Unit Topic/Focus:Addition and subtraction

Date:8.09.2015

AusVELS Domain(s):

Mathematics

Year level(s):Grade 1 Level 1.

AusVELS strand (s):Number and Algebra

Lesson duration:60 minutes each lesson

AusVELS sub-strand(s):Number and Place Value

AusVELS Dimension(s) or Religious Education Guideline: Represent and solve simple addition and subtraction problems.

(ACMNA015)

Learning Standard(s)/Outcome(s)/Objective(s):

At the conclusion of this lesson, the students will know:

- How to apply simple addition and subtraction strategies to practical situations.

- How to use visual aids and Ten frames to solve addition and subtraction.

- How to develop their own addition and subtraction problems.

At the conclusion of this lesson, the students will demonstrate the strategies of:

- Counting on, partitioning and rearranging parts in order to model addition and subtraction in

practical situations.

- Using the terms ‘add’, ‘plus’, equals, is equal to, take away and minus when explaining

addition and subtraction processes.

- Using concrete materials to model addition and subtraction strategies.

- Developing own addition and subtraction problems.

Assessment:

Assessment criteria for analysis:

- Students appropriately use various strategies to model addition and subtraction.

- Students successfully use correct terms to describe the process of addition and subtraction.

- Students practice addition and subtraction using concrete materials.

- Students develop appropriate addition and subtraction problems.

Teaching focus: Teaching skills that the pre-service teacher would like to personally develop:

- Providing constructive and valuable feedback to students.

- Scaffolding will be used throughout the entirety of lessons. This will allow for appropriate

tiered/ differentiation strategies.

- Questioning particularly open-ended questioning will be implemented throughout the lesson

particularly for tier groups 2 and 3. Praise and feedback should be given for thoughtful

answers. Group discussion will be determined from answers.

- Where possible effectively implement blooms taxonomy in order to guide appropriate

questioning and scaffolding. This is inferred throughout the lessons but not explicitly stated.

- Ensuring that instructions are clear and that all students understand what is required.

- Group students based on ability levels and learning requirements.

- Mixed ability grouping and cooperative groups.

- Teacher needs to continually make judgments as to student understanding and progress

which will allow them to determine which students will need assistance through tier 1 and

tier 2.

- A focus on Howard Gardner’s Multiple Intelligences, where a range of activities and

resources are provided during planning in order to cater for a vast array of learning styles.

Background to the learning:A.References for teacher background knowledge:

Booker, Bond, Sparrow & Swan. (2014). Teaching Primary Mathematics (5th ed). NSW,

Australia: Pearson.

Brantley, A. (2012). Differentiating Math, Crazy for First Grade. Retrieve online:

http://www.crazyforfirstgrade.com/2012/02/differentiating-math.html

Carter, J. (2007). Chapter 28, Unit 6: Engaging all learners, How do I differentiate

Instruction to meet the needs of all learners. Retrieve online from:

http://ptgmedia.pearsoncmg.com/imprint_downloads/merrill_professional/pdf/

KronowitzCh.28.pdf

Gough, J. (2014). Diagnostic mathematical profiles. Victoria, Australia: Deakin University

Press.

Reys,R., Lindguist, M.M., Lambdin, D.V., & Smith, N.J. (2012). Helping Children Learn

Mathematics (10th ed). USA, USA: John Wiley & Sons, Inc.

Swan, M., Binns, B., & Gillespie, J. Design a board game, Numeracy through problem

solving. Retrieve online from:

http://www.mathshell.com/publications/numeracy/boardgame/boardgame_teacher.pdf

Van De Walle, J.A., Karp, K.S., & Bay- Williams, J.m. (2013). Elementary and Middle

School Mathematics Teaching Developmentally (8th ed). USA, USA: Perason.

B. Identify students’ current knowledge

- Knowledge of number systems from 1 to 20.

- Knowledge of ordering numbers from 1 to 20 with understanding of which values are

smaller and larger.

- Some former experience with addition and subtraction but only beginning understanding of

its use with story problems.

- Knowledge of investigation strategies, such as looking through books or searching the

Internet, used to develop background understanding for a project or concept.

