Mathematics Department Unit Document
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UNIT FOCUS
Standard Emphasis
Standards for Mathematical Content
Critical Important
3.C.5: Multiply and divide within 100 using strategies, such as the relationship between multiplication and division (e.g., knowing that 8 x ********
5 = 40, one knows 40 ÷ 5 = 8), or properties of operations.
3.AT.1: Solve real-world problems involving addition and subtraction of whole numbers within 1000 (e.g., by using drawings and equations ********* with a symbol for the unknown number to represent the problem).
3.AT.2: Solve real-world problems involving whole number multiplication and division within 100 in situations involving equal groups, arrays, and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem).
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3.AT.5: Determine the unknown whole number in a multiplication or division equation relating three whole numbers.
3.C.3: Represent the concept of division of whole numbers with the following models: partitioning, sharing, and an inverse of multiplication. Understand the properties of 0 and 1 in division.
3.C.4: Interpret whole-number quotients of whole numbers (e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each).
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Mathematical Process Standards:
PS.1: Make sense of problems and persevere in solving them.
PS.2: Reason abstractly and quantitatively
PS.4: Model with mathematics
PS.8: Look for and express regularity in repeated reasoning
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Additional
Big Ideas/Goals
Essential Questions/
Learning Targets
“I Can” Statements
Vertical Articulation documents for K – 2, 3 – 5, and 6 – 8 can be found at: http://www.doe.in.gov/standards/mathematics (scroll to bottom)

Division can be seen as repeated subtraction.
The results of division can be obtained by repeated subtraction.
Division can also be used in the following ways:
Partition- given the total amount and the number of equal groups, then determine how many much in each group
Measurement- given the total amount in a group determine how many groups of the same size can be created
There is a relationship between the divisor, the dividend, the quotient and any remainder.
As the divisor increases, the quotient decreases; as the divisor decreases, the quotient increases.
Divisibility rules help us determine if a number will divide into another number without actually having to divide.
How are subtraction and division related?
How are division and subtraction alike?
How can division help you solve this problem?
How can I use what I know about skip counting, equal sharing, and forming equal groups to solve division problems?
How do the parts of a division problem relate to each other?
What do the parts of a division problem represent?
What happens to the quotient when the dividend increases or decreases?
How do you know if a number is divisible by 2,3,5,or 10?
I can demonstrate products of whole numbers.
I can divide any two numbers with a quotient within 100 by choosing the correct strategies.
I can determine when to divide in word problems.
I can identify the divisor, dividend, and quotient of any division problem.
I can determine relationship between quotient and divisor.
I can use divisibility rules to determine quotient
Beginning of Unit – Pre-Assessment
Assessment Name: Show Me What You Know
Assessment Type: Pre-Assessment
Assessment Standards: 3.C.5, 3.AT.1, 3.AT.2, 3.AT.5, 3.C.3, 3.C.4
Assessment Description: This assessment should allow students to internalize the meaning of the process standards by formulating a way for them to put them in their own words and give examples of work that represent the standard.
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Throughout the Unit – Formative Assessment
Assessment Name : Divisors
Assessment Type: Formative Assessment
Assessing Standards: 3.C.5, 3.AT.1, 3.AT.2, 3.AT.5, 3.C.3, 3.C.4
Assessment Description: Students need to experience problem-solving involving equal groups (whole unknown or size of group is unknown) and multiplicative comparison (unknown product, group size unknown or number of groups unknown) Students need to recognize the operation of division in two different types of situations. One situation requires determining how many groups and the other situation requires sharing (determining how many in each group). Students should be exposed to appropriate terminology (quotient, dividend, divisor, and factor).
Assessment Name: Find The Unknown Number
Assessment Type:
Assessing Standards: 3.C.5, 3.AT.1, 3.AT.2
Assessment Description: Students work in pairs to determine the unknown factors. Students solve problems with known facts.
Assessment Name: Word Problems
Assessment Type: Exit Ticket
Assessing Standards: 3.C.5, 3.AT.1, 3.AT.2
Assessment Description: Students should be able to read, interpret, solve and compose word problems dealing with multiplication and division.
End of Unit – Summative Assessments
Assessment Name: To Divide (TBD)
Assessment Type: Performance Task
Assessing Standards: 3.C.5, 3.AT.1, 3.AT.2, 3.AT.5, 3.C.3, 3.C.4
Assessment Description: Students will be assessed on division and multiplication facts. They
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will need to know and understand division as an unknown factor problem. They should be able to divide fluently within 100 using strategies and patterns between division factors
Unit Vocabulary
Key terms are those that are newly introduced and explicitly taught with expectation of student mastery by end of unit. Prerequisite terms are those with which students have previous experience and are foundational terms to use for differentiation.
Key Terms for Unit Prerequisite Math Terms
Dividend
Division
Divisor
Quotient
Equal parts
Equal shares
Multiplication
Remainder
Group
Divisible by
Difference
Array
Product
Factor
Include district and supplemental resources for use in weekly planning
Targeted Process Standards for this Unit
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PS.1: Make sense of problems and persevere in solving them
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway, rather than simply jumping into a solution attempt. They consider analogous problems and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” and "Is my answer reasonable?" They understand the approaches of others to solving complex problems and identify correspondences between different approaches. Mathematically proficient students understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
PS.2: Reason abstractly and quantitatively.
Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.
PS.3: Construct viable arguments and critique the reasoning of others
Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They analyze situations by breaking them into cases and recognize and use counterexamples. They organize their mathematical thinking, justify their conclusions and communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. They justify whether a given statement is true always, sometimes, or never. Mathematically proficient students participate and collaborate in a mathematics community. They listen to or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.
PS.4: Model with mathematics
Mathematically proficient students apply the mathematics they know to solve problems arising in everyday life, society, and the workplace using a variety of appropriate strategies. They create and use a variety of representations to solve problems and to organize and communicate mathematical ideas.
Mathematically proficient students apply what they know and are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later.
They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.
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PS.5: Use appropriate Tools Strategically
Mathematically proficient students consider the available tools when solving a mathematical problem.
These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software.
Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.
PS.6: Attend to precision
Mathematically proficient students communicate precisely to others. They use clear definitions, including correct mathematical language, in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They express solutions clearly and logically by using the appropriate mathematical terms and notation. They specify units of measure and label axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently and check the validity of their results in the context of the problem. They express numerical answers with a degree of precision appropriate for the problem context.
PS.7: Look for and make use of structure
Mathematically proficient students look closely to discern a pattern or structure. They step back for an overview and shift perspective. They recognize and use properties of operations and equality. They organize and classify geometric shapes based on their attributes. They see expressions, equations, and geometric figures as single objects or as being composed of several objects.
PS.8: Look for and express regularity in repeated reasoning
Mathematically proficient students notice if calculations are repeated and look for general methods and shortcuts. They notice regularity in mathematical problems and their work to create a rule or formula. Mathematically proficient students maintain oversight of the process, while attending to the details as they solve a problem. They continually evaluate the reasonableness of their intermediate results.
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