CDU A&R Assignment 2 Part 1 Maths sample Grade 4.

The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics (ACARA)

At this year level Grade 4:

Understanding includes making connections between representations of numbers, partitioning and combining numbers flexibly, extending place value to decimals, using appropriate language to communicate times, and describing properties of symmetrical shapes

Fluency includes recalling multiplication tables, communicating sequences of simple fractions, using instruments to measure accurately, creating patterns with shapes and their transformations, and collecting and recording data

Problem Solving includes formulating, modeling and recording authentic situations involving operations, comparing large numbers with each other, comparing time durations, and using properties of numbers to continue patterns

Reasoning includes using generalising from number properties and results of calculations, deriving strategies for unfamiliar multiplication and division tasks, comparing angles, communicating information using graphical displays and evaluating the appropriateness of different displays

By the end of Year 4, students choose appropriate strategies for calculations involving multiplication and division. They recognise common equivalent fractions in familiar contexts and make connections between fraction and decimal notations up to two decimal places. Students solve simple purchasing problems. They identify unknown quantities in number sentences. They describe number patterns resulting from multiplication. Students compare areas of regular and irregular shapes using informal units. They solve problems involving time duration. They interpret information contained in maps. Students identify dependent and independent events. They describe different methods for data collection and representation, and evaluate their effectiveness.

Students use the properties of odd and even numbers. They recall multiplication facts to 10 x 10 and related division facts. Students locate familiar fractions on a number line. They continue number sequences involving multiples of single digit numbers. Students use scaled instruments to measure temperatures, lengths, shapes and objects. They convert between units of time. Students create symmetrical shapes and patterns. They classify angles in relation to a right angle. Students list the probabilities of everyday events. They construct data displays from given or collected data.

What the student can do:

· Understands value and order of numbers not involving decimal place, to tens of thousands (Q16, Q23) (ACARA ACMNA072)

· Student can correctly perform addition with decimals if there is no required change of decimal place. (Although this does not necessarily demonstrate understanding (Q12)

· Choose appropriate strategies for multiplication

· Student is able to correctly perform multiplication, addition, subtraction, involving units, tens and hundreds but only if this does not involve decimal places. (Q1, Q8, Q20) (ACARA ACMNA076)

· Student can correctly perform division with decimals up to tens place only if there is no required change of decimal place. (Compare Q 25 correct with Q19 incorrect)

· Student is able to multiply whole numbers not involving decimal places (Q12)

· (ACARA ACMN076)

· Student is able to recognise maximum point in a graph and select data from a graph (Q 4 Wk 36)

· Student can interpret and calculate 8-minute intervals in time (Q 21, Wk 36) (ACARA ACMMG086)

· What student is unable to do correctly.

· Student cannot perform the operation of subtraction involving numbers with different place values (Q2, i.e., 4.3 + 0.9)

· Student is unable to subtract numbers expressed as a fraction (Q4)

· Student is unable to express a fraction in an equal but different parameter

· (Q5, i.e., 10/30 = /15)

· Student is unable to correctly perform addition when units are expressed with more than one decimal place (Q7, i.e., 0.03 + 8 +0.2)

· Student is unable to interpret cm as a fraction of a meter (Q9)

· Student is unable to perform operations involving letter substitution for numbers. i.e., algebraic equations (Q11)

· Student is unable to interpret roman numerals (Q13, Q17, Wk 36)

· Student is unable to interpret ml as a fraction of a litre (Q14)

· Student is unable to name a quadrilateral shape (Q15)

· Student is unable to multiply or subtract numbers that are expressed in decimal points (Q18, Q21)

· Student is unable to perform division with numbers involving tens and hundreds (Q19)

· Student is unable to perform subtraction of numbers involving minutes and seconds expressed as a decimal (Q21)

· Student unable to round numbers involving decimals to hundredth place (Q22)

· Student unable to express a fraction as a decimal (Q24)

· Student either unable to interpret minimum point on a graph, or does not know order of months or hurried the answer (Q4, Wk 36)

· Student unable to interpret relationship between fractions (Q5)

· Student unable to correctly apply multiplication to real life scenario (Q12, Wk 36)

· Student unable to perform division involving numbers with 100th place value (Q19)

· Student unable to do long division (Q13, Wk 36)

· Student unable to correctly interpret meters as a fraction of a km and apply to a real life scenario (Q23, Wk 36)

· Student unable to interpret a ratio (Q24, Wk 36)

· Student does not understand the concept of scales and balance to measure weight (Q17)

Student does not understand the following

· Concept of decimal place (Q2, Q7, Q18)

· Concept of fractions or how recorded (Q4) (Q2)

· Relationship between decimals and fractions (Q18)

· How to interpret roman numerals (Q13, Q 17, Wk 3)

· Relationship between ml and ltrs; meters and Km (Q9, Q14 & Q 23 Wk 36)

· how to apply mathematical concepts to everyday problem solving (Q21, Q23, Wk 36, Q24, Wk 36

· How to represent common equivalent fractions (Q 5)

· How to interpret algebraic problems (Q 11)

· How to interpret the cross section of a solid (Q 15, Q 14 Wk 36)

· Student does not

· Choose appropriate strategies for division

· Recognise common equivalent fractions

· Locate familiar fractions

· Solve simple purchasing problems

· Understand that fractions can be represented as decimals (WS2)

· Show fluency in problem solving (Compare Q6, correct answer with Q19, Wk 36, incorrect answer due wording)

Outline of assessment of student work and teaching implications.