- Experience with subitising.

LESSON 1:

Lesson focus: Addition

Lesson resources:- Appendix 1: Brain gym instruction sheet (1 copy for the teacher). - White board markers.- Appendix 2: laminated cookies (1 copy).- Appendix 3: Ten frames (2 copies). - Appendix 4: Roll and Add worksheet (enough for every student). - 1 die per person.- Grey led pencils - Appendix 5a: zoo animal puppets (1 copy). - Appendix 5b: Elephants birthday party story print out (1 copy for teacher). - Class set of laminated Ten Frames (Appendix 6). - Large container of Unifix Blocks. - Appendix 7: example hand activity (1 copy for teacher). - Coloured paper.- White paper.- Scissors.- Glue. - Classroom set of Ipads.

Lesson content: A. Introduction _15_ mins- Students to grab their water bottles and come and sit down as a group.- The Teacher will instruct brain gym (appendix 1). Particularly for students who have difficulty concentrating. - The teacher will Introduce the topic of Addition: - They will write the learning intentions on the board and guide a group discussion surrounding these. - Brain storm group activity: “what we know about the word addition” Teacher to write this in the middle of a mind map on the board, and encourage students to raise their hand with anything that they think the word might mean”. - We want students to use words such as ‘add’, ‘both’, ‘in all’, ‘altogether’, ‘total’, ‘sum’, ‘plus’, (these words should be added and discussed if not already stated by students). - This mind map/ word map will be left on the board and revisited as part of the lesson consolidation - The Teacher should discuss ‘plus’ sign and ‘equals sign’: “It uses numbers and symbols instead of words. When we write out expressions with addition, we use two symbols: + and =.The plus sign (+) means two things are being added together”

B. Development Consolidation, practice,__40__ mins

DIFFERENTIATED INSTRUCTION

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TIER 1 WHOLE CLASS INSTRUCTION

DIFFERENTIATED INSTRUCTION (overall strategy)

Tier 1: Universal Core Curriculum - All students:The Teacher to explain the following problem to their students: (they should ensure that students are aware not to call out the answer if they know it straight away).“ I have decided to make some cookies for my friends birthday party. The only problem is, is that she told me that I needed 8 cookies for the boys and 5 cookies for the girls. How will I work out how many cookies I need altogether, do you think you can help me?” - Using the cookies (Appendix 2 & 3) the teacher needs to model placing 8 cookies on one ten frame and 5 cookies on the other ten frame.- They will ask the students to raise their hands if they know an easy way to add the two sets of cookies together (model what each student suggests, however we want them to place all the cookies on the first ten frame and the left overs on the next ten frame which allows them to effectively subitise.- The Teacher will explain that what the students have just done is called addition. They also need to explain how the ten frame is used to assist us with working out addition problems.- Teacher to model problem using the addition equation written on the board.

Tier 1: Whole Group Instruction (10 minutes)- Brain gym (appendix 1)- Word map to introduce vocabulary and appropriate language for addition.- Cookies scenario. (appendix 2 & 3)- Introduces students to the concept of adding two lots together to find a total amount.- Introduce to ten facts in order to help them subitise.- The students who had difficulty with this task as well as addition needs students will move onto tier 2 and the rest of the class will engage in anchor activity rotations.

Tier 2: Small Group FOCUSED Instruction (10 minutes)If students did not fully understand the concept of addition after the whole class instruction, the teacher will provide another example using more structured scaffolding and visual aids.- Story telling addition problem with accompanying visual aids (Puppets).- Students will use puppets alongside the story, where they need to work out a total amount (Appendix 5a and 5b). The teacher will guide the small group through this process and then allow them to use 1 ten frame each and Unifix to display their data (Appendix 6). Students within tier 2 will also participate in tier 3 as these students will benefit from creation of a visual aid. Questions to guide the students are required. “How many Unifix do we need first” ect.- The students who are still struggling and addition needs will move on to tier 3.

