Early&Years!Math!!
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Manitoba(Rural(Learning(Consortium(
Early(Years(Math(
Backward(Planning(Sample(
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Acknowledgements!
Introduction!
Grade!1!Math,!Strand:!Number!
Grade!2!Math,!Strand:!Number!
Grade!3!Math,!Strand:!Number!
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© 2013 mRLC – Manitoba Rural Learning Consortium
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Manitoba(Rural(Learning(Consortium(
Early(Years(Math(
Backward(Planning(Sample(
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Early!Years!teachers!from!across!rural!Manitoba!have!developed!this!document.!The!mRLC!Early!Years!Math!Backward!Planning!Cohort!was!made!up!of!the!
following!members:!
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Janice!Hamilton!!!!!!!!
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Lois!Mauthe!!!!!!!!!!!
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Stephanie!Hildebrand!!!!!!!!!!!!
Tabitha!Johannesson!!!!!!!!!!!!!
Amber!Bieganski!!!!!!!!!!!!!!
Natalie!Hlady! !
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Andrea!Maxwell!
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Connie!Johnson!!
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Tara!Reimer! !
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Trish!Goosen! !
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Allan!Stevenson!!
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Kim!Koop!
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© 2013 mRLC – Manitoba Rural Learning Consortium
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Prairie!Spirit!
Pine!Creek!
Garden!Valley!
Evergreen!
Whiteshell!!
Sunrise!
Sunrise!
Hanover!
Hanover!
Lord!Selkirk!
Sunrise!
mRLC!Facilitator!
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Introduction
This draft document is intended to support teams of Early Years teachers in planning, teaching, assessing, and reporting on their Math programs. Teams of
rural teachers developed the backward planning samples you see here. They used the mRLC Essential Learning and backward planning templates, the
Manitoba Curriculum, and other related resources. The mRLC Essential Learning and backward planning templates helped teachers summarize and
plan around important ideas and core processes that are central to the discipline and that have lasting value beyond the classroom.
This sample material includes:
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a backwards plan template (that was used with the corresponding mRLC Essential Learning template)
an outcome based grade book page
a common assessment (s)
samples of student work and rubrics based on a the report scale of 1-4
black line masters (where applicable)
a list of resources
mRLC believes that a collaborative planning process using mRLC Essential Learning documents and backward planning is key in developing teachers’
knowledge, expertise and professional competencies. This in turn improves student engagement and learning. mRLC Essential Learning and backward
planning documents challenge the status quo of those existing planning, teaching and assessment practices that are often done in isolation with little regard
given to such questions as,
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“Why is this important to teach in the first place?”
“What are the essential skills, 21st century values and dispositions that must be imparted to students through this course of study?”
“ How can this be accomplished in an engaging and creative way that will capture all students’ interest and talents?”
“ What and how will evidence be collected to determine what students know, have learned, or have yet to learn?”
Backward Planning captures the important ideas and core processes that are central to the discipline, it allows for a 21st century lens and the integration of
provincial initiatives such as student engagement, social justice, sustainable development…. mRLC believes teachers will best acquire these skills together,
overtime - learning constructively with “ an expert” guiding the process.
This is work that requires deep thinking, time and practice to get it right. mRLC thinks this is time well spent.
The value is in the doing.
If the planning process is rigorous and thoughtful all students will be well served. It will take multiple years for teachers to master the backward planning
process. It’s a process that will fundamentally impact every level of learning and teaching. Divisions that embark on supporting a backward planning
process will, overtime, create a professional culture where standards and experience are shared as a way of doing business. They will have cultivated a level
of professional practices that will have a huge impact on student learning.
What we do know is that shift takes multiple years and requires a lot of guided professional practice, trail, error, reflection, collegiality and administrative
support to accomplish.
© 2013 mRLC – Manitoba Rural Learning Consortium
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Teachers are expected to design plans that create engaging 21st century learning environments for their students - environments that are inquiry based,
collaborative and problem solving in nature and that use important ideas – this being the case then it is incumbent that professional development experiences
provide 21st learning environments for teachers. How else will they be able to duplicate this in their classrooms?
