MATHEMATICS UNIT PLANNER

Topic: Volume and capacity Year Level: 1/2 Term: 4 Week: 8 Date:

Key mathematical understandings (2-4 understandings only; written as statements believed to be true about the mathematical idea/topic): • Compare the capacity of objects using

informal units.

• Use 1 liter as a benchmark to compare and categorize objects.

• Use the same unit to compare shapes/containers

Key AusVELS Focus / Standard (taken directly from AusVELS documents): Content strand(s): Number and Algebra Measurement and Geometry Statistics and Probability Sub-strand(s): Level descriptions: • Measure and compare the lengths and capacities of pairs of objects using uniform informal units

(ACMMG019) • Compare and order several shapes and objects based on length, area, volume and capacity using

appropriate uniform informal units (ACMMG037) Proficiency strand(s): Understanding Fluency Problem Solving Reasoning •

Key skills to develop and practise (including strategies, ways of working mathematically, language goals, etc.) (4-5 key skills only):

• Filling containers to the top without over filling or under filling.

Key equipment / resources:

• Goldilocks and the three bears

• Rice, sand and water

• Various measuring cups and containers

• Various types of building blocks

• Centi-cubes

Key vocabulary (be specific and include definitions of key words appropriate to use with students) • Capacity -Container • Equal -Volume • More /less • Full • Empty • More than • Less than • Estimation and actual

Possible misconceptions (list of misconceptions related to the mathematical idea/topic that students might develop):

• Taller containers always hold more liquid • Over estimating or under estimating the size

or a litre • Using different means of measurements to

compare. E.g. blocks and teddy bears (need for same unit to compare)

Key probing questions (focus questions that will be used to develop understanding to be used during the sequence of lessons; 3 – 5 probing questions): • If a container is taller does it always mean

it hold more water?

Links to other contexts (if applicable, e.g., inquiry unit focus, current events, literature, etc.): • Literacy – The Three Bears (narrative) • Science – accurate measurement

Lear

ning

st

rate

gies

/ sk

ills

Analysing Checking

Classifying Co-operating

Considering options Designing

Elaborating

Estimating Explaining

Generalising Hypothesising

Inferring Interpreting Justifying

Listening

Locating information Making choices

Note taking Observing

Ordering events Organising

Performing Persuading

Planning Predicting Presenting

Providing feedback Questioning

Reading

Recognising bias Reflecting Reporting

Responding Restating Revising

Seeing patterns

Selecting information Self-assessing Sharing ideas Summarising Synthesising

Testing Viewing

Visually representing Working independently Working to a timetable

MATHEMATICAL FOCUS

(what you want the children to come to understand as a result of this lesson – short,

succinct statement)

‘TUNING IN’ (WHOLE CLASS FOCUS)

(a short, sharp task relating to the focus of the lesson; sets the scene/ context for what students do in the

independent aspect. e.g., It may be a problem posed, spider diagram, an

open-ended question, game, or reading a story)

‘INVESTIGATIONS SESSION’

(INDEPENDENT LEARNING) (extended opportunity for students to

work in pairs, small groups or individually. Time for teacher to probe children’s thinking or work with a small group for part of the time and to also

conduct roving conferences)

‘REFLECTION & MAKING CONNECTIONS

SESSION’ (WHOLE CLASS FOCUS)

(focused teacher questions and summary to draw out the mathematics and assist children to make links. NB.

This may occur at particular points during a lesson. Use of spotlight,

strategy, gallery walk, etc.)

ADAPTATIONS

- Enabling prompt (to allow those experiencing difficulty to engage in active experiences related to

the initial goal task) - Extending prompt

(questions that extend students’ thinking on the initial task)

ASSESSMENT STRATEGIES

(should relate to objective. Includes

what the teacher will listen for, observe, note or analyse; what

evidence of learning will be collected and what criteria will be used to

analyse the evidence)

Session 1 • I can investigate capacity and volume

Brainstorm What is capacity? What is volume? Where are some places where you have seen capacity or volume?

