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Base-Ten Models and Simple Multiplication

Unit Plan

Base-Ten Models and Simple Multiplication

Objectives

Students investigate how the pattern of groupings of tens in three-digit numbers is generalized to understand greater numbers up to 10,000. Students will:

  • understand that 10 in any position makes a single group and in the next position it makes a different group.
  • understand that the oral and written patterns for three-digit numbers are duplicated in a pattern for every three digits to the left (100 groups of thousands, 10 groups of thousands, and 1 group of thousands).
  • learn multiple methods for simple multiplication including grouping and arrays.

Essential Questions

How are relationships represented mathematically?
How can data be organized and represented to provide insight into the relationship between quantities?
How can expressions, equations, and inequalities be used to quantify, solve, model, and/or analyze mathematical situations?
How can mathematics support effective communication?
How can patterns be used to describe relationships in mathematical situations?
How can probability and data analysis be used to make predictions?
How can recognizing repetition or regularity assist in solving problems more efficiently?
How is mathematics used to quantify, compare, represent, and model numbers?
What does it mean to estimate or analyze numerical quantities?
What makes a tool and/or strategy appropriate for a given task?
When is it is appropriate to estimate versus calculate?
  • How is mathematics used to quantify, compare, represent, and model numbers?
  • How are relationships represented mathematically?
  • What makes a tool and/or strategy appropriate for a given task?
  • How can expressions, equations, and inequalities be used to quantify, solve, model, and/or analyze mathematical situations?
  • How can data be organized and represented to provide insight into the relationship between quantities?

Related Unit and Lesson Plans

Related Materials & Resources

The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.

  • Math Mats resources

http://mathwire.com/strategies/mats.html

  • National Library of Virtual Manipulatives

http://nlvm.usu.edu/en/nav/grade_g_2.html

  • Math practice site

http://ca.ixl.com/math/grade-3

  • Remedial place-value game

http://www.softschools.com/math/practice/place_value.jsp

 

Formative Assessment

  • View

     

    Multiple-Choice Items:

    1. What is the number form of forty thousand two-hundred six?

    A

    40,260

    B

    40,026

    C

    40,206

    D

    42,006

     

    1. Order the following numbers from least to greatest:

    937

    1,082

    854

    A

    854    937    1,082

    B

    937    854    1,082

    C

    1,082    854    937

    D

    854    1,082    937

     

     

    1. Which set of base-ten blocks shows 2,470?

     

    A

     

     

    B

     

    C

      

    D

     

     

    1. A total of 6 parents drove all the members of the soccer team to their game. Each parent brought 3 soccer players. How many soccer players were there in all?

    A

    2 soccer players

    B

    3 soccer players

    C

    9 soccer players

    D

    18 soccer players

     

     

    1. Mr. Ford bought a movie ticket for each of his 4 children. The cost of each ticket was $8. What was the total cost of the movie tickets?

    A

    $2

    B

    $4

    C

    $12

    D

    $32

     

    1. Sam has 6 bunches of bananas. There are 3 in each bunch.

    Which repeated addition sentence matches the picture?

    A

    3 + 3 + 3 = 9

    B

    3 + 3 + 3 + 3 + 3 + 3 = 18

    C

    6 + 6 + 6 + 6 = 24

    D

    6 + 6 + 6 + 6 + 6 + 6 = 36

     

     

     

     

     

    1. Mr. Cowell has the array of chalk below.

    Which sentence describes the array?

    A

    4 rows of 9 pieces of chalk is 36 pieces of chalk

    B

    9 rows of 4 pieces of chalk is 36 pieces of chalk

    C

    4 rows of 8 pieces of chalk is 32 pieces of chalk

    D

    8 rows of 4 pieces of chalk is 32 pieces of chalk

     

    1. Kris has the array of pillows below.

    4 rows of 6 pillows is _______ pillows.

    A

    18

    B

    24

    C

    28

    D

    30

     

    1. 7 rows of 9 candlesticks is _______ candlesticks.

    A

    49

    B

    63

    C

    72

    D

    81

     

    Multiple-Choice Answer Key:

    1. C

    2. A

    3. C

    4. D

    5. D

    6. B

    7. A

    8. B

    9. B

     

     

     

    Short-Answer Items:

    Solve each problem. You may use counters to help you.

    Your answer should include:

    • a proof drawing
    • a repeated-addition sentence
    • a number sentence telling the answer for each problem

     

    1. Juan has cupcakes. He placed 9 cupcakes onto each of 2 plates. How many cupcakes does Juan have?

     

     

     

    1. Terry decorated cookies for her friends. She gave 3 cookies to each of her 4 friends. How many cookies did Terry decorate?

     

     

     

     

    1. Allie has 3 bunches of balloons. She has 5 balloons in each bunch. How many balloons does Allie have?

     

     

     

    Short-Answer Key and Scoring Rubric:

    Solve each problem. You may use counters to help you.