These backward plans can serve as a testament to a process that engages groups of teachers in a collaborative process of designing engaging and rigorous 21st
century learning and assessment opportunities for students. It is important to note that the attached templates are intended to serve as an example of how
teachers might plan using essential learning and backward planning. The document should be used alongside the Manitoba Curriculum Framework of
Outcomes for Math, as well as the grade-specific support documents. In addition, teachers are encouraged to consider the following issue:
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Although the templates have been organized by specific strands of the Math curriculum, the overall program is intended to be presented
as a spiral curriculum using a planning approach that is interwoven and explored throughout the year and over multiple years.
What is backward planning?
Backward planning is a method of designing curriculum"so that the curriculums’ intention is realized. Setting goals before choosing instructional methods
and forms of assessment"breathes"life"into"the"curriculum. Backward planning of curriculum involves three stages:
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Identify the results desired
Determine acceptable levels of evidence that the desired results have occurred
Design activities that will make desired results happen
Backward planning challenges "traditional" methods of curriculum planning. In traditional curriculum planning, a list of content that will be taught is created
and/or selected. In backward planning, the educators starts with goals, creates or plans out assessments and finally makes lesson plans. Backward planning
process is like using a "road map". In this case, the destination is chosen first and then the road map is used to plan the trip to the desired destination. In
contrast, in traditional curriculum planning there is no formal destination identified before the journey begins.
The idea in backward planning is to teach toward the "end point" or learning goals, which typically ensures that the content taught remains focused and
organized. This, in turn, aims at promoting better understanding of the content or processes to be learned by students. The teacher is able to focus on
addressing what the students need to learn, what data can be collected to show that the students have learned the desired outcomes and how to ensure the
students will learn. (Wiggins, McTighe)
What mRLC teachers are saying about backward planning….
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“ It’s extremely beneficial having the opportunity to collaborate with colleagues. This was awesome professional development
and it gave me great insight and ideas.”
“I grew as a professional. I made new contacts. I have shared learning with the grade groups in my school and division. I got
another chance to use backward design.”
“ I taught our draft unit and the growth was significant for my students and myself!”
“ Enhanced clarity and consistency in instruction and assessment, the development of exemplars for each grade scale of the new
provincial report card sets a consistent standard.”
© 2013 mRLC – Manitoba Rural Learning Consortium
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Grade&1!Mathematics*! !
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!! !Strand!!
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Table(of(Contents(
1. Backward!Planning!Sample!Template! !
2. Grade!Book!Sample!
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3. Assessments!
Pre!Assessments:!!
All!the!facts!with!Student!Samples!
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Strategy!Sort!with!Student!Samples!
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Number!Web!with!Student!Samples!
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Common!Assessments:!
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Tariq!and!the!Horses!with!Student!Samples!
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Fact!Family!Story!Problem!with!Student!Samples!
People!on!the!Bus!with!Student!Samples!!!!!!!
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Create!your!own!Story!Problem!with!Student!Samples!
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Math!Problem!of!the!Day!with!Student!Samples!
10!Facts!!Count!on!1!More!!Make!a!10!with!Student!Samples!
10!Facts!!Count!Back!1!Less!!Use!Doubles!with!Student!Samples!
4. Black!Line!Masters!
Fact!Families!
Doubles!
More!Fact!Families!
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© 2013 mRLC – Manitoba Rural Learning Consortium
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Grade(1(
Strand:(Number(
Backward(Planning(Sample(Template(
Stage(One:(Identify(Desired(Learning(
What%aspect%of%the%strand/unit%are%you%focusing%on%in%this%plan?%%
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Mathematical(Processes(
Communication!(C)!
Connections!(CN)!
Reasoning!(R)!
Technology!(T)!
Visualization!(V)!
Problem!Solving!(PS)!
Mental!Math!and!Estimation!(ME)!
1.N.9!and!1.N.10!