Students are given an opportunity to “play” with different containers an their capacity” Students are shown to measure capacity they need to fill the container up to the top to show accurate capacity

Students come down to the floor to discuss their findings. Do the taller container always have the greatest capacity? If I overfill my container does that show me the real capacity of the container? What if I under-fill?

Enabling Students are guided. How do I fill my object? To the top? Do you think a taller object will fill more? Lets check our theory. Extending Students are given measurement cups. How could you use the numbers on the cup to work out which is the biggest and which is the smallest? Can you test your theory?

Assessment Roving through the classroom a “capacity and volume” checklist is marked on each student to gage their knowledge.

Session 2 • I can compare The capacity and volume of objects

Goldilocks and the three bears. The class is read goldilocks and three little bears the class are shown 3 bowls, which one of the bowls do you think is papa bears? Which one is baby bears? Which one is mumma bears? How do you know?

Goldilocks accidently broke all the bear’s bowls when she was tasting their porridge. They got vey upset and now they need new bowls!! Students rotate around different stations. At each station there are a variety of different containers. Students need to find the three bears new containers. The smallest one will be the for baby

Students come back to the floor. What strategies did you use to decide which container to choose for which bear? How did you know that baby bears container had the smallest capacity? Etc?

Extending: Can you find a set of containers where baby bears bowl has half the capacity of papa bears? How will you check? Enabling : Students are given 3 containers. Which one is the biggest which one is the smallest? How do you know? How can you prove

Assessment Students complete a self assessment sheet (appendix 1) The questions are read aloud for the EAL and low literacy students.

Which one will have the largest capacity? The students are encouraged to justify their choices. e.g place the bowls inside eachother measure uing rice or sand how can we check? Etc

bear the medium sized one for mumma bear and the one that can hold the most with the largest capacity for poppa bear. The class are spilt into 6 mixed ability groups. ( 5 groups of four and 1 group of 5) At each station they need to choose a container for each bear and record their choices. 2 stations of rice 2 stations of sand 2 stations of centicubes blocks?

it?

Session 3 • compare volumes of different objects and to create a benchmark of what a container that holds a litre looks like. I can use 1 litre as a benchmark

The three bears are having a dinner party and are organising all the drinks for their guests. Poppa bear, Mumma bear and baby bear have invited all their friends. The only problem is that they have lots and lots of different glasses and containers for the drinks. Poppa bear wants to make sure that his friends get more then a litre to drink mumma bear’s friends need ony 1 litre to drink and baby bear’s friend’s need less than a litre. They need HELP!!

- What is a litre?

-where have you seen

Students are broken up into mixed ability groups. Each group is given a 1 litre ‘bench march’ as a group student categorise the containers at each station into -Less that 1 litre -1 litre -More than one litre 1 station is a water station which is supervised by a teacher. -Water -sand -rice Students take photos on their Ipads of their choices.

Students come back to the floor. Which strategies did you use to know which containers were bigger or smaller then 1 litre? How did you know they were bigger or smaller than 1 litre?

Enabling: Students are only given 3 containers to compare. Which is the litre? How do you know? If you pour the lire into the smaller cup is there still more left in the litre bottle? Does that mean it is more or less than one litre etc. Extending. Students are not given a litre as a bench mark but use other measuring cups to create the litre What makes 1 litre? Students are provided with cooking measurements and other measurement objects. Which of these measuring cups can you use to make 1 litre?

Assessment The photos are review and assessed based on students container choice and verbal justification of how they used the 1 litre bench mark.

a litre? - how will I know whether my container/cup is bigger or smaller than a litre?

How many different ways can you make 1 litre?

Session 4 • Students

become aware that units must be the same to know how much capacity I can estimate how much capacity is in my object.

