal. Use decimal fractions and locating them on the number line. Use area models to represent equivalent fractions and decimals. This lesson involves mathematical content in the standards from across the grade, with emphasis on: 4.NF Extend understanding of fraction equivalence and ordering. (Note: Ordering of fractions is not addressed in this lesson.)Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Understand decimal notation for fractions, and compare decimal fractions. This lesson involves a range of Standards for Mathematical Practice with emphasis on: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Look for and make use of structure.

Grade 5: Volume

This lesson is intended to help you assess how well students are able to model three dimensional figures and find their volume. In particular, this unit aims to identify and help students who have difficulties with: Recognizing volume as an attribute of three-dimensional space. Measuring volume by finding the total number of same-size units of volume required to fill the space without gaps or overlaps. Measuring necessary attributes of shapes, in particular the base area, in order to determine volumes to solve real world and mathematical problems. This lesson involves mathematical content in the standards from across the grade, with emphasis on: Measurement and Data 5.MD Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. This lesson involves a range of Standards for Mathematical Practice with emphasis on: Make sense of problems and persevere in solving them. Model with mathematics. Look for and make use of structure.

5th grade: Division and Interpreting Remainders – Number & Operations in Base Ten

This concept-based lesson is intended to help you assess how well students are able to use a variety of strategies to multiply. In particular, this unit aims to identify and help students who have difficulties with the traditional division algorithm,representing division in multiple ways, and interpreting remainders. This lesson involves a range of mathematical practices from the standards, with emphasis on: Reason abstractly and quantitatively, Look for and make use of structure, Look for and make use of repeated reasoning. This lesson asks students to select and apply mathematical content from across the grades, including the CCSS Number and Operations in Base Ten: 5-NBT: Perform operations with multi-digit whole numbers and 6-NS: Compute fluently with multi-digit numbers and find common factors and multiples.

5th grade: Pizza with Friends – Number & Operations in Base Ten

This lesson unit is intended to help you assess how well students are able to model addition and subtraction of fractions. In particular, this unit aims to identify and help students who have difficulties with: Using equivalent fractions to add and subtract fractions, Using benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers, and Solving word problems involving the addition and subtraction of fractions.
This lesson asks students to select and apply mathematical content from across the grades, including the CCSS Number and Operations 5.NF Use equivalent fractions as a strategy to add and subtract fractions.
This lesson involves a range of Standards for Mathematical Practice, with emphasis on: 1. Make sense of problems and persevere in solving them. 3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics. 7. Look for and make use of structure

5th grade: Multiplication and Division with Decimals – Number & Operations in Base Ten

Grades 1-4: Snail in the Well – Operations & Algebraic Thinking

This problem solving lesson is intended to help you assess how well students are able to use addition and subtraction in a problem-solving situation. In particular, this lesson aims to identify and help students who have difficulties with:

Choosing an appropriate, systematic way to collect and organize data;
Examining the data and looking for patterns;
Describing and explaining findings clearly and effectively.

Grades K-3: Caterpillars and Leaves – Number & Operations in Base Ten

This problem solving lesson is intended to help you assess how well students are able to use addition and subtraction in a problem solving situation. In particular, this lesson aims to identify and help students who have difficulties with:
·         Choosing an appropriate, systematic way to collect and organize data.
·         Examining the data and looking for patterns
·         Describing and explaining findings clearly and effectively.

Grades 4-6: Where are the Cookies? – Number & Operations – Fractions

This problem solving lesson is intended to help you assess how well students are able to use fractions in a problem solving context. In particular this lesson aims to identify and help students with difficulties:

Conceptualizing fractional parts or different wholes;
Choosing an appropriate, systematic way to organize multiple steps;
Conceptualizing fractional comparisons and fractional parts of other fractions.

Grades 4-8: Beads under the Blanket – Patterns from Operations & Algebraic Thinking to Functions

This lesson is designed to help you assess how well students are able to identify patterns (both linear and exponential) in a realistic context. In particular this lesson aims to identify and help students that have difficulty:

Choosing an appropriate, systematic way to collect and organize data;
Examining the data and looking for patterns;
Describing and explaining findings clearly and effectively