""1.N.9."Demonstrate"an"understanding"of"addition"of"numbers"with"answers"to"20"and"their"corresponding"subtraction"facts,"concretely,"pictorially,"
and"symbolically,"by"
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Using familiar and mathematical language to describe additive and subtractive actions from their experience
Creating and solving problems in context that involve addition and subtraction
Modeling addition and subtraction using a variety of cornet and visual representations, and recording the process symbolically
"""""""(C,"CN,"ME,"PS,"R,"T,"V)"
1.N.10."Describe"and"use"mental"mathematics"strategies"including"
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Counting on, counting back
Using one more, one less
Making ten
Starting from known doubles
Using addition to subtract to determine basic addition and related subtraction facts to 18
"""""""(C,"CN,"ME,"PS,"R,"T,"V)"
© 2013 mRLC – Manitoba Rural Learning Consortium
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Key Vocabulary:
Operations: addition, add, sum, total, more, subtract, subtraction, difference, less, story problem, fact.
Strategies: counting on, counting back, one more, one less, making 10, doubles, addition fact, subtraction fact
Enduring!Understanding:!
Essential!Questions:!
1. How!can!mental!math!strategies!enable!me!to!become!an!
efficient!mathematician!in!my!world?!
2. (How!are!mental!math!strategies!going!to!make!math!easier!
for!me?)!
3. How!can!being!able!to!solve!addition!and!subtraction!
problems!affect!my!quality!of!daily!life?!
4. (How!can!solving!problems!help!me!make!decisions?)!
Students!will!know!and!understand!how!to!take!apart!and!put!together!
quantities!and!understand!that!addition!and!subtraction!are!inverse!
operations.!
Students!will!know….!
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Students will know and understand how to take apart and
put together quantities and understand that addition and
subtraction are inverse operations.
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Students!will!be!able!to…!
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Students will answer addition and subtraction questions to
20, concretely, pictorially, and symbolically
Facts to 18: making doubles, making 10’s, start from
known doubles using addition and subtraction
Use familiar and mathematical language to describe
additive and subtractive actions from their experience
Create and solve problems in context that involve addition
and subtraction
Describe and use the following mental math strategies
counting on and counting back
Using one more and one less
Making ten
Starting from known doubles
Using addition to subtract
To determine the basic addition and related subtraction
facts to 18
Recall of one more and one less, complementary
(compatible numbers) that adds up to 5 and 10, doubles
(5+5), and that are related subtraction facts is expected
by the end of grade one.
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© 2013 mRLC – Manitoba Rural Learning Consortium
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Grade(1((
Strand:(Number(
Stage(Two:(Determine(Acceptable(Evidence(
Address the questions through these assessments …
Formative(
Summative(
Pre!AssessmentZ!
Write!
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All!the!facts!
PartZPart!Whole!Dot!Flash!Cards!
Strategy!Sort!
Number!web!
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Write!and!solve!your!own!addition!word!problem.!Show!your!
answer!pictorially!and!using!a!number!sentence.!Prove!your!
answer!using!subtraction.!!
How!Many!Ways!
All!the!Facts!
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Say!
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Verbally!explain!the!strategy!you!used.!
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Do!
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• Show!how!you!got!your!answer!using!manipulatives.!i.e.!Base!
Ten!Blocks,!Manipualtives!etc.!BLM!1.N.9!and!10.1!(gr.1!support!
document)!
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© 2013 mRLC – Manitoba Rural Learning Consortium
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What are the performance indicators?
Report Card
Categories
Knowledge and
Understanding
Questions
How can I take apart and
put together quantities?
Level 1
Has difficulty...
Level 2
Needs
some
support...
Mental Math and
Estimation
How can I take apart and
put together quantities
using mental math
strategies?
Has difficulty...
Needs some
support...
Problem Solving
How can I create and
solve problems using
addition and subtraction?
Has
difficulty....
Needs some
support...
Level 3
Level 4
Usually arrives
at an accurate
solution...
Consistently and independently
demonstrates an understanding of
addition of numbers with answers to and
their corresponding subtraction facts,
concretely, pictorally and symbolically.
Usually arrives
at an accurate
solution...
Consistently and independently finds
the sum and differences for quantities to
20(concretely, pictorally and
symbolically) using: doubles, making
10,one more, one less, starting from a
known double and using addition to
solve subtraction
Usually arrives
at an accurate
solution...
