# Planning differentiated lessons in math for grades 1-4

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Planning differentiated lessons in math for grades 1-4
By: Aimee Tyszka & Jessica Rinaldi

Planning a Focused Curriculum Means Clarity About What Students Should …
KNOW Facts Vocabulary Definitions UNDERSTAND Principles/ generalizations Big ideas of the discipline BE ABLE TO DO Processes Skills

Know These are the facts, vocabulary, dates, places, names, and examples you want students to give you. The know is massively forgettable. “Teaching facts in isolation is like trying to pump water uphill.” Carol Ann Tomlinson

Facts, names, dates, places, information
KNOW Facts, names, dates, places, information There are 50 states in the US Napoleon Bonaparte 1066 The Continental Divide The multiplication tables

Major Concepts and Subconcepts
Understand Major Concepts and Subconcepts These are the written statements of truth, the core to the meaning(s) of the lesson(s) or unit. These are what connect the parts of a subject to the student’s life and to other subjects. It is through the understanding component of instruction that we teach our students to truly grasp the “point” of the lesson or the experience. Understandings are purposeful. They focus on the key ideas that require students to understand information and make connections while evaluating the relationships that exist within the understandings.

UNDERSTAND Essential truths that give meaning to the topic
Stated as a full sentence Begin with, “I want students to understand THAT…” (not HOW… or WHY… or WHAT) Multiplication is another way to do addition. People migrate to meet basic needs. All cultures contain the same elements. Entropy and enthalpy are competing forces in the natural world. Voice reflects the author.

BE ABLE TO DO Skills (basic skills, skills of the discipline, skills of independence, social skills, skills of production) Verbs or phrases (not the whole activity) Analyze Solve a problem to find perimeter Write a well supported argument Evaluate work according to specific criteria Contribute to the success of a group or team Use graphics to represent data appropriately

KUD’s Count to one hundred in units of ten.
Multiplication is another way to do addition. Find the missing addend using counters. Subtraction and addition have an inverse relationship. The multiplication tables 0-12. Clue words for addition are sum, and, altogether, in all, combine, join, plus, and total. The value of a digit depends on its place in the number. Write the value of the underlined digit in each number.

In Other Words: KUDs Matter Because
They create clear learning goals Allow us to align goals, assessments, teaching, and learning tasks They allow us to incorporate standards AND make meaning for students They give us a basis for differentiation. Who needs which K’s & D’s How do we ensure that every student gets meaningful access to the U’s They tell us what strugglers should invest in They give us a platform for extending for advanced students

Instructional Strategies that Support Differentiated Instruction
Learning Centers – pgs Cubing – pgs RAFT – pgs Graphic Organizers – pgs Think DOTS – pgs Learning Contracts – pgs Web Quests – pgs *See Marcia Imbeau’s PowerPoint for further explanation of each strategy.

Lesson Title: Think Dots Curriculum Area (s): Math Grade Level: 1

Using counters, show the many ways to make the number 10.

Roll the dice to make addition sentences.

Lesson Title: 3- digit Place value centers Curriculum Area (s): Math
Unit Title: Addition Lesson Title: 3- digit Place value centers Curriculum Area (s): Math Author: Jessica Rinaldi Grade Level: 2 Author Contact: Time Required: minutes Instructional Groupings: groups Standards: NOA 2.1 To represent three digit numbers as groups of hundreds, tens, and ones in the base ten number system. Materials: Chairs labeled hundreds, tens, and ones, place value charts, base ten blocks Overview:   Students need to understand that every digit has a different value depending on its position in the number before they can understand quantitative relationships. What will I differentiate? Process How will I differentiate?    Using the different modalities            As a result of this lesson/unit students will… Understand: TSW understand that every digit has a value depending on its position in the number. Know: TSW know10 ones=1 ten, 10 tens=1 hundred, and 10 hundreds= How to count by 1, 10, and 100’s. A digit is the 0,1,2,3,4,5,6,7,8,and 9. Do (Skills): TSW model and write the value of the digit in the ones, tens, and hundreds place. Pre-Assessment: Given a couple days before to see what students prior knowledge of the material is. TSW be assessed on ability to count by 10’s and 100’s. They will also be asked to label the values of each place. TSW also be assessed on ability to identify the value of each digits. Steps in the Lesson: Day 1: Whole group: present the knows- identify the digits, the value of each position in the number (represent on chart and using labeled chairs), and counting by 1’s to 10, by 10’s to 100, and 100’s to Explain that only one digit can sit in each chair/place. With Smart Board display 3 digit numbers using the base ten blocks. (Demonstrate how to model numbers each way so tomorrow students already know what to do in their centers.) Guided practice: Students draw base ten blocks to model 3-digit numbers, while others model using the base ten blocks, and another 3 students show the number by sitting in the correct chair. Day 2: At work station- Students will apply skills learned yesterday about identifying the value of the given digit. Closure Activity/Wrap up: Groups share how they model 3-digit numbers. Post-Assessment: Exit ticket: students will identify value of the underlined digit in 3- digit numbers.

