Education  Mathematics (Elementary)
Curriculum topics  lessons
 General
 Addition & subtraction
 Counting
 Estimating
 Fractions, percentages & decimals
 Geometry
 Measurement
 Multiplication & division
 Number sense
 Patterns
 Problem solving
 Statistics & probability
 Transformations
 Variables, equations & algebra
Websites

Invitations to mathematicsFree ebooks to assist mathematics teachers of Grades 4, 5, 6 focused on various math strands such as number sense and estimation, geometry, data management, probability, patterns and algebra and measurement.

Lesson supportsfrom Ontario Junior Math Resources

Math Central: Resource Roomfrom University of Regina

Math to the maxEdmonton Public School Board, 19992002Series developed to support the Alberta math curriculum. Topics are: Patterns & Relations, Statistics & Probability, Number Operations, Number Concepts, Measurement, and 3D objects, 2D shapes & Transformations.
See also these topics in Curriculum topics  Lessons in this library guide for specific grade information. 
NRICH: enriching mathematicsClick on student homes, lower and upper primary for elementary level lessons.from University of Cambridge
Doucette resources

Double dare you [kit] : amazing math games using double dicePublication Date: 2003

Math Detective Beginning by Critical Thinking Publishing Staff; Terri HustedISBN: 9780894558023Publication Date: 2013

Math for Humans: : teaching math through 8 intelligences by Mark H. WahlISBN: 9780965641487Publication Date: 1999

Math Jam. 1 [CD] / Judy & David.Publication Date: 2007

Websites

Number: Adding and taking awayfrom: NRICH: enriching mathematicsPrimary grades 
In these activities, you can practise your skills with adding and taking away. You can also solve problems about what happens when we add or take away different numbers!
Articles

Complex Counting in KindergartenA team of teachers from the same New York City public school met to discuss and compare the Common Core State Standards for Mathematics (CCSSM) to their current math curriculum. The group consisted of four kindergarten teachers, a representative from the firstgrade teaching team, and the school's math coach. During the first meeting, the firstgrade teacher expressed a concern that many first graders relied on "counting up" to solve addition problems. She explained to the group that students who could not understand the commutative property when they arrived in September struggled when increasingly advanced addition strategies were taught. The goal for the group became clear: To find areas of the CCSSM that would provide opportunities for kindergarten students to build a strong foundation for advanced addition strategies. This article presents how the composing and decomposing small sets of objects can allow young students to see the whole group as well as the subsets that created the whole.
Doucette resources

Developing Essential Understanding of Addition and Subtraction for Teaching Mathematics in PrekindergartenGrade 2 by Janet H. CaldwellISBN: 9780873536646Publication Date: 2010

Math to the max: number operationsEdmonton Public School Board
Gr. 14, 6 available (Gr.5 missing)
Websites

Number: Counting, What's next?from: NRICH: enriching mathematicsPrimary grades  These challenges are all about counting and exploring the order of the numbers.
Doucette resources

Math to the max: number conceptsEdmonton Public School Board
Gr. 16 available. 
Math to the max: number operationsEdmonton Public School Board
Gr. 14, 6 available (Gr.5 missing)
Websites
Doucette resources

Math to the max: number conceptsEdmonton Public School Board
Gr. 16 available.

Estimation station [kit]Publication Date: 2011
Websites

Number: Bits of things (intermediate grades)from: NRICH enriching mathematicsIntermediate grades  What happens when you split an object or a few objects into different piles? Try these activities to find out more about fractions!

Number: Bits of things (primary)from NRICH: enriching mathematicsPrimary grades  What happens when you split an object or a few objects into different piles? Try these activities to find out!
Articles

Iteration: Unit Fraction Knowledge and the French Fry TasksOften, students who solve fraction tasks respond in ways that indicate inadequate conceptual grounding of unit fractions. Many elementary school curricula use folding, partitioning, shading, and naming parts of various wholes to develop children's understanding of unit and then nonunit fractions (e.g., coloring three of four parts of a pizza and naming it as threefourths). Yet, using parttowhole models for fractions rarely develops notions of rational numbers necessary for later proportional and algebraic reasoning. Through collaborative research and as an alternative to the partwhole approach, this article's aim is to teach fractions and solidify children's multiplicative notions of unit fractions through a core activity of unit iteration (i.e., using a single item, such as a paper strip of specific length, and repeating it a number of times to create and/or "measure" another unit). This article provides educators with an explanation of what the authors call the French Fry tasksa series of tasks based on unit iteration that work to bring about children's unit fraction knowledge.