Tier 3: Individual or small group INTENSIVE Instruction (10 minutes)- For students who are still having difficulty with the concept of addition particularly understanding complex vocabulary will find it useful to explore visual and practical methods for finding a total amount. (Vital for dyslexic and autistic children as well as visual learners).- The teacher will show students an example of the aid that they will be creating (Appendix 7).- Students make their own addition aid. (this will also be useful when learning subtraction).

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)TIER 2: TARGETED SMALL GROUP INSTRUCTION

For students who didn’t fully graspLearning covered in whole-group Tier 1 Instruction.This will be determine on observation of child involvement during group time as well as previous understanding of students ability level.

Tier 2 Targeted Small Group Instruction- Teacher calls on 4 students to each collect an animals finger puppet and another group of 3 to each collect a finger puppet (Appendix 5a).- One group will be standing on one side of the teacher (4 students) and the other group will be standing on the other side (3 students)- Teacher to explain the following scenario holding the elephant puppet: (Appendix 5b) “Elephant needs out help. See he has decided to have a party for his 5th birthday, so he has invited 4 of his animal friends from one zoo and 3 of his animal friends from another zoo. But he is very confused because he doesn’t know how may people will be at his birthday altogether. Do you think you can help him?”- Teacher to guide a group discussion asking students how they think they could work this problem out.- Teacher to provide each student with a laminated ten frame (Appendix 6).- Teacher to ask students to use 4 green Unifix blocks to display the animals from the first zoo and 3 blue Unifix to display the animals from the second zoo.- Teacher will count by ones with the students to work out the total amount.- They will ask students if anyone knows how many more we need to make a total of 10 zoo animals, as Elephant was allowed to have 10 animals at his party.

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)TIER 3: INTENSIVE TARGETED INDIVIDUAL INTERVENTIONFor those students, who after Tier 2 Small groupInstruction, still require assistance to facilitateunderstanding.This will be determine on observation of child involvementDuring group time as well as previous understanding of students ability level.

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STUDENT ANCHOR ACTIVITY: Consolidation and practice(may operate concurrently with Tier 2 and Tier 3 Activities)

Tier 3: Intensive Individual/ small group instruction- For the students who are having difficulty with the concept of adding two different amounts together. Or difficulty processing the language involved with story telling.- Students will create a visual aid/ representation of the process of counting using our fingers to be utilized for both addition and subtraction lessons.- Teacher to show students the example of what they will be making (Appendix 7).- Students need to collect paper and trace around both of their hands. They then cut them out and stick only the palms of each on to the paper.- Each finger needs to be folded inwards.- The students will practice using their aids while the teacher reads out two numbers (under five).Students display one number using the fingers on one hand and the second number using the fingers on the second hand.- They then use this to count how many fingers there are altogether.- (This aid allows students to visually count numbers that add up to ten).- The teacher will continue to ask an additional 5 addition problems for students to work out using their visual aid.

WHOLE CLASS works in pairs and quietly on the Anchor activity: (30 minutes)- Students will be placed in pairs (one student will have a high level of

understanding and the other student will benefit from some peer assistance)- Each pair will be provided with two ten frames each (Appendix 3), a handful

of two different coloured Unifix counters each and two six sided die to share.- The students take it in turns to roll both the die.- The number rolled on one die will be displayed using one colour Unifix on

their Ten Frame and then number rolled on the second die will be displayed using the different colour.

- The students need to colour in the accompanying worksheet (Appendix 4) with the number of spaces on the ten frames covered and work out how many they have all together.

- The students will each have 5 goes over a period of 30 minutes.- Early finishes/ extension activity listed below.

C. extension

- (early finishes)- Addition app on classroom ipad: Counting and Addition: Tribal Nova (2010).

D. Closure _4__ mins

Lesson/activity transition:

Step 1: Students need to pack up any materials used throughout the lesson.

Step 2: Students to re group and sit in a circle.

- Each student needs to share something that they have learnt about addition or anything that

they found interesting or difficult.

- This will allow consolidation of the information learnt in regards to addition including

strategies implemented.

Step 3: Teacher will ask students what they know about the term ‘Subtraction’ as this is next

lessons focus. This will be done using think, pair share, where each pair reports back to the group.

