Ideas for Tier 1 Mathematics Instruction Types of Mathematics Lessons Exploratory provide opportunities to introduce concepts in ways that allow the student to construct meaning and to respond to experiences through his or her level of understanding open structure with opportunities to make and test conjectures Developmental takes students from the discovery stage through the stage in which they recognize a pattern, make a generalization, or describe a rule regarding a particular concept Transitional connects knowledge at the concrete or representative level to an abstract level of understanding Secondary Review Story Headline provides the student with opportunities to revisit learning typically with the intent of anchoring knowledge The textbook is not the centerpiece of a lesson; the students and the blending of content and activities should be. The teacher s task is to masterfully orchestrate these variables, not simply guide the students through the material in the book. The latter may be less threatening and easier, but the former is teaching. -Heddens and Speer
What s in a lesson? Activator: To capture the interest and attention of your learners, you must open your lesson with a motivational activity or two. An activator can engage students cognitively, identify students current knowledge, surface misconceptions, and empower the learner. Development: Contains a series of activities that will foster student learning new content (concepts, information, and/or skills). The series of activities are presented in a logical order, where one activity flows into and builds upon another. Closing: The closing includes the concluding/summarizing activity of the lesson. It is an opportunity to check for understanding, surface confusion or misconceptions, deepen understanding, support retention, and gather formative assessment data. Ideas to Use The next few pages contain many instructional ideas that can be used during the activator, the development, and/or closing of the lesson. There are some that you can use at any time. The choice is yours! As always, please feel free to adapt any of the ideas to make them meaningful to the students in your classroom. Page 2 Ideas for Tier 1 Mathematics Instruction
Carousel Brainstorming (Activator, Development, Closing) Large sheets of newsprint paper are posted on the wall (or on desks) at various points around the room. Each sheet has a question or topic written on it. Students are divided into groups of 4-6 and assigned to a sheet of newsprint. Sample topics: equivalent fractions (each chart has a different fraction at top) equations/expressions: each chart has a number on it. Groups brainstorm and list equations/expressions that equal that number. attributes of shapes: each chart has a shape on it. Groups brainstorm and list the properties of the shape. Directions for students: 1. Each group starts with a different colored marker; groups stand in front of one of the pieces of newsprint. 2. Choose a recorder. 3. Brainstorm responses to the posted question/topic quickly. 4. After 2 minutes and at the signal, move one sheet to your right. 5. Brainstorm quickly and add to the new sheet (2 minutes). 6. At the signal, move to your right and repeat the process. 7. Continue until each group has brainstormed responses to all of the questions. 8. Optional last step: Each group ends up at the chart where it began with a few minutes to: -look the chart over and see what developed after they left it; -group the ideas into categories; eliminate repeated ideas Alternative: put each question or topic on a clipboard and have students pass the clipboards in rotation from group to group. Other Uses: Cooperative Leaning Jigsaw; Expert Jigsaw; Summarize, Review, and Reinforce Sort Cards or Pictures (Activator, Development, Closing) Students are given cards and must sort them. This can be done at students desks or you can hand each student one card and have them stand with students who share their match. This can be used to put students into cooperative groups. For example, during a unit on the study of fractions, one fraction is written on each card. The students who have the cards ½, 2/4, 3/6, 4/8, and 5/10 stand with each other, holding the fraction in front of them. They can now be a group of 5 for the development of the lesson. After teaching something that has multiple categories, provide students with index cards with individual facts/concepts/examples and have students organize them into appropriate categories which they can label and defend. Listen to the conversations among group members and to their reasoning for placing cards in specific categories. Page 3