The student understands the value and order of numbers up to hundred thousand - place value and can perform the operation of addition, subtraction and multiplication up to the thousands when using whole numbers. The student can also perform simple division but has not yet developed strategies for larger numbers or those not divisible without a remainder i.e., long division. The student has not yet grasped the concept of fractions, decimal place, their relationship to each other and their different forms of expression.

Fluency is lacking in regard to problem solving and applying mathematical concepts to everyday situations. Roman numerals, algebraic expressions and operations using decimal currency are not yet mastered.

Teaching implications i.e., “where to next”

Assess student’s knowledge using a format other than written worksheet.

Assess using a Grade 3 worksheet to see where student “is at”

Research why their performance might be low

Give explicit instruction about fractions, percentages and decimal place

Provide opportunity for student exploration and practice. Scaffold their learning. Use games such as concentration, snap or old maid.

Consider an adapted curriculum if it was found that this student suffered from some disorder such as autism, foetal alcohol syndrome, otis media, family problems or otherwise.

Step 1: Show an interesting u tube in relation to fractions and decimals, to gain attention.

Plan an explicit teaching session showing how groups can be broken into parts. That these selected parts are a proportion of the whole. That the proportion can be expressed as a fraction.

Step 2: Talk the student through (scaffolding) taking a proportion from a group and expressing it as a fraction. Number selected / Total number available. i.e., Take 2 oranges out of the fruit box that contains 6 apples. Therefore written as 2/6. Demo as pairs to show the same as 1 part: 2 parts i.e. 2 fruit: 4 fruit. Use fraction cards.

Step 3: Provide the opportunity for the student to explore by them self as well as part of a group.

Authentic examples are: (i) Packing a picnic with specific fractions of fruit

(ii) Sharing out pieces of cake (iii) Making a cake, measuring ingredients.

Step 4: Play some games for consolidation:

Step 5: Conduct assessment: (to help forward plan and give feedback).

Correctly measure ingredients i.e. 2/3 cup of flour and record it on a worksheet. Correctly give change from a shopping transaction, when buying ingredients. Correctly cut cake so the group all get an equal square and all cake used up. Maths worksheet.Use an on line computer resource to consolidate explanations and consolidate understanding through practice problem solving exercises.

Step 6: Reassess through further worksheets and a project.

Resources:

http://www2.mathsonline.com/

http://www.teachingideas.co.uk/maths/contents_fractions.htm

http://www.acara.edu.au/curriculum/worksamples/AC_Worksample_Mathematics_4.pdf

Writing sample grade 3

Year 3 Australian Curriculum

Language:

Text structure and organization:

Uses sentence structure to tell a story (ACELA 1478)

Uses the type of sentence structure found in a narrative text (ACELA1478)

Uses the correct tense for telling a story (ACELA1478)

Expressing and developing ideas:

Demonstrates use of a clause with correct subject verb agreement (ACELA1481)

Demonstrates correct use of verbs to represent doing/action (ACELA1482)

Demonstrates correct use of tense structure to express timing of an event (ACELA1482)

Demonstrates correct knowledge of sound-letter relationships (ACELA1485)

Literature:

Demonstrates ability to create a text using characterization, mood and dialogue (ACELT1791)

Literacy:

Demonstrates ability to plan, draft and publish an imaginative text, using text structures and language features, appropriate to the audience (ACELY1682)

Demonstrates ability to type using a computer and a software program to word process a document to a limited degree (ACELY1685)

Where to from here

Expand upon and consolidate an understanding of how paragraphs form a key organisational feature of written texts.

Introduce word contractions as used in informal language and model how apostrophes of contraction are used to signal missing letters.

Explain that a unit of grammar with a subject verb agreement is referred to as a clause. Model some examples. Practice with work sheets E.g. Cloze.

Explain and model use of commas.

Model ways of expressing an opinion in a text.

Practice and consolidate high frequency sight words.

Summary

This text demonstrates solid evidence of correct use of tense and an emerging use of good sentence structure. There is a strong sense of a storyline, however more guidance is required to develop a better flow of ideas through the use of connecting words and phrases. Punctuation needs to be improved upon, incorporating the use of use of more phrases, commas, capital letters and full stops. Knowledge of sight words is poor and needs regular practice.

Resources: The Australian Curriculum, First Steps Writing, 2nd edition , Winch et al. Literacy 4th Edition, Ed helper.

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J.Ramsay Student No S994096

ETP425 A&R Assignment No.2