Estimating and actual. Students sit on the floor and are shown a container. If you were to estimate how many teaspoons of rice were in this container how many would there be? How do I estimate? What is estimating? How do I prove if my estimate is correct? Students are reminded that when they are estimating it is important to make sure each nit is the same size. e.g not to overfill or under fiil

Estimate and actual Using the worksheet in appendix 1 Students are given a list of objects that then need to estimate how many -Teaspoons of rice/sand/ -cups -mugs are in certain objects and then write down the actual. students then complete the sentence _____ had the smallest capacity ______had the largest capacity Students go off into mixed ability groups

Discussion What did you notice about your predictions and the actual amount? Were you surprised how many teaspoons fit in each container? What container had the smallest capacity? Which container had the largest capacity?

Enabling Students are placed in pull out group with a teacher to practice measuring and form discussion about how we could estimate what would have the largest capacity and which would have the smallest. Do my estimations match the size of the containers? Extending Find the difference between your estimate and actual using calculators (extended pull out group)

Assessment The post checklist begins to be marked and each student is assessed on whether they are able to estimate and understand the features of measuring.

Session 5 • How many

cubes fit in my box?

I can use the same unit to compare shapes.

Which one do I choose? Do I always have to use rice sand or water to measure the capacity of something or can I use anything?

4 posters 4 posters are put up around the room. They are labelled Less than 5 cubes Between 5-15 cubes

Discussion On the floor students look at the posters and we look at the less than 5 poster.

- What do we notice about all the objects on this

Extending Students make an estimate and then work out the actual. Then formulate the difference.

Assessment Checklist is check on the relevant categories.

Between 15-30 More then 30 Students are each given 6 post it’s each. Using unifix cubes, students measure how many unifix cubes are in: -Their shoe -a container of their choice -a patty pan and 3 other objects of their choice. Students draw the object and the relevant number of cubes onto a post it or write the name of the object and stick it onto the corresponding poster.

poster?

If there are less cubes does that mean there is less capacity? Twist and turn.

Enabling Students are given 5 shapes to measure which will all require less counting and have a spread across all poster categories.

Session 6 Volume I can use blocks to estimate the volume of a shape.

A discussion is had on volume. Who remembers what volume is? What does volume tell us? Where might I use volume? An example of a shape is built and as a class they “calculate” the volume.

In maths group students go to different stations containing different types of building blocks. Students build and record their buildings and their sizes.

Students come back to the floor and discuss their findings. Prompting questions such as. If your shape was 6 blocks in volume will it always look the same or will it look different?

Extending Pull out group Create a rectangular shape. volume and an array? Students are encouraged to Enabling Build something that uses 12 blocks Can you build another shape that uses 12 blocks but looks different? Why do you think it looks different?

The checklists are amended based on roving around the classroom and observing students.

Appendix Appendix 1:

Session 7 Brainstorm of volume and capacity. I have learned? Twist and turn to your partner and discuss some things you have learnt about capacity and volume

In mixed groups students create posters titled “I have learnt about capacity and volume”

Students bring posters back to the floor to share their ideas and what they have learnt.

Enabling : Students are given materials used throughout the previous 6 lessons to prompt memory.

The volume and capacity checklists are finalized on each individual and compared with original checklist.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Capacity!!!!!!!!!!!!!!!!!!!!!!!!!Name_______________!I"understand"what"capacity"is."""

""I"know"a"way"to"measure"capacity.""

"I"know"the"correct"way"to"fill"a"container"if"I"want"to"measure"it."""

"

Mixed ability grouping

Literacy Group 1 Group 2 Group 3 Group 4 Group 5 Samantha Caitlin Derrick Faith Sarah V Jennifer Nicholas Chelsea Phillip Chloe Harsha Sophia Minh Marga Sarah S Christian Jordan Vi Ganesh Richi Deana Ken Truong Leandro Bahkita Joyce

Mathematics Group 1 Group 2 Group 3 Group 4 Group 5 Phillip Samantha Caitlin Derrick Faith Minh Sarah S Jennifer Nicholas Chelsea Harsha Sophia Truong Bakhita Marga Jordan Christian Ganesh Sarah V Joyce Richi Deana Ken Chloe Leandro Vi