Brainstorm and Categorize (Activator, Development, Closing) Brainstorm things that you already know and sort/categorize them. You can organize it in a data table (shown in example below) or make a web. Example: Shape isosceles triangle square rhombus trapezoid hexagon Category triangle quadrilateral quadrilateral quadrilateral polygon Writing Prompts/Quickwrites (Activator) In 8 lines or more (or whatever you choose as teacher), write the things you know, things you think you know, or questions you have about. Even though we have not read or discussed it yet, what does the term (or concept or phrase) mean to you? What do you think this (picture, formula, abbreviation, notation, chart, word, mark, symbol, phrase) means? What do you think a looks like? How do you think a is solved (or behaves or is constructed)? Line-Ups (Activator, Development, Closing) Students are given cards with information on them (values, estimation, numbers, etc.) and then must line up the cards. To get the students up and moving, give each student one card and have them arrange themselves in a line in the front of the room. You may also give students cards to line up at their desks. Example: Students are given cards with decimals on them. They must put them in order from least to greatest. This can be done at students desks or you can hand each student one card and have them line up in the front of the room. Page 4 Ideas for Tier 1 Mathematics Instruction
Wordsplash (Closing) A wordsplash is a collection of key terms or concepts selected from a reading, a chapter in a textbook, etc., which students are about to read. Most terms selected for a wordsplash are vocabulary familiar to students. The selected terms are displayed randomly and at angles on a visual (projector or chart). Students are asked to brainstorm and generate complete statements which predict the relationship between each term and the broader topic. Example: Polygons is the topic. The following words are splashed around the word: quadrilateral, parallelogram, triangle, regular polygons, square, rectangle, isosceles triangle, equilateral triangle, trapezoid, rhombus, etc. An example of a statement would be, A square is a rectangle, but a rectangle is not a square. Exclusion Brainstorming (Development, Closing) Present students with multiple concepts/examples and ask them to identify the concept/ example that does not belong with the others. Then explain (orally or in writing) the reasoning. Cooperative Group Roles (Development) When placing students in cooperative groups, it may be helpful to assign specific roles to help keep students on task. The following are some ideas for roles: Leader: makes sure that every voice is heard; focuses work around the learning task Recorder: Compiles group members ideas on collaborative graphic organizer; writes on the board for the whole class to see during the presentation Time Keeper: Encourages the group to stay on task; announces when time is halfway through and when time is nearly up Presenter: Presents the group s finished work to the class Errand Monitor: Briefly leaves the group to get supplies or to request help from the teacher when group members agree that they do not have the resources to solve the problem Spy: briefly leaves the group to gather ideas from other groups; reports back to students in group (this should only be done for a few minutes at a time during group work time) Page 5
Red Green Yellow (Development) Each student has three small pieces of construction paper - red, green, and yellow - at his/her desk. While working on a given assignment, one of the 3 pieces of paper is made visible, indicating the student s level of understanding. Green : I m doing great and moving ahead with my work; I don t need any help. Red : I ve stopped working because I m stuck; I need help. Yellow: I can do some of the work, but I need help to get it all done, or I just want you to check on me to make sure I m answering the problems correctly. A/B Pyramid (Activator, Development, Closing) Students pair up and sit so Student A is facing the board, and Student B is facing the opposite side. Student A reads the word on the board and must give clues about the word to Student B without saying the word. When Student B gets the answer, the pair raises their hands. When everyone completed the activity, have the students switch chairs and begin again. Think-Pair-Share (Activator, Development, Closing) 1. Students listen while the teacher poses a question. 2. Students are given wait time so each one can think of an appropriate response. 3. Students are cued to pair with a neighbor to discuss their responses. 4. Students are then invited to share their responses with the whole group. Page 6 Ideas for Tier 1 Mathematics Instruction
Active Participation (Development) Dry Erase Boards: Students record responses and hold up boards. PRS (personal response systems): These are electronic devices that have questions programmed ahead of time. When students respond to given questions, responses are immediately tabulated and presented to teacher and students. A-B-C-D Cards: Each student has a set of 4 cards with the letters A, B, C, and D on them. Present students with multiple choice questions. Each student holds up the letter corresponding to the correct answer. Formative Assessment Quick Checks/Dipsticking (Development) Thumbs Up-Down-Sideways: Student presents thumb up if he fully understands the concept, thumb down if he s lost & confused, or thumb sideways if he sort of understands. Fist-of-Five: Student holds up a designated number of