LESSON 2:

Lesson focus: Subtraction

Lesson resources:

- Appendix 1: Laminated brain gym instructions (1 copy for teacher).

- Smart board.

- Appendix 9: laminated eggs (1 copy).

- Class set of laminiated Ten Frames.

- Container of Unifix blocks.

- Appendix 10: Word problem activity (enough copies for tier 2, small group children and

teacher).

- Grey Led Pencils.

- Pip cleaners.

- Coloured beads.

- Appendix 11: Colour by subtraction worksheet (enough for every student).

- Colouring in pencils.

- Five copies of the laminated draw a story problem activity (Appendix 12).

- One copy for each student of the ‘draw a story problem’ associated worksheet. (As part of

appendix 12).

Lesson content: A. Introduction __15_ mins

- Students to grab there water bottles and come and sit down as a group.

- The teacher will instruct brain gym (appendix 1) in order to get the students brains working

(Particularly for students who have difficulty concentrating).

- Introduce the topic of Subtraction:

- “Subtraction is taking things away. When you have an amount and you subtract from it, the

amount becomes smaller. Subtraction happens a lot in real life”.

- The teacher will refer back to learning intentions from last lesson, which should still be written on

the board.

- Developing vocabulary for subtraction activity: Glue word cut and paste activity to differentiate

between addition and subtraction vocabulary (Appendix 9). Students to move back to their tables. -

- The teacher will read and explain instructions outlined on the sheet.

B. Development, Consolidation, practice,__30__ mins

DIFFERENTIATED INSTRUCTION

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Tier 1: Universal Core Curriculum - All students (10 minutes)- Teacher to access http://www.gcflearnfree.org/additionsubtraction/3 which demonstrates an interactive example of subtraction. The teacher will need to read the accompanying vocabulary.- The teacher will then work through the problem with the whole group using ten frames to guide subtraction. This will be done using a laminated Ten frame and laminated eggs (Appendix 8 and 9).- They will need to introduce and explain that the minus sign (-) means one thing is being subtracted from another. This is why we put it after the first group of eggs — we had 8 eggs and subtracted 5 of them. They will write full equation on the board.- Each student will collect a laminated Ten frame and a collection of Unifix and move back to their tables.- The teacher will read out 5 different subtraction problems and students need to display the process on their ten frames. (placing a number of Unifix on the Ten frame and then taking the required amount away.- The teacher should walk around the room and observe students understandings.

DIFFERENTIATED INSTRUCTION (overall strategy)SM

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TIER 2: TARGETED SMALL GROUP INSTRUCTION

For students who didn’t fully graspLearning covered in whole-group Tier 1 Instruction.

Tier 2 Targeted Small Group Instruction (10 minutes)- The teacher will gather the students in a small group

on the floor. Students will need to bring with them a board to lean on.

- The teacher will provide each student with appendix 10.

- The teacher should read out the word problem and work through each of the working out methods.

- The teacher will ask students other ways that they think they could work out the problem. And which ways they find easier.

- Students who are still struggling with the concept of subtraction will move on to tier three and the rest of the students will move on the anchor activity rotations.

Tier 1: Whole Group Instruction 10 minutes

- Online video of subtraction process.- Students work out subtraction process using Ten frames and using the equation.- Modeling subtraction using Ten frames.- The students who had difficulty with this will move onto tier 2 and the rest of the class will engage in anchor activity rotations.

Tier 2: Small Group FOCUSED Instruction (10 minutes)

- A small group of students is guided through the subtraction story problem (Appendix 10).- The students who can successfully grasp the concept at this point will move onto an Anchor activity.

Tier 3: Individual or small group INTENSIVE Instruction (10 minutes)

- Students create beaded number rods (10 beads). These assist them by providing a visual and hands on aid for working out subtraction problems.

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)TIER 3: INTENSIVE TARGETED INDIVIDUAL INTERVENTIONFor those students, who after Tier 2 Small groupInstruction, still require assistance to facilitateunderstanding. Tier 3: Intensive Individual/ small group

instructionStudents will create a 10 bead number rod as a visual aid for assisting them with subtraction problems. (This may also be utilized for addition problems).Individuals or small group will gather on a table with the teacher.- They need to collect a pipe cleaner and 10 beads.- Each bead needs to be threaded onto the pip cleaner.- The Teacher will demonstrate how they can be utilized with a number of examples and encouraging students to act it out also.

