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Jimmy Hunt

30052409

Assessment Task 2For this task I chose to prepare lessons to address the Victorian Curriculum for Fractions and Decimals for Level 1 and Level 2. I chose Fractions and Decimals because this is an area I have neither taught nor seen taught recently, and it provided me with a challenging opportunity to creatively construct activities without simply copying things I have seen. The basis for catering to both Level 1 and Level 2 is that in my first professional experience as a preservice teacher, I am placed in a multi-grade class consisting of grade one and grade two students. The school at which I am placed has five such grade one and two classes, and similar for grades three and four, and five and six. I am aware of other primary schools in the Ballarat region operating multi-grade classes like this, so I believe it is good practice to prepare for a multi-grade class.

The Victorian Curriculum for Fractions and Decimals at Level 1 maintains that students should “Recognise and describe one-half as one of two equal parts of a whole,” including the elaborations of “sharing a collection of readily available materials into two equal portions” and “splitting an object into two equal pieces and describing how the pieces are equal” (Victorian Curriculum and Assessment Authority, 2016). Level 2 sees students “Recognise and interpret common uses of halves, quarters and eighths of shapes and collections” including “recognising that sets of objects can be partitioned in different ways to demonstrate fractions” and “relating the number of parts to the size of a fraction.” I broke these down into three steps to form the three lessons.

The first lesson (see Appendix A for Lesson Plan 1) teaches the concept of halves, quarters and eighths being parts of a whole, with grade one students focusing on halves while grade two students focus on quarters and eighths, in reflection of the curriculum. The second lesson (see Appendix B for Lesson Plan 2) shows that halves, quarters and eighths are equal. Again, grade one students study halves while grade two students study quarters and eighths. The third lesson (see Appendix C for Lesson Plan 3) promotes that halves, quarters and eighths can be of numbers other than one, also focusing on halves for grade one and quarters and eighths for grade two. This logical progression ensures students are not discouraged by overwhelming information and are able to build their knowledge gradually.

The lessons are designed to be both fun and practical in order to engage the students throughout each lesson. There is substantial variety across the three lessons in terms of groupings, materials and content. Students work individually, in pairs and in groups, where groups may reflect similar ability or varied ability. This encourages both independent work and teamwork, and giving and receiving help. The activities range from worksheets to manipulating tangible items to games involving technological resources, creating excitement and different ways of learning. Physical representations are important because the mathematical concepts are abstract for children (Booker, Bond, Sparrow & Swan, 2014). Games are also essential as they keep children focused and promote high level thinking (Booker et al., 2014). There are also extension activities and focus groups which cater to students who are either advanced or struggling, or perhaps require close monitoring for behaviour.

Peter Sellings, 05/06/17,

See my comments for each lesson plan. There are some activities that would strengthen this further.


This is a nice link.

To illustrate that halves, quarters and fractions are parts of whole shapes or objects, the whole class activity in the first lesson sees students form whole shapes from half-shape pieces, and then quarters and eighths. The individual worksheets (see Appendix D for Lesson 1 Worksheets) help students practice recognising halves or quarters and eighths of common geometric shapes as well as demonstrate their ability to identify these fractions by colouring them. This practice of partial colouring helps students see these fractions as parts of a whole rather than single units (Booker et al., 2014). These worksheets can be scaffolded by use of the half, quarter and eighth pieces of shapes used in the whole class activity.

Learning that halves, quarters and eighths are equal, students in the second lesson indicate the distinction of these fractions in two dimensional shapes, and observe examples and non-examples. They go on to analyse three dimensional objects for their abilities to be separated into the same fractions. A focus group manipulates play dough into shapes to be partitioned into halves, quarters and eighths. This partitioning of objects is a necessary activity for some children (Booker et al., 2014).

The third lesson’s focus on separating groups into halves, quarters and eighths sees students play a game incorporating technology which tests their ability to determine these fractions of numbers up to 12 (see Appendix E for Lesson 3 Slideshow Game). They then separate groups of physical objects into these fractions while a focus group has the opportunity to determine the correct distributions without using the objects themselves.

Each class contains teacher-led discussions in which students can share several strategies or explanations for the benefit of others. Higher order thinking is encouraged by the questions included in each lesson plan, promoting rich mathematical communication. Questions such as “how many halves?” and “do you need to turn the piece another way (to form a shape from two halves)?” reflecting the lower levels of Bloom’s Taxonomy (Kugelman, n.d.) are included early in, and throughout, each lesson. Higher level questions such as “can you think of something that has two halves joined?” and “is it important to recognise the parts of shapes?” are included in the reflection and discussion parts of each lesson to encourage higher order thinking.