fingers to show her level of understanding 5 = fully understands and could explain it to another student; 4 = in pretty good shape to try some on my own; 3 = sort of understand it, but need more explanation; 2 = only understand a little; 1 = don t get it at all. Understanding can be assessed discretely by having students hold their hands right in front of their chests, not raising their hands; or you can have students close their eyes. Paired Verbal Fluency (Development) Students get into pairs. One student is #1 and the other student is #2. The teacher assigns a topic. When the teacher says, Go, student #1 starts telling as many ideas about the topic that he/she can. Student #2 listens, but does not say anything. After about 30 seconds, student #2 talks, but cannot repeating anything that student #1 had already said; student # 1 listens. This can be repeated for several rounds, with a shorter amount of time given for each round. Page 7
Tic-Tac-Toe for Tiering (Development) Students are given a tic-tac-toe board of tasks to complete and are asked to choose any three in a row horizontally, vertically, or diagonally. To adjust for various abilities, students can be directed to complete tasks in a certain pattern. For example, a student may be more successful if directed to complete 3 tasks that appear all in one column. Example: Summarize/ describe Compare (e.g. to one of the other 2 concepts) Apply/create a problem mean median mode 10-2 (Development) Instructor lectures or presents material for 10 minutes then stops for two minutes. During this pause student teams share their notes, fill in gaps in their own notes, and help each other clarify concepts. Unresolved questions are reserved for the last 5 minutes of the period. The time structures can be varied, depending on the class and the complexity of the material. Learning Buddies/Clock Buddies (Activator, Development, Closing) Learning Buddies: Designate groups of 3 students who will get together periodically throughout the course of instruction to summarize and review what has been taught. These are students who don t normally work with each other; they actually have to get up and move to get with the group. Clock Partners : Students are given a handout that has a clock face on it. They sign up with twelve other people for partner assignments. Once they have a buddy for each time on their clock, you are ready to go. Next time you want students to work with a partner, tell them to work with their 9 o clock buddies (or whatever number you prefer). Students have choice in terms of who they work with, but they also work with different people. Page 8 Ideas for Tier 1 Mathematics Instruction
T-List/Two Column Notes (Development) Students organize knowledge into main ideas with supporting details and/or examples. Main Ideas A. B. C. Details/Examples 1. 2. 3. 1. 2. 3. 1. 2. 3. The Frayer Model (Development, Closing) Present students with one concept written in the center of the graphic organizer and have them complete the four surrounding sections. The topic in each of the 4 surrounding sections can be modified to meet the class needs. Student Created Test Prep (Closing) Student Created Test Questions: Prior to an assessment, have students create questions that could be included on the upcoming quiz/test. Have them include an answer sheet. Cheat Notes: During the days prior to a test, students create a page of cheat notes that can be used during the test. The cheat notes are turned in with the exam. Throughout the course, the teacher works with the students to improve their study skills. As the course progresses, students are allowed to use only a half page of cheat notes, then a 4x6 index card of notes, then a 3x5 index card of notes, and eventually no cheat notes at all. The set of cheat notes and the manner in which they are organized provide the teacher with a formative assessment an indication of the students readiness for the material and, perhaps, where review might be needed. Page 9
Writing Prompts to Check Students Understanding (Closing) Please feel free to adapt/change the number of examples, etc. to fit your lesson needs. What were three of the most important points from our class discussion? In your own words, write the meaning of in a way that a classmate would understand and be able to answer correctly on a test. Explain two ways that and are similar (or different). What two strategies might you use to solve this problem? Give two reasons why this cannot be a correct answer for this problem. Explain. Tell me three things that are wrong with the statement (problem). What are three things you could change to make this open response better? All but one of the following belong to a category because they have several common characteristics. Give this category a name and give two reasons the one does not belong in the category. If you were summarizing today s discussion for a friend who was absent, what two ideas do you think might show up on our weekly test? Describe a pitfall to avoid when doing this problem. If the answer is, write two questions that would go with that answer. Writing