Consistently and independently creates
and solves problems in context that
involve addition and subtraction
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© 2013 mRLC – Manitoba Rural Learning Consortium
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Grade(1(
Strand:(Number(
Stage(Three:(Plan(Learning(Experiences(
Learning%Sequence:!
Activate:!Shake!SSpill!and!Record!(partZpart!whole!activity)!Put!10!twoZsided!coins/beans!in!a!container.!!Spill!onto!table.!!Have!students!sort!them!into!the!
two!groups.!!(i.e.!white!and!red).!!Record!the!number!sentences!as!a!class.!!Do!this!several!times.!!Discuss!any!patterns!they!see.!!ReZdo!the!activity!with!a!
different!number!of!counters!and!models.!(ie.!ten!frames,!dot!cards,!etc.)!!!What!do!students!notice?!
Acquire:!Use!a!real!life!problem.!!I!have!10!cookies.!!I!have!to!share!some!with!my!dad.!!!I!do!not!have!to!share!them!fairly.!!What!are!the!different!ways!I!
could!share!them!with!him?!!Draw!and!share!your!answer.!!RoleZplaying!it!is!an!option!as!well.!!As!a!class,!discuss!the!different!possible!answers!and!why!
they!each!work!or!don't!work.!
Play!"Power!of!Ten"!games!such!as!"Power!of!10",!"Power!of!9"!and!"Power!of!8"!!(Trevor!Calkins!resource)!
Build!number!trains!to!represent!different!number!combinations!to!represent!i.e.!7.!(See!Grade!1!support!document!for!BLM's!for!students!to!record!their!
work!in!different!colors.)!!Record!fact!families!for!these!trains!symbolically.!
Fact!Sorts!and!Number!webs!to!discuss!how!different!students!would!solve!different!facts!(purpose!Z!to!discuss!and!name!strategies/common!vocabulary.)!!
Suggestion!to!create!a!bulletin!board!of!facts!and!strategies!used.!!
Use!various!Greg!Tang!stories!to!have!students!share!how!they've!determined!the!number!of!objects!in!an!illustration.! !
Apply:!!Provide!students!with!word!problems!to!solve.!!Then!students!create!and!solve!their!own!problems.!!(See!page!45!of!Grade!1!Math!Support!
Document!to!be!sure!a!variety!of!different!kinds!of!word!problems!are!used!with!students!throughout!the!year.)!!!
Note:!!These!lessons!are!a!series!of!lessons!that!are!meant!to!be!taught!repetitively!throughout!the!year,!varying!the!manipulatives!being!used!and!the!
complexity!of!the!numbers.!!Both!subtraction!and!addition!should!not!be!taught!exclusively!alone.!
Resources:!!
Mathematics!Support!Document!Z!gr.1!
Power&of&Ten&Trevor&Calkins&
Teaching&Student&Centered&Mathematics&Grades&KZ3!John!A.!Van!de!Walle!
Hands&on&Problem&Solving&Jennifer&Lawson&
© 2013 mRLC – Manitoba Rural Learning Consortium
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Sample Grade Book
Grade One Math
Strand: Number
4 Very good understanding
3 Good understanding
2 Basic understanding
1 Limited understanding
ND Not yet demonstrated
Enduring Understanding: Students will know and understand how to take
apart and put together quantities and understand that addition and subtraction
are inverse operations.
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Report Card Categories
Knowledge and Understanding
Essential Question
How can I take apart and put together
quantities?
Mental Math and Estimation
Essential Question
How can I take apart and put together
quantities using mental math strategies?
Evidence from Assessments
Using Ten
Frame(s)
# web
Problem Solving
Essential Question
How can I create and solve problems using addition and
subtraction?
Evidence from Assessments
Strategy Sort
All the Facts
(addition)
Evidence from Assessments
All the Facts
(subtract.)
Represent/ solve
an addition story
problem
pictorially or
symbolically
Represent/
solve a
subtraction
story problem
pictorially or
symbolically
Create and
Solve a story
problem
(addition)
Create a word
problem for a
given fact family
Students
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