Assessment is included in all three lessons. The first lesson utilises a worksheet by which the teacher is able to analyse the students’ understanding of the content and ability to demonstrate it. The second lesson involves an activity in which the teacher can summon any student to demonstrate their ability to separate a shape into two equal halves. An activity in the third lesson provides assessable physical evidence of the students’ capabilities and comprehension of the task. All three lessons provide ample dedicated time for discussion and several planned questions which assess the students’ lower and higher order thinking skills, giving each lesson multiple opportunities for assessment in a variety of forms.


A few more links to the theory also would have strengthened your reflection.


I would have liked more discussion of assessment. Some of the capabilities should have been assessed through tick sheets to show how the students were working as groups for example.

References

Victorian Curriculum and Assessment Authority (2016). Victorian Curriculum Foundation-10.

Retrieved May 8, 2017, from

http://victoriancurriculum.vcaa.vic.edu.au/mathematics/curriculum/f-10

Kugelman, F. (n.d.). Bloom’s Taxonomy Cheat Sheet. Retrieved from

http://www.bloomstaxonomy.org/Blooms%20Taxonomy%20questions.pdf

Booker, G., Bond, D., Sparrow, L. & Swan, P. (2014). Teaching Primary Mathematics (5th ed.).

Melbourne, Australia: Pearson.

Appendix A

Lesson Plan 1

Grade/Class/Year: 1/2 Date:

Curriculum Area/s: Strand/ Sub Strand:

Mathematics Fractions and Decimals

Cross Curriculum Priorities and Capabilities:Critical thinking is required for the worksheet. Creative thinking is required for the extension activity.

Where are they now?Curriculum descriptor/s:

Mathematics- http://victoriancurriculum.vcaa.vic.edu.au/mathematics/curriculum/f-10

Grade 1: Recognise and describe one-half as one of two equal parts of a whole (VCMNA091)

sharing a collection of readily available materials into two equal portions splitting an object into two equal pieces and describing how the pieces are equal

Grade 2: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (VCMNA110)

recognising that sets of objects can be partitioned in different ways to demonstrate fractions relating the number of parts to the size of a fraction

Prior Knowledge/ Learning:

N/A

Where to next?Learning Intentions/ Outcomes:

Grade 1: Understand halves as parts of a whole; a whole can be separated into two halves, and two halves form a whole

Grade 2: Understand quarters and eighths as parts of a whole; a whole can be separated into four quarters or eight eighths, and four quarters or eight eighths form a whole

Success Criteria/ Indicators:Students will:

Grade 1: Demonstrate ability to match half shapes to their corresponding whole shapes Grade 1: Describe things which are commonly separated into halves, and things which are formed

by two halves. Grade 2: Demonstrate ability to match quarter/eighth shapes to their corresponding whole shapes


Your success criteria are very measurable which is pleasing to see.


Grade 2: Describe things which are commonly separated into quarters/eighths, and things which are formed by four quarters/eight eighths.

Key Vocabulary/ Metalanguage:

Grade 1: Half, halves, whole, separate

Grade 2: Half, halves, whole, quarter, eighth, separate

Group Structure:

Students will work individually on worksheets for the main activity.

Notes for inclusive practice:

A focus group for struggling students and extension activity are included.

How? Lesson SequenceWarm-Up/ Engage:

Ask students “who likes cake?” Tell the students you bought a small cake last night and wanted to share it with a friend, but it wasn’t cut. Ask the students what you could have done. Lead them to say “cut it in half” and then enquire about what that means;

What is a half? How many halves in a whole cake? If I get half of one cake and half of a different cake, will they make a whole cake? What if they’re different sizes? What if there were four people? (lead grade 2s to say quarters) How about eight people? (lead grade 2s to say eighths) Do only cakes have halves, or other things too?

Time Allocation: 10

Whole Class Experience/ Explain:

Stick halved shapes (made from paper/cardboard and magnets) on the board, jumbled. Choose one student to find two halves and put them together. Repeat until all objects are whole. Stick quartered shapes on the board and repeat, then eighths – focusing on grade two students for this part. If a student struggles, the teacher may nominate a student to help.

Do these pieces look the same? Do you need to turn the piece another way? Which way do they go together? What shape do you think this piece will make? How many pieces will you need to make a whole shape? Is this piece a half, a quarter or an eighth?