Prompts/Quickwrites for Reflection (Closing) Please feel free to adapt/change the number of examples, etc. to fit your lesson needs. When you think about, what are some of the things you wonder about? Write down two hard questions about. What part of today s discussion about would you find difficult to explain clearly to someone else? In last night s homework, what was the hardest part for you to solve (or understand, complete, read, collect)? If you were going to solve (or do or read or study) again, what would you do differently? What went well with your group project? What would improve the group s work? As you think about what we did in class today, what was easiest (or most fun, most challenging, something you would like to do again differently)? What are other ways we can get the same solution? What tools (or formulas, instruments, reference materials) do you think were used to accomplish this? Page 10 Ideas for Tier 1 Mathematics Instruction
3-2-1 (Closing) 3-2-1: A structure for a student summary. It can be tailored to suit the activity or content which is being summarized. For example, write 3 things you found interesting, 2 things that were a bit confusing, and one thing you would like to know more about. Example: List 3 applications for knowing slope and y-intercept in the real world. Identify 2 skills you must have in order to determine the slope and y-intercept from a set of points (or from a line). If (x 1, y 1 ) are the coordinates of a point W in a plane, and (x 2, y 2 ) are coordinates of a different point Y, what is the slope of WY? Journal Prompts (Closing) To summarize a lesson, give students 5 minutes to respond in their journals to: I learned that I wonder why The part that frustrated me the most was I noticed a pattern in I was surprised that I was confused by... This is similar to A better way for me to learn this would be A problem I had and overcame was I think I need to spend more time on I d like to learn more about Before I did this, I thought A-B-C Summarize (Closing) Each student is given a letter of the alphabet and they must think of one word or idea beginning with that letter and related to the topic studied. Page 11
Relay Summary (Closing) This format is used to summarize. Students are divided into teams of 4-5 students. The first student in each team starts with a blank piece of paper and writes one summary sentence, then passes it to the next teammate. That student adds a sentence, passes it on, etc. until the whole team has added or until the number of required sentences are on paper. Ticket to Leave/Exit Card (Closing) A student may not be dismissed from class until they answer the question the teacher asks. This is a quick, two minute activity. Last One Standing (Closing) 1. Students record 3 facts (or 4, or 5, or as many as possible in a given time limit) and then stand up. 2. Each student reads her list of facts, but only the ones that have not been previously mentioned by others. 3. As classmates hear facts written on their own lists, they cross them off. 4. When all facts are crossed off, students sit down. 5. Students continue until the last classmate has shared. 6. The last one standing is the winner. 7. Teacher can summarize what was and was not mentioned. GO-GO-MO: Give One, Get One, Move On (Closing) 1. Students are given a sheet with the topic and 6 boxes. Individually, students fill in TWO of the 6 boxes with ideas they have learned from this class/unit. 2. Students get up and find classmates with whom to share. 3. They give one idea away and get an idea from each classmate they meet. The goal is to have a different idea in each box. 4. When all boxes are filled in, students sit down. Page 12 Ideas for Tier 1 Mathematics Instruction
The Important Thing About (Closing) Using the pattern from Margaret Wise Brown s Important Book, students create a paragraph length summary about a topic they have studied. The first and last sentences contain the same idea; the center includes related and/or supporting details. Template: The important thing about is that it is. It is. It is. And it is. But the most important thing about is that it is. Luck of the Draw (Closing) At the beginning of each class period, a teacher wants to include 3-5 minute summary of important ideas from yesterday. All student names are put in a fishbowl. The teacher does the summary at beginning of class on the first day then reaches into the fishbowl, pulls out a name and this student has won the Luck of the Draw it will be his/her turn tomorrow to begin the class with a summary of today. That student will select the name for the following day. As an attention move, the name for next day can be drawn at the beginning of class, but it is not announced until the end of the period. Last Word (Closing) The topic studied becomes an acronym. Students brainstorm all the things they can remember about the topic and then use the ideas to fit the structure of the letters. Example: Shape with 4 lines of symmetry Quadrilateral Unique because all 4 sides are congruent Also a parallelogram Rectangle Every angle is a right angle Page 13