STUDENT ANCHOR ACTIVITY: Consolidation and practice(Operates concurrently with Tier 2 and Tier 3 Activities) students who can successfully grasp the concept of tier 2 can move on to this activity will teacher works with tier 3).

C. extension __10__ mins

- All students to engage in the following activity.

- Students need to re group on the mat and the teacher will explain the ‘draw a story problem

activity’ using the teaching notes attached to appendix 12.

- Students will move back to their tables to complete this task in groups of fours (teacher to

assign groups with mixed ability levels in each).

- This allows students to create their own addition or subtraction problems using the cards

that they have drawn and write and solve the associated equation.

D. Closure __3__ mins

Lesson/activity transition:

Step 1: Students to put away any materials utilised throughout the lesson.

Step 2: The Teacher will explain that during next lesson students will be combining the information

that they have learn about addition and subtraction to make their own board games.

Step 3: The teacher will ask the students to start thinking about some ideas of games that they could

create or to think about existing games that they could modify to incorporate addition or

subtraction.

WHOLE CLASS works independently and quietly on the Anchor activity:- (10 minutes)- Students to sit on the mat while the teacher explains the instructions.- Students are handed Appendix 11. They need to work out a series of subtraction problems where the answer guides them as to what colour they need to use.- The Teacher will need to explain the subtraction equations when it is set out as one number on top of the other, as students will come across these on the worksheet.- Students instructed to collect the coloured pencils and move back to their tables to complete this task individually.- Teacher to allow students to use the laminated ten frames and unifix to assist them in the subtraction problems.

LESSON 3:

Lesson focus: Apply addition and subtraction knowledge. Lesson resources:

- Brain gym appendix 1- (teacher use).

- Examples of mathematical board games: Appendix 13 (1 laminated copy of each).

- Processes and instructions for board games: Appendix 14 (one for each group).

- Grey led Pencils for writing.

- Smart board to access youtube video.

- Class set of Ipads (which are connected to the internet).

- Poster paper.

- Coloured paper.

- Couled pencils.

- Textas.

- White paper.

- Glue.

- Scissors.

Lesson content: A. Introduction __10__ mins

Students to grab there water bottles and come and sit down as a group.

- The Teacher will instruct brain gym (appendix 1) in order to get the students brains working

(Particularly for students who have difficulty concentrating).

- The Teacher explains to the students “that today we are going to be using the information

and knowledge that we have developed about addition and subtraction to work in groups to

develop mathematics board games”.

The teacher will ask students the following open ended questions in order for them to develop

some background information about addition and subtraction games:

Can anyone think of some addition or subtraction games that they are aware of?

What popular games could be adapted to involved addition and subtraction components?

Where will we go to help us find out information or ideas to help us plan for and create our

board games?

How will we plan for the development of our board games?

B. Development, Consolidation, practice,__40__ mins

DIFFERENTIATED INSTRUCTION

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Tier 1: Universal Core Curriculum - All students- Students remain sitting in the group on the mat.- After the teacher and students have discussed the questions they will explore some

examples of board games.- The teacher will show them some examples (appendix 13). Explaining the mathematical

content in each. (these provides students with a coherent structure for their work).- Students will be placed intro mixed ability groups with 4 students in each. (the groups will

be depicted based on their level of understandings during the previous addition and subtraction lessons).

- The teacher needs to explain that students firstly need to allocate a leader for each group who will collect and hold onto resources.

- Each group will be provided with appendix 14 which outlines the process/ steps and outline for a draft in which they will work through in order to create their board games.

- Teacher instructions/ scaffolding: Students to find a space in the classroom to work with their groups. They need to write their group members name on the front of the worksheet. Students can access the classroom resources and the internet on their ipads to

investigate and research ideas/ design elements. Ensure that students know that they can also adapt an already existing game. Students need to complete the peer contribution section of the worksheet which

ensures that each student within the group has an important role. Students need to construct a draft and materials list within the allocated space in

the worksheet. Students construct their board game as well as associated instructions. Students will present their board game to the rest of the class explaining what

mathematics is involved and how it works.

