Desired Results bvsd standard(s)/Essential Learnings



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Unit Design Template


Desired Results

BVSD Standard(s)/Essential Learnings

  • Students develop number sense and use relationships amongst whole numbers to solve problems

  • Students use the mathematical processes of problem solving, reasoning and proof, communication, connections and representations to acquire and use mathematical knowledge.




Unit Enduring Understandings

  • Precise language helps us express mathematical ideas and resolve them



Unit Essential Questions

  • Why do some numbers have few factors and others have many?

  • What is the relationship between the multiples of a number and the factors of a number?

  • How are factors of a number and dimensions of a rectangle related?

  • How do (multiplicative) relationships between whole numbers help us solve problems?

Students will know……

  • That a specific list of factors is finite

  • That a specific list of multiples if infinite

  • That one is a factor of every number

  • Every number is a factor of itself

  • 1 is neither prime nor composite

  • 2 is the only even prime number
  • Square numbers have an odd number of factors


  • Know that every number can be written as a unique product of prime numbers

  • That there is exactly one LCM and GCF for every set of whole numbers

  • The relationship between a rectangle with a given area and the factors of that number

  • That factors come in pairs

Students will be able to……

  • Generate all factors of a number

  • Generate a finite list of multiples of a number and understand the list is infinite

  • Classify numbers as prime, composite, square, even, and odd

  • Use factors and multiples to solve problems and explain facts of everyday life

  • Write any number as the product of prime numbers

  • Use mathematical language accurately to express whole number relationships

  • Identify the GCF and LCM for a given set of whole numbers

  • Apply GCF and LCM to solve problems and explain facts of everyday life

  • Apply the relationship between factors and dimensions/areas of a rectangle

  • Compare and contrast characteristics of whole numbers

  • Use visual representations to demonstrate understandings of factors and multiples

Assessment Evidence

Performance/Transfer Tasks

  • Visual representations of factors via rectangular models

  • Vocabulary poster

  • LCM/GCF poster

Other Evidence


  • Warm ups

  • Exit slips

  • Homework

  • Class work

  • Weekly mini assessments

  • Summative assessments

Rubric

  • See summative assessments: 5, 4, 3, 2, 1

  • Vocabulary poster rubric

  • LCM/GCF poster rubric

  • See vocabulary warm ups

Student Self-Assessment and Reflection

  • Is it a cycle/repeat/together/multiple problem? PROVE IT

  • Is it a sharing/dividing/equal/factor problem? PROVE IT

  • Scavenger Hunt




Unit Design Template (continued)


Learning Plans

Learning Activities

  • Warm ups

    • Series of vocabulary warm ups designed to support student use of content vocabulary and to distinguish between terms. Given word bank and a set of numbers with many relationships amongst them, students write sentences using the vocabulary and given numbers. Rubric encourages use of “bonus words” and multiple words in a sentence.
    • Series of number line warm ups designed to support student use of content vocabulary and to distinguish between terms. Also designed with use of a familiar model and to reinforce correct placement/spacing of numbers—important concept in fractions unit. Students given a task such as “place all factors of 12 on the number line”, leads to discussion of where to begin, spacing, etc. 2nd number line or double line for common factors, (or multiples). Continue with sentences—begin with fill in the blanks.


  • Exit slips

    • These slips are designed as a quick check in and usually center around a key question that has been on the board sometimes just for the day, and sometimes for multiple days. The key questions usually stem from the unit essential questions, what the students will know and be able to do. Example, “Why is there no greatest common multiple?” or “What is always the least common factor and why?” Students are encouraged to answer in Q in A format to encourage language use.

    • Sometimes these slips are designed around a task. Example, “list all of the factors of 20 and all of the multiples of 20 up to 200”. Again a quick check in stemming from what we want students to be able to do.

  • Vocabulary Sheets: students will keep up to date vocabulary sheets as a)new terms arise or b)for pre teaching. Included in the sheets are “term”, “example of picture”, and “definition—own words, any language”. Discuss non-examples and need to include on sheet—use Frayer model.

  • Homework: includes various ACE problems from Prime Time. Also included are skill and practice sheets. Purpose is to reinforce daily classwork/discussions/concepts, etc.

  • Class work

    • Product game via computer: Teacher vs class, student vs. student

    • Product game via paper copy: student vs. parent

    • Factor game via computer: Teacher vs class, student vs student

    • Factor game via paper copy: student vs parent

    • Prime Time-various investigations—some modified

    • Individual assessments throughout unit –some formative, two summative

    • My Number posters: Using content vocabulary and given number, students work with partner generating list of factors and writing sentences about the relationships amongst given number and its factors


    • Visual representations of factors via rectangular models: students model factors of given numbers with rectangular models

    • Scavenger Hunt: using the rectangular models, students work with a partner seeking odd, even, square, composite, prime numbers.

    • Compare and contrast whole numbers using Venn Diagrams

    • Looking for clues to determine if a problem warrants finding factors or multiples in order to solve. Generated list of clue words for board.

    • GCF/LCM poster: given a variety of problems, students must decide if they are LCM or GCF problems. Solve two of given problems and then write a unique problem for each category.

    • Real world applications of common factors and common multiples-video of cicadas from Planet Earth series




Materials

  • Square tiles

  • Grid paper/construction paper/scissors

  • Multiplication charts

  • Venn diagrams

  • Frayer Model Templates

  • Vocabulary Templates

  • Ratio Tables

  • Poster paper/markers

  • Paper copies of product game

  • Paper copies of factor game

  • Paper clips

  • Planet Earth DVD

Accommodations

  • Extra time

  • Oral script
  • Manipulatives, (square tiles, faux money)


  • Scaffolded assessments

  • Multiplication chart

  • Word banks

  • Venn diagrams w/ lines

  • Extra large Venn diagrams

 

Technology Integration

  • Various websites: NLVM, Illuminations

  • TI 73 Factor Activity

  • Clicker Activity

  • Planet Earth-cicadas clip






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