Same ability groups

Literacy

Group 1 High

Group 2 Medium

Group 3 Medium

Group 4 Medium

Group 5 Low

Samantha Jennifer Nicholas Chelsea Deana Caitlin Phillip Harsha Chloe Ken Derrick Sophia Minh Bakhita Truong

Faith Marga Sarah S Jordan Leandro Vi Christian Ganesh Sarah V Richi

Mathematics

Group 1 High

Group 2 Medium

Group 3 Medium

Group 4 Medium

Group 5 Low

Phillip Jennifer Nicholas Chelsea Deana Samantha Harsha Sophia Truong Ken

Caitlin Bakhita Marga Sarah s Chloe Derrick Jordan Christian Ganesh Leandro

Faith Sarah V Joyce Richi Vi

Minh

Thinking Routines Matrix from Making Thinking Visible by Ritchhart, Morrison & Church

Routine Key Thinking Moves Notes

Routines for INTRODUCING & EXPLORING IDEAS See-Think-Wonder Description, Interpretation & Wondering Good with ambiguous or complex visual stimuli Zoom In Description, Inference, & Interpretation Variation of STW involving using only portions of an image Think-Puzzle-Explore Activating prior knowledge, wondering,

planning Good at the beginning of a unit to direct personal or group inquiry and uncover current understandings as well as misconceptions

Chalk Talk Uncovers prior knowledge and ideas, questioning

Open-ended discussion on paper. Ensures all voices are heard, gives thinking time.

321 Bridge Activates prior knowledge, questioning, distilling, & connection making through metaphors

Works well when students have prior knowledge but instruction will move it in a new direction. Can be done over extended time like the course of a unit.

Compass Points Decision making and planning, uncovers personal reactions

Solicits  the  group’s  ideas  and  reactions  to  a  proposal,  plan  or  possible  decision.

Explanation Game Observing details and building explanations Variations of STW that focuses on identifying parts and explaining them in order to build up an understanding of the whole from its parts and their purposes

Routines for SYNTHESIZING & ORGANIZING IDEAS Headlines Summarizing, Capturing the heart Quick summaries of the big ideas or what stands out CSI: Color, Symbol, Image Capturing the heart through metaphors Non-verbal routine that forces visual connections Generate-Sort-Connect-Elaborate: Concept Maps

Uncovering and organizing prior knowledge to identify connections

Highlights the thinking steps of making an effective concept map that both organizes  and  reveals  one’s  thinking

Connect-Extend-Challenge Connection making, identify new ideas, raising questions

Key synthesis moves for dealing with new information in whatever form it might be presented: books, lecture, movie, etc.

The  4  C’s Connection making, identifying key concept, raising questions, and considering implications

A text-based routine that helps identifies key points of complex text for discussion. Demands a rich text or book.

Micro Lab A protocol for focused discussion Can be combined with other routines and used to prompt reflection and discussion

I used to think Reflection and metacognition Used to help learners reflect on how their thinking has shifted and changed over time.

Routines for DIGGING DEEPER INTO IDEAS What makes you say that? Reasoning with evidence A question that teachers can weave into discussion to push students to give

evidence for their assertions. Circle Viewpoints Perspective taking Identification of perspectives around an issue or problem. Step Inside Perspective taking Stepping into a position and talking or writing from that perspective to gain a

deeper understanding of it. Red Light, Yellow Light Monitoring, identification of bias, raising

questions Used to identify possible errors in reasoning, over reaching by authors, or areas that need to be questioned.

Claim Support Question Identifying generalizations and theories, reasoning with evidence, counter arguments

Can be used with text or as a basic structure for mathematical and scientific thinking.

Tug of War Perspective taking, reasoning, identifying complexities

Identifying and building both sides of an argument or tension/dilemma

Word-Phrase-Sentence Summarizing and distilling Text-based protocol aimed at eliciting what a reader found important or worthwhile. Used with discussion to look at themes and implications.