Math Tool Options - Task 1 PDF

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Summary

Reflection on multiple math tools that can be used in the classroom....

Description

Part One: Tools A. Evaluate four hands-on tools that elementary-age students can use to explore mathematical concepts, including the following for each tool: 

Two Colored Counters are used to explain mathematical concepts (addition, subtraction, multiplication and division). One advantage of this tool is they help in a variety of visual mathematical concepts, such as sorting, counting, probability, place value and much more. A disadvantage is that the counters are not easy to use with larger numbers.

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Rulers are used when teaching measurements (length, area and perimeter). One advantage of this tool is to help student visually understand measurement concepts, but there is a disadvantage due to the limitations of only being able to be used with objects twelve inches or less.

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Cuisenaire Rods are used when teaching fractions and common denominators. One advantage is that they are a visual aide that helps students see fraction concepts, but a disadvantage is because of the limit in denominator use.

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Base Ten Block are used with a variety of different ways (adding/subtracting, place value, counting, etc.). An advantage is they are versatile and allow students to visualize what they are calculating. A disadvantage is they are unrealistic when using larger numbers due to the time it takes to arrange the blocks.

B. Evaluate four virtual tools that elementary-age students can use to explore mathematical concepts, including the following for each tool: 

Virtual Geoboards allows the students to build geometrical shapes and move them around in various positions. One advantage is that students will not get distracted by rubber bands. A disadvantage is the missed opportunity to practice fine motor skills when stretching the rubber bands to make shapes. https://www.mathplayground.com/geoboard.html

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Virtual Currency allows student to comprehend the value of a dollar. An advantage is students are able to work with an infinite amount of money. One disadvantage is that students have a tendency to play on their computers more than listening, making it difficult for the teacher to lead a whole group lesson and another is that apps might use coins that are similar to actual coins but are construed and look different. This does not allow students to clearly understand which coin is which…other than by size. https://apps.mathlearningcenter.org/money-pieces/

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Virtual Rekenrek use multi-colored counters that allow student to find numbers, learn counting and memorize added numbers. One advantage is they allow students to make a model of how to compose/decompose numbers, while growing their understanding of numbers. A disadvantage is that students can lose interest due to the lack of numerous color usage. https://www.didax.com/apps/rekenrek/

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Virtual Clocks are used to help students practice telling time on an analog clock. An advantage is when using these programs, teachers are able to stop or remove specific clock hands to increase/decrease the assignment difficulty. A disadvantage is that some younger students struggle if they do not know their numbers. https://www.roomrecess.com/Tools/InteractiveClock/play.html

Part Two: Lesson Plan C. Direct Instruction Lesson Plan Template

General Information Lesson Title: Communitive Property Subject(s): Mathematics Grade/Level/Setting: 3rd Grade Prerequisite Skills/Prior Knowledge: Before this lessons, students will have a full understanding of how to work the four basic math skills (addition, subtraction, multiplication and division.

Standards and Objectives State/National Academic Standard(s): (Missouri standards) 3.RA.B Understanding properties of multiplication and the relationship between multiplication and division.

Learning Objective(s): Students will apply properties of operations as strategies to multiply and divide. Students will need to be able to work problems using the distributive property, associative property and the communtative property while making a score of 85% or higher.

Materials       

Math book white board pencils eraser expo marker math organizer computer

Technology The Smartboard will be utilized for students to see clearly how I am working problems from their math book. I would have the particular problem pulled up on the Smartboard and work the problem out the way that is the easiest for the students to comprehend. I will be able to distinguish steps with different colors. I will also be showing students how they can use two-colored counters to work multiplication problems. Students will be able to access this technique on their computers at their desk.

Language Demands Specific ways that academic language (vocabulary, functions, discourse, syntax) is used by students to participate in learning tasks through reading, writing, listening, and/or speaking to demonstrate their understanding Language Function(s): Identify - Students will be able to identify which method by looking at how the problem is originally presented and solve the problem(s) correctly.

Vocabulary: 1. Distributive Property 2. Commutative Property 3. Associative Property Discourse and/or Syntax: Discourse – Working with partners, students will be able to use oral language to problem solve which method to use and also the proper steps needed to answer the problem. Planned Language Support: During the original discussion of each method, the teacher will discuss and write the proper techniques on a separate poster that students will be able to refer to during the course of study. Throughout the discussions of each method, the teacher will discuss and show students using the mathematic organizer. This will be something the students can refer to throughout the year.

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Instructional Strategies and Learning Tasks Anticipatory Set: Activity Description/Teacher   

How do we multiply two sets of numbers together? What is the correct order of operations? What are some visuals we can draw that will help us map out our problem solving skills? The teacher will pull up two-color counter app on the Smart Board and talk with students showing ways this app will help them get to the answer.

Student Actions 

Students are raising their hands waiting for their names to be called to give their answers/examples to the questions.

Problems will start out simplistic (i.e. 2 x 2). Presentation Procedures for New Information and/or Modeling: Activity Description/Teacher 

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Lead a group discussion on proper techniques to use when solving communitive property, associative property and distributed property) problems in from each method and/or mathematical process (addition, subtraction, multiplication, and division). Problems will come from math book (specific property lesson will be taught on different days and will be specified on substitute notes if/when needed). Complete a visual chart using several techniques (one being the two-colored counters) during the discussion so that students will be able to use whichever technique as a reference during the course of study. Students will be expected to show work on all assignments and test. This is what the students will be grasping during the first portion of the lesson. Students will be asked to have a drawing (similar to a two-color counter on their assignments/tests). Work out problems after students have made an attempt.

Student Actions  

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Students will watch and discuss observed techniques. Students will work out problems either using two-color counters or whiteboards and raise their hand so the teacher can walk by to see what students worked up without discussing anything more so that other students are able to complete without being distracted or corrected. Students will guide the teacher in the correct technique previously discussed by a show of hands, once everyone has attempted to solve on their own.