DIFFERENTIATED INSTRUCTION (overall strategy)

Tier 1: Whole Group Instruction(10 minutes)

Students are placed in mixed ability groups where they will work together to research, design and create a board game, which includes the concepts of addition and subtraction.

Tier 2: Small Group FOCUSED Instruction(10 minutes)

- Students who do not fully understand what the task is will stay sitting on the mat for further instruction and questioning.

Tier 3: Individual or small group INTENSIVE Instruction(5 minutes).For the students who learn more productively when provided visual/ interactive mentoringStudents will watch a You tube video which outlines steps and ideas for the development of mathematics board games.

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)TIER 2: TARGETED SMALL GROUP INSTRUCTION

For students who didn’t fully graspLearning covered in whole-group Tier 1 Instruction.

Tier 3:

Intensive Individual/ Small Group Instruction:For those students, who after Tier 2 Small groupInstruction, still require assistance to facilitate

Tier 2 Targeted Small Group Instruction (10 minutes)- Students are placed in mixed ability groups where it is hoped that the higher ability

students will assist the rest of the group (peer teaching exercise).- When the other students are asked to move into their groups to begin working on

their board games the teacher will ask whether there are any students who do not understand what they are meant to do and these students will remain on the mat.

- The teacher will scaffold the following questions in order to provoke further understanding about their projects.

- Questioning to guide students in the process of designing their board games: (these questions are also outlined on the worksheet (appendix 13) for students to refer back to)

What theme or topic is your board game Will it include addition, subtraction or a combination of both? How many players is the board game for? Has everyone in your group been allocated a role? Have you drawn a draft of what your board game will look like? Have you come up with a clear set of instructions for your game?

- The teacher will write ‘Board games’ in the middle of the white board.- Students need to brainstorm different aspects of board games, which will assist them

to create their own.- The students who understand what they are required to do will return back to their

groups.

Tier 3: Intensive Individual/ Small group instruction (5 minutes)

- For those students who are still struggling with the concept of investigation and creation of an addition or subtraction board game.

- Particularly for the students who required visuals or hands on/ interactive approaches to instruction (dyslexic student, autistic student and ESL students).

- Students will watch the following video that provides scaffolding about creating a mathematics board game.

- https://www.youtube.com/watch?v=IT5ll4H5nMk - Teacher to ask students if they have any further questions or concerns about their

project.- If they now understand what they are meant to be doing they will move back to

join their groups.

ANCHOR ACTIVITIES while teacher engages in direct instruction with Tier 2 or Tier 3 students.

C. Closure __10__mins

- Step 1: The students will re group on the mat.

- The leaders of each groups name will be placed in a container.

- The teacher will draw out a name, which will depict the order for presenting their board games.

- When the groups name is drawn out they will get up in front of the group and present their board

game to the rest of the class.

- Step 2: Students to collect all used materials and return them to the correct shelves.

- Step 3: Students to close I pads up and pack them away.

- Step 4: Students to re organise tables if they were moved.

- Step 5: Students to give their board games to the teacher who will pack them away to be

used as resourcing during future lessons.

WHOLE CLASS works independently and quietly on the Anchor activity:- Students will be instructed to move back to their tables with their groups to work through

aspects in the worksheet to develop their projects. - The Teacher will ensure that students aware of the timetable to complete their project of 45

minutes.- Once the students are up to the drafting stage of their board game they need to show these to

the teacher for constructive feedback and or assistance.- Once students from tier 2 and tier 3 have grasped the instructions and content they will move

back to their group and be assigned a task to investigate.- Once the teacher has finished with tier 2 and tier 3 groups they will walk around and provide

scaffolding to ensure all groups are engaged within the task.- Students need to allocate one group member to be the presenter during the next part of the

lesson.- Students need to discuss the component they need to discuss in their presentation such as:

theme, content, mathematics, number of players, what will be learnt and instructions of their board game.