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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.
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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.
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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.
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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.
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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.
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Appendices Appendix A: One More Than and Two More Than
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Appendix B:
Near Doubles Fact
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Appendix C: Subtraction as Think Addition
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Appendix D: Move It
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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:
___ + ___ = ___ - ___