    Include:

    • a proof drawing
    • repeated addition sentence
    • number sentence telling the answer for each problem
    1. Juan has cupcakes. He placed 9 cupcakes onto each of 2 plates. How many cupcakes does Juan have?

     

    1. Terry decorated cookies for her friends. She gave 3 cookies to each of her 4 friends. How many cookies did Terry decorate?

     

    12. Allie has 3 bunches of balloons. She has 5 balloons in each bunch. How many balloons does Allie have?

     

    Scoring Rubric for Items 10–12:

    Points

    Description

    2

    The student’s answer:

    • includes a proof drawing that is accurate and clear.
    • includes a repeated addition sentence that is clear and correct.
    • includes a number sentence that is correct.
    • demonstrates understanding of the mathematical concepts.

    1

    The student’s answer:

    • includes one of the three correct parts: proof drawing, repeated addition sentence, or number sentence.
    • demonstrates minimal understanding of the mathematical concepts.

    0

    The student’s answer:

    • is incorrect or missing all of the three parts.
    • demonstrates no understanding of the mathematical concepts.

     

     

    Performance Assessment:

    Luke draws the moons below.

     

     

    1. Put the moons into two equal groups.

     

     

    1. How many moons are in each group? ____________

     

    Now put the moons into 4 equal groups.

     

    1. How many moons are in each group? ____________

     

     

    1. How many moons are there in all? _____________

     

     

    1. Write a number sentence to show how many moons Luke has.

     

    ______________________________________________________

     

     

    1. Make an array with 4 rows and 5 columns by circling moons below.

     

     

     

    1. How many moons are circled? ____________

     

    Make an array of 7 groups of 3 by circling moons below.

     

    1. How many moons are circled? ____________

     

     

    1. Fill in the blanks to tell how many moons are in the array that you made.

     

     

    ____________moons by ___________moons make__________moons.

     

     

    1. Write a number sentence to show how many moons are in the array that you made.

     

    ______________________________________________________________________

     

     

    1. Draw a dot array to show 6 × 4.

     

    Performance Assessment KEY

    Luke draws the moons below.

     

    1. Put the moons into two equal groups.

     

     

    1. How many moons are in each group? 8

     

    Now put the moons into 4 equal groups.

    1. How many moons are in each group? 4

     

    1. How many moons are there in all? 16

     

    1. Write a number sentence to show how many moons Luke has.

     

    4 × 4 = 16

    1. Make an array with 4 rows and 5 columns by circling moons below.

    One possible array:

    1. How many moons are circled? 20

     

    1. Make an array of 7 groups of 3 by circling moons below.

    One possible array:

     

    1. How many moons are circled? 21

     

    1. Fill in the blanks to tell how many moons are in the array that you made.

    ______7_______moons by _____3_______moons make _____21_______moons.

     

    1. Write a number sentence to show how many moons are in the array that you made.

    3 × 7 = 21

     

    1. Draw a dot array to show 6 × 4.

     

     

    Performance Assessment Scoring Rubric:

    Points

    Description

    4
    • Grouping is accurate and clear with related questions 2, 4, and 5 answered correctly.
    • Arrays are indicated clearly with related questions 8, 10, and 13 answered correctly.
    • Number sentences for questions 6, 11, and 12 are correct and clear.
    • The student meets or performs beyond the problem requirements possibly incorporates multiple methods/solutions.

    3
    • Grouping is accurate with two of the three related questions 2, 4, and 5 answered correctly.
    • Arrays are indicated clearly with two of the related questions 8, 10, and 13 answered correctly.
    • At least two of the number sentences for questions 6, 11, and 12 are correct.
    • The student meets all problem requirements.

    2
    • Grouping is accurate in one of the two tries with one or two of the related questions 2, 4, and 5 answered correctly.
    • Arrays are indicated in one of the three tries with one of the related questions 8, 10, and 13 answered correctly.
    • At least one of the number sentences for questions 6, 11, and 12 is correct.
    • The student meets most of the problem requirements.

    1
    • Grouping is inaccurate or missing with at least one of the related questions 2, 4, and 5 answered correctly.
    • Arrays are not indicated clearly with at least one of the related questions 8, 10, and 13 answered correctly.
    • One of the number sentences for questions 6, 11, and 12 is correct.
    • The student does not meet a majority of the problem requirements.

    0
    • Grouping is inaccurate with no related questions 2, 4, or 5 answered correctly.
    • Arrays are incorrect or not indicated with none of the related questions 8, 10, or 13 answered correctly.
    • None of the number sentences for questions 6, 11, and 12 are correct, or no number sentence attempted.
    • The student does not meet any of the problem requirements.
Final 05/10/2013
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