Unwrapping Students' Ideas about Fractions :Sandwiching formative assessment items and instruction can yield insight into why students use particular strategies or notation.Supporting students to develop an understanding of the meaning of fractions is an important goal of elementary school mathematics. This involves developing partitioning strategies, creating representations, naming fractional quantities, and using symbolic notation. This article describes how teachers can use a formative assessment problem to elicit and understand students' ideas about the meaning of fractions. The fraction problem described in this article was designed using research on children's thinking in elementary mathematics, and it enables teachers to uncover students' understanding of the following essential aspects of understanding the meaning of fractions: (1) partitioning strategies; (2) representations; and (3) language and notation.
Doucette resources

Math Discoveries about Fractions and Decimals by Maxwell, Terry Burke.ISBN: 1564511901Publication Date: 1996

Math to the max: number conceptsEdmonton Public School Board
Gr. 16 available.

Pieceapizza fractions [kit].Publication Date: 2008

Uncomplicating Fractions to Meet Common Core Standards in Math, K7 by Marian SmallISBN: 9780807754856Publication Date: 2013
Websites

3D objects and 2D shapesfrom: Galileo.org

Geometry and Spatial Sense, Grades 4 to 6 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6from Ontario Ministry of Education, 2008

Shapes, Position and Movement: Shapesfrom: NRICH: enriching mathematicsPrimary grades  These activities are all about shapes!
Articles

Unfolding a ProblemIn this article, Sarah Currier, a math specialist at Elizabeth Hall International School in Minnesota, describes how she used origami in a deliberate manner to teach content. She shares how she uses paper folding to teach mathematical concepts, reinforce vocabulary, and as a problemsolving model. She also offers ideas for using origami in other classrooms.
Abstractor:
ERIC
Doucette resources

Building a Fish RackISBN: 1550592580

KEVA® maple.Publication Date: 2013

Magnatiles : 3D magnetic building tiles [kit]Publication Date: 2014

Math discoveries about geometry with manipulatives by Wallaker, Jillayne Prince.ISBN: 1564511685Publication Date: 1996

Math to the max: 3D objects, 2D shapes and transformationsEdmonton Public School Board
Gr. 16 available. 
Math to the max: patterns & relationsEdmonton Public School Board
Gr.16 available.

Patterns and Parkas  KitISBN: 9781550593082

Websites

Measurement, Grades 4 to 6 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6from Ontario Ministry of Education, 2008

Measurementsfrom: Galileo.org
Articles

Measures: Sensible guessesfrom: NRICH: enriching mathematicsPrimary grades  A sensible guess is a guess that you can back up with some information. Can you make some sensible guesses in these activities?

Tales, Tasks, Tools, and TalkThe importance of a literacybased approach to content learning, especially within elementary school grades, is not a new idea. During the past quartercentury, the use of children's literature as an effective teaching tool has gained popularity across all content areas (Thiessen 2004). The definition of literacy has expanded not only to include various print and nonprint media but also to incorporate quantitative literacy through the development of number, number sense, and measurement. Integrating measurement tasks with children's literature and classroom discourse builds a base for a quantitatively literate child. Providing opportunities for children to read, write, listen, and speak mathematically strengthens their connections among number, quantity, and symbol as well as linking language literacy and quantitative literacy. Foley, Strayer, and Regan (2010, p. 6) define quantitative literacy as "a form of general literacy" that combines numerical reasoning, measurement, statistical reasoning, modeling, and mathematical communication. The Better Mathematics through Literacy (BMTL) project has convinced the authors that quantitative literacy can be developed in concert with general language literacy, cognitively engaging tasks, and purposeful classroom discussion. The BMTL project is a professionaldevelopment initiative that shows teachers and intervention specialists how to use children's literature as a basis for studentcentered mathematics instruction in Kgrade 5. The tasks used in BMTL are tied to the tales in children's books, giving enhanced meaning to the phrase "story problem." Wellchosen measurement activities from BMTL invite earlygrade learners into the mathematical practices of sense making and reasoning through tales, tasks, tools, and talk. This article highlights teaching tips and sample tasks from the BMTL project that develop students' understanding of quantity and fluency in measurement for Kgrade 5 within the context of children's literature, writing, and communicating.

Unfolding a ProblemIn this article, Sarah Currier, a math specialist at Elizabeth Hall International School in Minnesota, describes how she used origami in a deliberate manner to teach content. She shares how she uses paper folding to teach mathematical concepts, reinforce vocabulary, and as a problemsolving model. She also offers ideas for using origami in other classrooms.

