Unit of Study: Multiplication Unit- Exploring Context, Computations, & Order of Operations Grade: 5

Big Ideas /
  • Multiplication can be used to describe a wide range of mathematical situations in the real world. Mathematicians use multiplication and multiplicative relationships to explore rate, combinations, comparisons, and to calculate and describe cubic unit measurements for rectangular solids.
  • Mathematicians can use a variety of computational strategies for multiplying real numbers based on associative and distributive properties. These strategies can be proven and evaluated for efficiency in problem solving situations.

Goals
What do I want students to learn as a result of this unit? /
  • Students will understand the concepts of multiplication and the contexts in which it occurs
  • Student will explore the volume of 3-d right rectangular shapes and connect multiplicative reasoning to volume calculations and relationships
  • Students will understand different symbolic representations of multiplication
  • Students will be able to use different algorithms to multiply and explain/prove how the algorithms function
  • Students will identify and use which algorithm is most efficient for the situation and works best for them
  • Students will evaluate expressions using term grouping and order of operations procedures

Prior Knowledge
What prior knowledge do students need to enter this Unit of Study? What routines do I expect students to know? / Fluency with basic multiplication facts through 12.
Standards Addressed
What concepts will this unit address? / Understand the place value system.
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.
2. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10
Perform operations with multi-digit whole numbers and with decimals to hundredths.
Fluently multiply multi-digit whole numbers using the standard algorithm.
Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
1.Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
  1. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.
  2. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
2.Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
  1. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.
  2. Apply the formulas V = lwh and V = b hfor rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.
  3. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.
Order of Operations
1.Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
Bends in the Road
What bends (or series of lessons) will support each of the goals for this unit? /
  • Establishing a context for multiplicative thinking (story problems)
  • Making sense of Computational Strategies
  • Order of Operations

Ways to Challenge/Provide Extra Support
Which students do I anticipate needing a challenge? Which students do I anticipate will need extra support? / Challenge Strategies:
  • Lattice Method
/ Extra Support Strategies:
Assessment / Students will complete a Multiplication Unit Exam that assesses ability to reason using multiplicative thinkingand demonstrate fluency and understanding of multiplicative computational algorithms.
Bend in Road: Establishing a context for multiplicative thinking / Strings / Materials / Notes
Focus Lessons / Multiplication can be used to describe situations and relationships in the real world.
Let’s explore the language and thinking for both grouping and area/array problems. Grouping situations are those in which objects are organized or replicated in equal groups. Area/array problems involve representing items or units into rows and columns. / Previous multiplication story books to immerse in.
Teacher and Student copies of grouping and area/array problems
Mathematicians also use multiplicative thinking to examine situations of combination (connect back). Discrete combinations may be represented as multiplicative relationships (and illustrated using visual representations such as tree diagrams). Multiplicative comparison involve a quantity being multiplied by a comparative factor (___ times as many). / Combination and multiplicative comparison problems
Rate problems also describe multiplicative relationships. In a rate problem, two different quantities are being compared. One number acts as the unit rate, telling how much is in one unit or group. The other numbers is the multiplier, telling how many sets of the unit you need to multiply. The important word is per, meaning “each”. / Rate problems
Mathematicians create authentic real world story problems that describe a range of multiplicative relationships and situations. / Rough draft materials
Mathematicians construct solutions to story problems that demonstrate thinking, edit, and revise story problems in preparation for publishing. / Publishing materials / Can be interdisciplinary work with writing
Mathematicians publish and share story problems with our communities to enrich the mathematical lives of those around us.
Bend in Road: Making Sense of Computational Strategies
Focus Lessons / Working with the Open Array
Partial Products / p. 190
Enriching Your Math Curriculum
Schuster
FOIL Method / p. 189
Enriching Your Math Curriculum
Schuster
Chunking Algorithm / p.187
Enriching Your Math Curriculum
Schuster
Standard Algorithm: Proving that it actually works! / p. 192
Enriching Your Math Curriculum
Schuster / Number puzzles for the traditional algorithm
Calculation Practice Using What We Know / p. 192-193
Enriching Your Math Curriculum
Schuster / Using algorithms flexibly
Calculation Practice Using What We Know / p. 192-193
Enriching Your Math Curriculum
Schuster / Writing and Journaling about their methods
Bend in Road: Order of Operations
Day / String/Warm-Up / Lesson / Share / Materials (title of book, page #, manipulative)
Multi-step single operation equations / Why is grouping terms necessary?
Add/Subtract- L to R
Multiply/Divide L to R then Add/Sub LtoR
Parentheses (explicit) groups) then Mult/Div then Add/Sub L to R / Intro and discuss PEMDAS
Order of operations- 2-3 days… Four strikes and you’re out (Shuster pg. 144),