Time Allocation: 15

Explore/ Main content:

Individually complete the halves worksheet (grade 1) or quarters-eighths worksheet (grade 2).

These worksheets can be used to assess students’ understanding.


The worksheets are okay – students with additional literacy needs would need to have these explained carefully to them.


I am not a big fan of worksheets at this level. I would rather see you use concrete materials with students showing you how they have made certain fractions. You can then get them to draw these fractions on a small whiteboard or in their maths books.


I would have liked to see a story about fractions here. IT would be a good way to lead into an activity.


This would work well as an introduction.

Time Allocation: 20

Extension Activity:

Advanced students (and any who complete the grade 2 worksheet early) can go on to draw their own shapes and the halves-quarters-eighths that comprise them. “Can you draw a circle and show how it has four quarters? What about other shapes?”

Teacher Group or Focus:

The teacher will help struggling students by using the half/quarter/eighth pieces from the first activity to form the shapes on the worksheet.

Reflection/ Evaluate/ Elaborate:

Each student can be asked a question to assess their understanding and achievement in relation to the learning objectives. Questions will reflect lower and higher order thinking skills.

What is a half? How many halves do things have? What does half of a circle/square/triangle/star look like? How do you know if a shape can be halved? Can you join half a triangle and half a circle to make a shape? Half a cookie and half a banana? Has anyone had to share something in halves before? Can you think of something that has two halves joined? (Oreo, lego…) Repeat for quarters and eighths, focusing on grade 2s.

Time Allocation: 15

Other ResourcesMaterials, Resources and Equipment:

Magnetic halves, quarters and eighths of shapes Worksheets Pencils or crayons for students Blank paper for the extension/focus activity

Self-Reflection on the lesson(Complete this after the lesson. Consider What worked well? What were the student’s reactions? Did everyone achieve the learning outcomes? If not, why not? What can I do this time to improve? How can I make this lesson engaging and achieve the lesson objectives? What improvements could be made for future lessons?)


Some great questions here. I would have all students with small whiteboards and I would ask them to draw pictures to show their answers to some of your questions.

Appendix B

Lesson Plan 2




Cross Curriculum Priorities and Capabilities:Critical and creative thinking are required for the group activities. Personal and social capabilities are important for the group activities.






recognising that sets of objects can be partitioned in different ways to demonstrate fractions relating the number of parts to the size of a fraction


Understanding fractions (halves for grade 1s, and quarter and eighths for grade 2s) as parts of wholes.


Understand that halves (and quarters and eighths for grade 2s) must be equal.


Demonstrate ability to identify equal halves (and quarter and eighths for grade 2s) of two-dimensional shapes

Demonstrate recognition of equal halves (and quarters and eighths for grade 2s) of three-dimensional objects


This is really important and a concept that students can struggle with.



Grade 1: Half, halves, whole, separate, parts, equal

Grade 2: Half, halves, whole, quarter, eighth, separate, parts, equal

Group Structure:

Students will work in same-grade groups, with a range of abilities in all groups. This will allow advanced students to guide and demonstrate to those who need help.


The focus group activity is suitable for struggling and advanced learners.


Show the class a bread stick (or pretzel stick). “I want to share this with my friend. What do I do?” Students say to break it in half/two pieces. Break it into two very uneven pieces. “Is this right? Why not? Are these halves?” Emphasise that halves must be the same size. Break another bread stick in half equally. Put one of the halves with one of the uneven pieces. Clarify that they can’t make one bread stick because one piece is not a half – the ‘whole’ bread stick is too big or too small.

Time Allocation: 5

Whole Class Experience/ Explain: (modelled / shared)

Draw a circle on the board. Ask a student to draw a line through it to ‘cut’ it in half. If their line is not through the middle, ask other students to explain whether it’s right and why/why not. If they get it right, the teacher draws a wrong line and students explain as above. Repeat with increasingly difficult shapes; squares to ovals to stars to different types of triangle, ensuring vertical and horizontal lines aren’t always applicable.

Repeat the activity for halves, quarters and eighths, having students help to demonstrate and explain. Some shapes will not be able to be split into quarters and eighths, but it is important to demonstrate this.

Time Allocation: 15


In same-grade groups, students separate classroom objects into halves (or quarters and eighths for grade 2s) using masking tape. While introducing the activity, the teacher will write some classroom object vocab words on the board, so the students can record their work.

