MATHEMATICS UNIT PLANNER Topic: Number Patterns Year Level: 3/4 Term: 4 Week: 9 Date: December 1st Key mathematical understandings (2-4 understandings only; written as statements believed to be true about the mathematical idea/topic):

Number relationships provide the foundation for

strategies that help remember basic facts

Combining knowledge of addition and subtraction

facts and partitioning aids computation.

Key AusVELS Focus / Standard (taken directly from AusVELS documents): Content strand(s): Number and Algebra Measurement and Geometry Statistics and Probability Sub-strand(s): Number and Place Value Level descriptions: Demonstrating the connection between addition and subtraction using partitioning or by writing equivalent number sentences Recognizing that certain single-digit number combinations always result in the same answer for addition and subtraction, and

using this knowledge for addition and subtraction of larger numbers Recognize and explain the connection between addition and subtraction Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for

computation Proficiency strand(s): Understanding Fluency Problem Solving Reasoning Understanding includes connecting number representations with number sequences, partitioning and combining numbers

flexibly.

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

Using object counting or verbal counting to determine the

answer

Using known information to logically determine an

unknown combination

Memorization of addition and subtraction facts in

isolation

Reinvent or generate known strategies or thought

patterns.

Key equipment/resources:

Whiteboard and whiteboard markers Maths books Pencils Dices Counters Ten-frames Quiz worksheet

Key vocabulary (be specific and include definitions of key words appropriate to use with students)

Addition: the act or process of adding or uniting

Subtraction: the operation or process of finding the

difference between two numbers or quantities, denoted

by a minus sign.

Equal: the same as, evenly proportioned or balanced.

Connection: association, relationship.

Computation: an act, process, or method of computing;

calculation.

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

The equal sign requires students to carry out an operation

The number to the right of the equal sign is the answer

Enthralled ideas of the use of mathematical language

Inadequate part-whole knowledge for the numbers 0 to

10 and/or an inability to trust the count

Key probing questions (focus questions that will be used to develop understanding to be used during the sequence of lessons; 3 5 probing questions):

What strategy could you use to work out the missing

number in a sentence?

What processes are opposite to each other?

What does the equal sign mean in an equation?

Links to other contexts (if applicable, e.g., inquiry unit focus, current events, literature, etc.):

Le

arni

ng 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 childrens 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 Using reasoning

strategies to enhance addition facts

Present students with an addition equation (4+2). Allow the students to answer it and discuss what other 2 numbers added together would equal the same as (4+2). Discuss the role of the equal sign and how the tuning in activity completed highlights equivalence.

Students will complete the activity One More Than and Two More Than with Dice and Spinners. In pairs; one partner will draw a circle with half labelled 2 more and the other half, 1 more, they will use their pencils as spinners. Using a dice the pair will alternate who will roll the dice. The number that it lands on becomes the focus number in that whichever side the spinner lands on the

As a class, we will share some of the equations created and discuss the strategies used develop new equivalent equations. What strategies did you

use to create new equations?

What new vocabulary would you use to describe 2 equations that are equal

Enabling prompt: Limit the range of options

on the spinner.

Extending prompt: Is it easier to create

equations that equal a larger number than smaller? Explain.

Direct observation of how well students were able to practice and enhance their addition facts completing the Spinner and Die activity. Students must show that they can create an equation that is of equal value to the one created using the dice and spinner.

pair together will either add 2 more or 1 more to the number rolled. Once they have created an equation using the dice and spinner they must create an equation of their own that equals the same.

to one another? If I changed the addition

sign to a subtraction would the equation still be equal?

Session 2 Using reasoning

strategies to enhance subtraction facts

We will recap the last session and refresh the students memory of addition facts through the Near-Doubles fact activity. They will need to put the near double on the double fact. This activity helps develop reasoning strategies to support them to move away from counting but instead become more efficient in recalling facts quickly and correctly.

Today we will be focussing on subtraction facts. In pairs, students will complete the activity Subtraction as Think-Addition. The idea of the activity is that, it is modelled in such a way that students are encouraged to think. Students will gradually use known addition facts to produce the unknown quantity or part. The activity highlights the relationship between parts and wholes between addition and subtraction. One partner will create a subtraction equation.

13 5 = 1. Count out 13 counters and

cover. 2. Count and remove 5,

keeping these in view. 3. Think: five and what

As a class, we will discuss the relationship between addition and subtraction emphasized in the Subtraction as Think-Addition activity. Students can share what they learnt and how the activity enhanced their learning of the topic. Did you notice that you

were using both addition and subtraction? How so?

Do you think this activity showed the relationship between addition and subtraction?