Using STEM to Reinforce Measurement SkillsTo master measurement, elementary school students need opportunities to discuss how they measured and applied their developing skills and reasoning in context. When measurement is taught without a context, students may struggle to make sense of the numbers and units involved. iSTEM (Integrating Science Technology Engineering in Mathematics) authors share ideas and activities that stimulate student interest in the integrated fields of science, technology, engineering, and mathematics (STEM) in K–grade 6 classrooms.
Doucette resources

Math to the max: shape & space: measurementEdmonton Public School Board
Grades 16 available.
Websites
Articles

Number: Multiplying and dividingfrom: NRICH: enriching mathematicsPrimary grades  Try these problems, which are all about multiplying and dividing different numbers.
Doucette resources

Factors, multiples and leftovers : linking multiplication and division. Teacher guide by Katherine Gavin; Linda Al  Sheffield; Suzanne Al  Chapin; Judith Al  DaileyISBN: 9780757532962Publication Date: 2006

Half & half : dividing & measuring [DVD]Publication Date: 2013

Lessons for Introducing Division: grades 34 by Maryann Wickett; Susan Ohanian; Marilyn BurnsISBN: 094135542XPublication Date: 2002

Math to the max: number operationsEdmonton Public School Board
Gr. 14, 6 available (Gr.5 missing)
Websites

Number: Why's ten important?from: NRICH:enriching mathematicsPrimary grades  In these tasks you can explore tens and ones, and learn about the place value of numbers.
Doucette resources



Math discoveries about numbers and operations with manipulatives by Callahan, Robert.ISBN: 1564511928Publication Date: 1996

Math to the max: number conceptsEdmonton Public School Board
Gr. 16 available.
Websites

Patterning and Algebra, Grades 4 to 6 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6from Ontario Ministry of Education

Patternsfrom: Galileo.org

Patterns: Working with patternsfrom: NRICH: enriching mathematicsPrimary grades  Have a go at making and exploring different patterns in these tasks.
Doucette resources

Designing PatternsISBN: 1550593188

Math to the max: patterns & relationsEdmonton Public School Board
Gr.16 available.

Pattern block sudoku [kit].Publication Date: 2008

Unifix sudoku [kit].Publication Date: 2007
Websites
Articles

Sharing Beans with FriendsUsing the children's book, Bean Thirteen to develop number sense and problem solving skills. (Bean Thirteen is available in the Doucette Library.)

Unfolding a ProblemIn this article, Sarah Currier, a math specialist at Elizabeth Hall International School in Minnesota, describes how she used origami in a deliberate manner to teach content. She shares how she uses paper folding to teach mathematical concepts, reinforce vocabulary, and as a problemsolving model. She also offers ideas for using origami in other classrooms.
Doucette Resources

Math to the max: number operationsEdmonton Public School Board
Gr. 14, 6 available (Gr.5 missing)

Navigating Through Problem Solving and Reasoning in Grade 6 by Denisse Rubilee Thompson; Bonnie H. LitwillerISBN: 9780873536073Publication Date: 2009

A Problem Solving Approach to Mathematics for Elementary School Teachers by Rick Billstein; Shlomo Libeskind; Johnny W. LottISBN: 0321331796Publication Date: 2006

Problem Solving in All Seasons, PrekindergartenGrade 2 by Kim Markworth; Jenni McCool; Jennifer KosiakISBN: 9780873537711Publication Date: 2015


Websites

Chance and uncertaintyfrom: Galileo.org

Data: Understanding informationfrom: NRICH: enriching mathematicsPrimary grades  These challenges will test your understanding of different types of information.

Data analysisfrom: Galileo.org

Data Management and Probability, Grades 4 to 6 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6from Ontario Ministry of Education, 2008
Articles

Practical Problems: Using Literature to Teach StatisticsIn this article the authors describe an instructional unit designed and taught in two classes of kindergarten children. The goals of the unit were to present a "driving question" to motivate the process of statistical investigation, to genuinely engage children in the stages of statistical investigation, and to facilitate them in experiencing an alternative data collection method. In an elementary school classroom, data are usually collected through surveys (asking people their favorite icecream flavor) or observing events (counting the colors of cars in the parking lot). A survey is a popular and effective data collection method (compare Cook 2008); nevertheless, for this unit the teachers wanted the children to experience an alternative method of data collection, namely "observation." They also wanted the students to experience statistics as a tool to investigate everyday problems. So, they presented the children with an ordinary problem: What puppet should a teacher buy for her class? To solve the problem, they would have to collect data to identify the character that appeared most frequently in a piece of children's literature. The teachers used the PPDAC (problem, plan, data, analysis, conclusion) cycle (Wild and Pfannkuch 1999) as a guiding framework for the unit. A bibliography is included.
Doucette resources