Time Allocation: 20

Independent or Group Activities:

(As above)

Teacher Group or Focus:

The teacher will assist students with a play dough kit where they can create two dimensional and three dimensional shapes and cut them into halves,


I would use students here to make equal groups. You can easily have 8 students in a group and talk about making equal sized groups, splitting them in half and quarters (and even eights.)More detail here would have been good.

quarters and eighths, to show that these pieces are equal sizes and shapes.



Ask individual students to show one object from their group to the class and show they’ve split it successfully into equal parts.

How did you separate it into halves/quarters/eighths? How do you know the parts are even? Are there different ways to do this? Could the parts be used to make other shapes? Is it important to recognise the parts of shapes? Why?

Time Allocation: 20


Masking tape White board and markers Play dough kit

References/Sources:

N/A



This is quite a lot of time to spend on this. Another book or some other type of concrete material activity needs to be included.

Appendix C

Lesson Plan 3




Cross Curriculum Priorities and Capabilities:Critical thinking will be required when students encounter numbers which cannot be halved, quartered or split into eighths. Personal and social capabilities are important for the group activities.






recognising that sets of objects can be partitioned in different ways to demonstrate fractions

relating the number of parts to the size of a fraction


Understanding halves (and quarters and eighths for grade 2s) as parts, and as equal parts.

Matching halves (and quarters and eighths for grade 2s) of shapes to their wholes.

Separating whole two-dimensional shapes and three-dimensional objects.


Separate groups of objects into halves (and quarters and eighths for grade 2s)


Demonstrate knowledge of halves (or quarters and eighths for grade 2s) of numbers by distributing physical items equally



Grade 1: Half, halves, whole, separate, parts, halve

Grade 2: Half, halves, whole, quarter, eighth, separate, parts, halve

Group Structure:

Students will work in same-grade groups.


The focus activity suits advanced learners.


Remind the students of sharing the cake and then the bread stick with your friend. Tell a story about how your friend wanted to repay the favour and bought a bag of lollies to share. “Should I cut all the lollies in half? Why not? How else can we share equally?” Demonstrate with tokens, gradually increasing the total. Show that odd amounts can’t be halved. Choose students to participate. “What if there are four people sharing? Or eight?” Students help separate tokens into quarters and eighths.

Time Allocation: 10

Whole Class Experience/ Explain: (modelled / shared)

Teacher shows slides on interactive whiteboard/whiteboard with projector, separated into two columns. Each side has the same number of circles (outlines). One student stands on each side and races to stick magnets in half of the circles. Have students clarify who filled the correct amount of circles. “How many circles are there? Can we halve this number? What is half of this number? Are there two equal groups, one with magnets and one without?”

Slides get progressively harder (less alignment, more scattered) and students cycle through. Progress to quarters and then eighths for grade 2s and competent grade 1s.

Time Allocation: 20


Making party bags: Grade 1 students in pairs separate groups of gift items (stickers, toys, stationary, etc.) and halve to pack into two bags. Item quantities start at two and may range to over 20, including some odd quantities which can’t be evenly split. “How many of these do you have? Can we separate this number into two, or halve it? How many is half? If we separate these items into two equal groups, will there be any left over?”

Grade 2s separate into four and eight bags.

Time Allocation: 15

Independent or Group Activities: Teacher Group or Focus:


This is an approach that has been used for division. Is that where you would head next with the students in grade 2?


This is a good activity for students to do. Is there a way that you could have more students involved and up the front?

As above Some students will have an itinerary of the items the students are separating, and calculate how many items will be in each group’s bags. The teacher will assist with the mathematical process and using a calculator.

“Group A has six pencils which they need to separate into two bags. So we type ‘6’ into the calculator because there are six pencils, and then ‘divide’ which is like separating, and then ‘2’ which is how many bags there are, and then we press ‘equals’ and it tells us how many pencils to put into each bag.”



How can groups of things be halved? What kind of numbers can be halved? What kind of numbers can’t be halved? What strategies did you use to separate the items into halves? Was it a good strategy? Would you try something different next time? Similar questions for quarters and eighths.

Time Allocation: 15


Tokens/counters (substitute for lollies) Interactive whiteboard or whiteboard and projector, and slideshow game 20 magnets Large quantities of suitable gift items for children Itinerary of gift items, and pencils At least one calculator with large buttons

References/Sources:

N/A



All numbers can be halved – it is just they don’t all have a whole number answer. Be careful not to teach things in maths that students will later find as not true.

Appendix D

Lesson 1 Worksheets

Appendix E

Lesson 3 Slideshow Game

Level 1

Level 2

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