Would this activity be suitable for larger numbers?

Enabling prompts: What aspects of the activity

made subtraction easier? Focus on using numbers

that total to 10 or less. Make connections

between the modelling of the Subtraction as Think-Addition and session 1.

Extending prompts: Did you realize that you

were incorporating both processes together unconsciously?

Did the activity challenge you to use mental thinking strategies and then concrete materials?

The teacher will observe how well students were able to see the connection between addition and subtraction through the activity. That is, they were able to comprehend solving subtraction questions actually challenged them to use addition strategies instead.

makes thirteen? 8 is left. 13 minus 5 is 8.

4. Uncover. 8 and 5 is 13.

Session 3 Identifying

unknown quantities in subtraction equations

Pose the following task: if you did not know the answer to 8 + 5, how could you figure it out without counting? Encourage students to come up with more than one way. Students will Think-Pair-Share (ELLs and reluctant learners benefit from sharing their ideas with a partner and then with the class). We will discuss some of the strategies used that supported students to figure out the problem.

Independently students will complete the activity Take from the 20. Students need to roll a 10-sided dice and the number that is rolled becomes their answer to their equation. The equation will look like this:

20 (?) = ? (the number they rolled)

Students must identify the second number in the equation to make the equation true.

In pairs, students will test their partner using the equations they created and solved. They will read out their equation without telling the missing number and encourage their partner to solve it. In the same pairs, students will share one thing that they learnt from the activity.

Enabling prompts: Limit the starting number

to 10 instead of 20.

Extending prompts: What do we notice about

all the answers? If we used addition instead

of subtraction would the answers be greater?

How do you know this?

The teacher will rove amongst the groups of students during the session and listen in on the discussion of the processes they used when solving the equation. They will check this against their assessment checklist.

Session 4 Using reasoning

and visual strategies to enhance addition facts

Model using two ten-frames on the board. Without letting students see, place counters on each for example, six on one and seven on the other so that the top row is full (five counters) and the extras are in the next row of each ten-frame. Flash (uncover) for about 3 to 5 seconds and recover. Ask students how many counters they saw. Then uncover and have students explain how they

As a class we will complete the activity Move It, Move It. Students will work independently using a two ten-frames. Flash cards are placed next to the ten-frames, or a fact can be given orally. The students cover each frame with counters to represent the problem (9 + 6 would mean covering nine places on one frame and six on the other). Ask students to move it to

As a class we will discuss how Move It supported our understanding of visually representing the counters to utilize our number facts to become more efficient at addition. By moving the counters

how did it enhance your addition facts?

How did the ten-frames support your learning?

Enabling prompts: Limit the amount of

counters used.

Extending prompts: By moving the counters on

the ten-frame how did it enhance your learning visually? What number facts did you use?

The teacher will observe the students when we complete the task together. I will look for the use of number strategies and visual strategies on how and where the students placed the counter on the ten-frames.

saw it. Discuss how this activity supports students to recall addition facts.

decide a way to move the counters so that they can find the total without counting. Students will explain what they did and connect to the new equation. E.g. 9 + 6 may have become 10 + 5 by moving one counter to the first ten-frame. Emphasize strategies that are working for that student (5 as an anchor and/or Make 10 and/or Up Over 10).

How did you make the connection between the old equation and the new?

Session 5 Use equivalent

number sentences involving addition and subtraction to find unknown quantities.

As a class we will discuss what we have learnt throughout the unit. Using the students responses we will create a concept map.

Students will complete a mini quiz that highlights the relationship between addition and subtraction. The quiz encompasses number sentences separated with an equal sign and students are to fill in the blank spaces with a number that will make the number sentence true. There is also a question for more advance learners where they have the opportunity to create their own equivalent number sentence.

Students will reflect on the importance of using both addition and subtraction facts in mathematics and discuss how it enhances our learning.

The teacher will collect the students test sheets for correction. It is important for students to show both an understanding of addition and subtraction isolated but also vital for them to see the correlation between the two processes when creating equivalent number sentences.

Appendices Appendix A: One More Than and Two More Than

Appendix B:

Near Doubles Fact

Appendix C: Subtraction as Think Addition

Appendix D: Move It

Appendix E: Quiz

Name: ___________

Fill in the Missing Blanks Activity

5 + ___ = 10 2

3 + 7 = 17 - ___

9 + 6 = 20 - ___

4 + 3 = 7 - ___

12 + 3 = ___ - 3

8 + 1 = ___ - 3

15 + 4 = 20 - ___ 13 + 4 = ___ - 1 Create your own in the space below:

___ + ___ = ___ - ___