MADISON COUNTY PUBLIC SCHOOLS

District Curriculum Map for Mathematics: Grade 5

Unit 2

Unit Description / Unit 2
Operations with Whole Numbers
suggested Length: 3-4 weeks
Big Idea(s)
What enduring understandings are essential for application to new situations within or beyond this content? / Enduring Understanding
  • Develop fluency with whole number operations and reasonable estimates
Enduring Skills Rubric measures competency of the following skills:
  • Interpret appropriate operation for a word problem
  • Recognizes reasonableness of answer using estimation strategies
  • Fluently multiply and divide by 10 and powers of 10
  • Fluently multiply multi digit whole numbers with the standard algorithm
  • Accurately divides 4 digit dividends by 2 digit divisors using any strategy.
  • Constructs and communicates a well-organized and complete written response using a logical progression of steps.

Essential Question(s)
What questions will provoke and sustain student engagement while focusing learning? /
  • What is the relationship between multiplication and division?
  • How do we solve problems with whole numbers?

Standard(s) / Standards for Mathematical Practice
  1. Make sense of problems and persevere in solving them. Students solve problems by applying their understanding of operations with whole numbers, including the order of operations. Students seek the meaning of a problem and look for efficient ways to solve it.
  2. Reason abstractly and quantitatively. Students demonstrate abstract reasoning to connect quantities to written symbols and create a logical representation of the problem at hand. Students write simple expressions that record calculations with numbers and represent numbers using place value concepts.
  3. Construct viable arguments and critique the reasoning of others. Students construct arguments using concrete referents, such as objects, pictures, and drawings. They explain calculations based upon models and properties of operations and rules that generate patterns. They explain their thinking to others and respond to others’ thinking.
  4. Model with mathematics. Students use base ten blocks, drawings, and equations to represent place value. They interpret expressions and connect them to representations.
  5. Use appropriate tools strategically. Students select and use tools such as estimation, graph paper, and place value charts to solve problems with whole number operations.
  6. Attend to precision. Students use clear and precise language (math talk) in their discussions with others and in their own reasoning. Students use appropriate terminology when referring to operations with whole numbers.
  7. Look for and make use of structure. Students use properties of operations as strategies to add, subtract, multiply, and divide with whole numbers. They explore and use patterns to evaluate expressions. Students utilize patterns in place value and powers of ten and relate them to graphical representations of them.
  8. Look for and express regularity in repeated reasoning. Students use repeated reasoning to understand algorithms and make generalizations about patterns. Students connect place value and properties of operations to fluently perform operations.
Standards for Mathematical Content
5.NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm.
5.NBT.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
5.NF.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, notingthat 3/4 multiplied by 4 equals 3, and that when 3-wholes are sharedequally among 4 people each person has a share of size 3/4. If 9 peoplewant to share a 50-pound sack of rice equally by weight, how manypounds of rice should each person get? Between what two whole numbersdoes your answer lie?
Supporting Standard(s)
Which related standards will be incorporated to support and enhance the enduring standards? / 5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
5.MD.1 Convert among different sized standard measurement units within a given measurement system (e.g., covert 5 cm to 0.05 m), and use the conversions to solve multi-step, real world problems.
Instructional Outcomes
What must students learn and be able to by the end of the unit to demonstrate mastery? / I am learning to…
  • Fluently multiply a 4 digit factor by a 2 digit factor using the standard algorithm
  • Find whole-number quotients of whole numbers with up to four-digit dividends and two- digit divisors
  • Use strategies based on place value, the properties of operations, and/or the relationship between multiplication and division to solve division problems.
  • Illustrate and explain division calculations by using equations, rectangular arrays, and/or area models.
  • Solve word problems using the appropriate operation(s) in the appropriate order

Vocabulary
What vocabulary must students know to understand and communicate effectively about this content? / Essential Vocabulary
Algorithm
Divide
Dividend
Divisor
Factors
Groups of
Multiply
Partial quotient
Product
Quotient
Remainder
Supporting Vocabulary
Add
Addend
Area model
Difference
Reasonableness
rectangular array
subtract
sum
Resources & Activities
What resources could we use to best teach this unit? / Stepping Stones
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5.NBT.2
  • Module 1: Lesson 2
  • Module 8: Lesson 4
5.NBT.5
  • Module 1: Lessons 8-12
  • Module 3: Lessons 1-6
5.NBT.6
  • Module 8: Lessons 1-7
5.NF.3
  • Module 11: Lessons 1-2
Engage NY
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5.NBT.2
  • Module 1: Topic A, D, E
  • Module 2: Topics A, D, E, G
5.NBT.5
  • Module 2: Topics B, D
5.NBT.6
  • Module 2: Topics E, F, H
5.NF.3
  • Module 4: Topic B
Howard County Website
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K-5 Math Teaching Resources
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5.NBT.2
5.NBT.5
5.NBT.6
5.NF.3
Created by Beth Richardson ():
  • Division of the Day
Multiplication of the Day (Free from TPT:
From Common Core Sheets
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Illustrative Mathematics
Illuminations
Remember there are other sources in your school that may not be listed on this common resources list due to variation in each individual school. Examples of other great resources your school may have access to include: Everyday Math Games, Investigations, Everyday Partner Games, AVMR file folders, Ongoing Assessment Project, etc.

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