Place value work stations
Group 1 (Kinesthetic) 1. Pick an index card up with a digit written on it. 2. Pick a chair to sit in. 3. What number did you and your friends make? 4. What is the value of your digit? 5. Write answer on the data sheet. Group 2 (Visual) Roll the dice 3 times Write down each digit to create a 3 digit number. Draw base ten blocks to show your number. What is the value of each digit? Write answer on data sheet. Group 3 (Tactile) Pick 3 cards from the deck. Make a 3-digit number. 3. Build the number using the base ten blocks. 4. Write the value of each digit on your data sheet.

What is the value of your digit?
Name: _______________________________ Date: __________________ Place Value Hundreds Tens Ones What is your digit? What is the value of your digit? Ex 2 9 20

Unit Title: Multiplication (1 digit)
Lesson Title: Think Dots Curriculum Area (s): Math Author: Aimee Tyszka Grade Level: 3/4 Author Contact: Time Required: 3-4 weeks/entire unit Instructional Groupings: homogeneous Standards:  Understand and apply basic concepts of multiplication. Materials: Think Dot sheets (3 levels), dice, paper (lined and colored), pencils, I-Pad, worksheet copies Overview:   This lesson will provide practice of a concept previously taught. Students will formulate responses to a variety of multiplication scenarios, touching on Bloom's taxonomy. What will I differentiate? Content         Product How will I differentiate?    For readiness            As a result of this lesson/unit students will… Understand: TSW understand that multiplication is repeated addition Know: TSW know multiplication facts for 0-9 tables. Do (Skills): TSW show, solve, and describe the multiplication process Pre-Assessment: Pre-assessment will take place during observation of whole group work, small group meetings, completed classwork, and mad minutes, etc… Steps in the Lesson: 1. Whole class- oral/visual review of facts 2. Whole class- mad minute 3. Small group- meetings to reinforce, guide, and make corrections 4. Individual/partners- Think Dot activities Closure Activity/Wrap up: Closure will occur at the end of each day. Students will chart progress and notify teacher of which Think Dot activities were completed. Post-Assessment: Students may be grouped to new levels after teacher/students consult daily classwork, observations during group meetings, and outcome of Think Dot assignments. Students will have weekly opportunities to share finished products from Think Dot activities. Additional Resources: Splash Math- on I-pads

Multiplication (0-2 times tables)

How Low Can You Go? Directions:
Materials: 1 pair of blank dice (one die labeled 1-6, one die labeled with 3 zeros and 3 ones) Directions: Students will take turns rolling the dice, multiply the numbers that come up, and write the product. Each player gets 5 rolls. Players record the product for each roll and then find the sum of their products. The player with the lowest totals wins.

Multiplication (3-5 times tables)

Multiplication (6-9 times tables)

Multiplication Brain Game
Materials: 1 deck of cards (remove jokers, kings, queens, jacks, and tens) At least 3 players Directions: Students will shuffle the deck of cards and place it facedown between two players. Each player draws a card without looking and places it on her/his ‘brain’ or forehead with the card facing the third player. The third player will say the product of the two cards. The other two players will turn and face each other to see the other’s card. Each player now knows the product and the other factor. The first player to call out his own factor (the missing factor) wins. Players will rotate to each have turns naming the products and guessing the missing factors.