Kayak Design [Kit]ISBN: 9781550594041

Math discoveries about data and probability with manipulatives by Sammons, Kay B.ISBN: 1564511820Publication Date: 1996

Math discoveries about data & chance : grades 34 by Beth Mccord Kobett; Kay B. SammonsISBN: 1564511812Publication Date: 1999

Math to the max: statistics & probabilityEdmonton Public School Board
Gr.15 available.
Websites

Transformationsfrom: Galileo.org
Doucette resources

Math to the max: 3D objects, 2D shapes and transformationsEdmonton Public School Board
Gr. 16 available.

Studies in symmetry with pattern blocks [kit].Publication Date: 2088
Websites

Patterning and Algebra, Grades 4 to 6 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6from Ontario Ministry of Education

Relations and functionsfrom: Galileo.org

Variables and equationsfrom: Galileo.org
Articles

The Algebra ArtistMost people who are attracted to STEMrelated fields are drawn not by a desire to take mathematics tests but to create things. The opportunity to create an algebra drawing gives students a sense of ownership and adventure that taps into the same sort of energy that leads a young person to get lost in reading a good book, building with Legos®, playing a video game, or participating in a favorite hobby or sport. The Algebra Artist project described in this article for Algebra 1 Honors students asked for a minimum of twelve graphs to create the drawing. When an average of sixtythree graphs per student drawing were received, teachers knew that they had a project that captured student imagination, resulting in sustained effort, deep thinking (Carr 2010), and authentic learning. Creating algebra drawings inspires students to see graphing holistically, helping them achieve a "graphing sense" on par with number sense for elementary school and middle school students. Emphasis is on experimentation, discovery, and informal learning. Although much of the student work goes deep into high school curricula, some of the language and ideas are kept deliberately informal and appropriate for firstyear algebra students.

Just Say Yes to Early Algebra!Mathematics educators have argued for some time that elementary school students are capable of engaging in algebraic thinking and should be provided with rich opportunities to do so. Recent initiatives like the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) have taken up this call by reiterating the place of early algebra in children's mathematics education, beginning in kindergarten. Some might argue that early algebra instruction represents a significant shift away from arithmeticfocused content that has typically been taught in the elementary grades. To that extent, it is fair to ask, "Does early algebra matter?" That is, will teaching children to think algebraically in the elementary grades have an impact on their algebra understanding in ways that will potentially make them more mathematically successful in middle school and beyond? In this article, the authors share findings from a research project whose goal is to study the impact of a comprehensive early algebra curricular experience on elementary school students' algebraic thinking within a range of domains including generalized arithmetic, equivalence relations, functional thinking, variables, and proportional reasoning. The focus here is on the performance of thirdgrade students who participated in an early algebra intervention on a written assessment administered before and after instruction. The authors also discuss the strategies these students used to solve particular tasks and provide examples of the classroom activities and instructional strategies that they think supported the growth they saw in students' algebraic thinking. A bibliography is included.

Primary school students’ strategies in early algebra problem solving supported by an online gameIn this study we investigated the role of a dynamic online game on students' early algebra problem solving. In total 253 students from grades 4, 5, and 6 (1012 years old) used the game at home to solve a sequence of early algebra problems consisting of contextual problems addressing covarying quantities. Special software monitored the students' online working when solving the problems. Before and after the intervention a paperandpencil test on early algebra was administered. The data analysis revealed that the online working contributed to the students' early algebra performance. There was a significant gain in performance across all grades. The highest effect was found in grade 6. Out of the three strategy profile clusters that could be distinguished in the whole sample, the cluster dominated by using extreme values and the cluster characterized by the trialanderror strategy were most influential on the gain in early algebra performance. The students' level of online working, which was defined as a combination of online involvement and strategy use, appeared to have a marginally significant effect on the gain score for the total sample. Per grade there was no significant effect, yet the levels of online working were significantly related to grade. Free playing was mostly performed in grade 4, looking for answers in grade 5, and exploring relations slightly more in grades 5 and 6. About 17 % of the effect of grade on the gain score was mediated by the level of online working.
Doucette resources


Connecting arithmetic to algebra : strategies for building algebraic thinking in the elementary grades by Susan Jo Russell; Deborah Schifter; Virginia BastableISBN: 9780325041919Publication Date: 2011

Developing Essential Understanding of Algebraic Thinking for Teaching Mathematics in Grades 35 by Maria L. BlantonISBN: 9780873536684Publication Date: 2011

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Education, Undergraduate Education