Guided Practice: Activity Description/Teacher 

Teacher will lead the class in a classroom discussion with all students at their desk with their computer, whiteboard,

Student Actions 

Using their whiteboards, students will be working quietly and individually at their desk and hold up their answers once complete.

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expo marker and the math organizer. Problems will come from math book (specific property lesson will be taught on different days and will be specified on substitute notes if/when needed). Problems will be shown using the Smartboard and each student will work the problem out on their whiteboard, twocolored counter app or math organizer (depending on the technique they choose) and hold up their answer to the teacher.

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Students will create a specific area in the math organizer for whichever method was being taught and make proper notes designated by the teacher. One student will be chosen to go to the board and work the problem out so other students can see the process he/she chose. Another student can go to the board and show an alternative way (if available).

Independent Student Practice: Activity Description/Teacher 

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The practice test is something to help the student feel confident and show their understanding. The assignments will have specific prompts to ensure that students are working towards understanding by showing their work. Student can use their two-colored counter app to double check their work, only if approved by the teacher. Students will bring their practice test to get checked and explain at least one problem step-by-step.

Student Actions 

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Prior to starting the practice test, students will ensure they have completed all missing assignments for the unit. Students will work on the practice test and once complete have the teacher go over it to ensure they are fully understanding the unit. If approved by the teacher, students are allowed to use the two-colored counter app to check their work. This will allow students to check where they are messing up and why. Students will be asked to explain at least one problem by explaining how they came up with the answer they received.

Culminating or Closing Procedure/Activity: Activity Description/Teacher 

Students will partner up and work on handouts together using the two-colored counter app to help student work hands-on with each question, then the students will need to

Student Actions 

Students will need to work together to complete the handouts correctly and quickly. Once completed they will need to have their work checked and approved before moving on to the

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show their work on the handout. This will allow them to problem solve together and answer the problem. Students will need to complete as many handout pages as possible in a specific amount of time. Each page will receive a star from the teacher stating that they completed the handout correctly with no mistakes. Students will then wad up handouts and throw into one of two trash cans that will be placed at different distances. I would call this game “Trashketball”. Each basket is a specific amount of points and we will keep score on the expo board in the front of the room.

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next handout. Students are allowed to use twocolored counters to verify work. This will be stressed because students at this point will need to be understanding how to work problems, if not they will not perform well on the test.

Differentiated Instruction Consider how to accommodate for the needs of each type of student. Be sure that you provide content specific accommodations that help to meet a variety of learning needs. Gifted and Talented: students will have the same amount of problems but maybe some will be at a more difficult level than the rest of the class. EL: Students will have charts fully accessible to him/her, less number of problems to complete on homework, quizzes or test. Students with Other Special Needs: students can go to a designated resource room to get additional help/guidance needed to complete the task, they will have less amount of problems. Assessment Formative Bell ringers will be handed out at the beginning of the day. This will allow me to assess what students retained from the previous day’s work. These should be handed back in within the first 10 minutes of the beginning of class. If students do not finish they will need to complete them prior to doing any free time and/or recess.

During the set time of mathematics, the teacher will go over the morning’s bell ringer and discuss in detail the proper steps to complete the problem and untie any specific areas students struggled with. This will all be done in the first 5 minutes and prior to starting any new discussions. Summative Students will work individually and need to be able to complete the problems showing 85% accuracy of the methods and answers measured by techniques shown and reviewed prior to the test. The teacher will provide very limited guidance and only by asking questions so that the student can provide adequate responses based off of prior class discussions (specific vocabulary, hand gestures, etc.). The work students complete will be graded in two different ways 1.) did the student use the correct method (i.e. multiplying or dividing) to complete the problem and 2.) did the student correctly answer the problem. This will ensure the students are receiving the appropriate credit for their work and understanding (even if they did answer the problem incorrectly).

Part Three: Reflection D. Explain how the tool from part C will enhance student learning during the lesson. Some students might not have their multiplication facts down fully so having a technique to help students verify their multiplication prior to turning it in for a grade will help students find the issue in their work and correct their problem solving. Using the counters will allow students to check their work prior to handing it in, strengthen their mathematical skills and hopefully help them gain confidence. E. Explain how your lesson plan incorporates each of the following components: 1. conceptual understanding, 2. problem solving, and 3. procedural fluency In my lesson plan I have incorporated conceptual understanding when the students arrange the counters by creating two different ways to arrange the question (see ex. A). It also has student’s problem solving by requiring students to answer multiplication sentences (see ex. B and C). Procedural fluency is used during my direct instruction when I explain the different process we take to work commutative property of multiplication and what different methods we can use to complete the multiplication sentence.

F. Explain how one instructional strategy in your lesson plan (e.g., collaborative learning, modeling, discovery learning) supports learning outcomes. During the lesson when I am modeling the use of counters to show the different arrangements of a problem helps students to visualize that 5 x 4 = 4 x 5 which is one of the learning objectives in my lesson plan.

G. Work Cited

Geoboard Area and Perimeter | Math Playground. (n.d.). Math Playground. Retrieved August 14, 2021, from https://www.mathplayground.com/geoboard.html

The Math Learning Center. (n.d.). Money Pieces by The Math Learning Center. Retrieved August 14, 2021, from https://apps.mathlearningcenter.org/money-pieces/

20-Bead Rekenrek Virtual Manipulative. (n.d.). Didax. Retrieved August 14, 2021, from https://www.didax.com/apps/rekenrek/

Interactive Clock for Kids | Online Analog Clock. (n.d.). Room Recess. Retrieved August 14, 2021, from https://www.roomrecess.com/Tools/InteractiveClock/play.html...