Unit Title: Basic Fraction Concepts
Lesson Title: Naming and making equivalent fractions Curriculum Area (s): Math Author: Aimee Tyszka Grade Level: 3/4 Author Contact: Time Required: 1-2 weeks Instructional Groupings: homogeneous/small group/partners Standards:  Extend understanding of fraction equivalence and ordering Materials: Cubes (3 levels), dice, paper (lined and colored), pencils, worksheet copies Overview:   This lesson will provide practice of a concept previously taught. Students will formulate responses to a variety of scenarios involving fractions. What will I differentiate? Content         Product How will I differentiate?    For readiness            As a result of this lesson/unit students will… Understand: TSW understand that fractions are smaller parts of a whole. Know: TSW know how to read/say a fraction. TSW know terms such as numerator/denominator. Do (Skills): TSW show, solve, and describe how fractional amounts are related and compare fractions. Pre-Assessment: Pre-assessment will take place during observation of whole group work, small group meetings, completed classwork, etc… Steps in the Lesson: Whole class- oral/visual/written lesson 2. Small group- meetings to reinforce, guide, and make corrections 3. Individual/partners- Cubing activities Closure Activity/Wrap up: Closure will occur at the end of each day. Students will chart progress and notify teacher of which Cubing activities were completed. Post-Assessment: Students’ work will be evaluated and shared with the class. These activities are meant to be anchor activities, or used to reinforce what is being addressed in whole and small group learning experiences. Additional Resources:

THINKING CUBE Grade 4 Fractions (below) Play the Toss and Talk game.
Get a gameboad and number cubes from the red folder/basket. Use fraction strips to show 1/3 and 2/6 of one whole strip. Are 1/3 and 2/6 the same, or equal parts of the strip? Use 2 more fraction strips to show 2 other fractions that are equal. Label your strips with the fraction you made. Tom and some of his friends are having a party. Tom’s mother orders a pizza which is cut into 4 pieces. Each boy ate ¼ of the pizza, and the entire pizza was eaten. Explain how to figure out how many boys were at the party. Explain your answer and draw a picture of how the pizza was sliced. Which fraction is greater, 1/3 or 1/6? Use words and models to explain your answer. Create an interesting and challenging word problem that uses fractions. Show the solution. You have 6 tiles. 2/6 of the tiles are rectangles. The rest of the tiles are triangles. Draw a design using the tiles. THINKING CUBE Grade 4 Fractions (below)

THINKING CUBE Grade 4 Fractions (average) Play the Toss and Talk game.
Get a gameboad and number cubes from the yellow folder/basket. Use fraction strips to show 1/2 and 5/10 of one whole strip. Are 1/2 and 5/10 the same, or equal parts of the strip? Use 2 more fraction strips to show 2 other fractions that are equal. Label your strips with the fraction you made. Tom and some of his friends are having a party. Tom’s mother orders a pizza which is cut into 8 pieces. Each boy ate 2/8 of the pizza, and the entire pizza was eaten. Explain how to figure out how many boys were at the party. Explain your answer and draw a picture of how the pizza was sliced. Which fraction is greater, 4/5 or 4/8? Use words and models to explain your answer. Create an interesting and challenging word problem that uses fractions. Show the solution. You have 10 tiles. 4/10 of the tiles are rectangles. The rest of the tiles are triangles. Draw a design using the tiles. THINKING CUBE Grade 4 Fractions (average)

THINKING CUBE Grade 4 Fractions (above average)
Play the Toss and Talk game. Get a gameboad and number cubes from the green folder/basket. Use fraction strips to show 1/6 and 2/12 of one whole strip. Are 1/6 and 2/12 the same, or equal parts of the strip? Use 2 more fraction strips to show 2 other fractions that are equal. Label your strips with the fraction you made. Tom and some of his friends are having a party. Tom’s mother orders a pizza which is cut into 16 pieces. Each boy ate 4/8 of the pizza, and the entire pizza was eaten. Explain how to figure out how many boys were at the party. Explain your answer and draw a picture of how the pizza was sliced. Which fraction is greater, 2/3 or 4/7? Use words and models to explain your answer. Create an interesting and challenging word problem that uses fractions. Show the solution. Mary has 23 mables. 7/23 of the marbles are yellow and 13/23 of the marbles are blue. The rest of the marbles are green. How many marbles are green? Explain how you know. THINKING CUBE Grade 4 Fractions (above average)

Respectful Tasks Equally interesting, appealing, engaging
Focused on the same essential understandings & skills Requires all students to work at high levels of thinking (to apply, argue, defend, synthesize, transform, look at multiple perspectives, associate with, etc.)

Respectful or Not-so Respectful?
Scenario 1 Teacher B is assigning math homework. Some of her students are still struggling to master converting fractions to decimals, some understand the process but need more practice, and some are fairly proficient. Because she knows that it will take longer for some students to complete the problems, she decides to assign 10 problems to struggling students, 20 problems to on-grade level students, and 30 problems to advanced students.

Respectful or Not-so Respectful?
Scenario 2 One of Teacher K’s students got a 100 on her pre-test, so the teacher has her design homework worksheets that practice the skills that the class learned in that unit.