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Using Place-Value and Base-Ten Models to Solve Problems

Lesson Plan

Using Place-Value and Base-Ten Models to Solve Problems

Objectives

Students will review the important idea developed from three-digit numbers that ten in any position makes a single thing (group) in the next position (10 hundreds make 1,000) and vice versa. Students will:

  • match a symbolic representation of numbers with base-ten blocks.
  • match a whole number to its word name.
  • write numbers in expanded notation.
  • compare two whole numbers using <, >, =.
  • order whole numbers (least to greatest and greatest to least).

Essential Questions

  • 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 data be organized and represented to provide insight into the relationship between quantities?

Vocabulary

  • Expanded Notation: A way to write numbers that shows the value of each digit
    (e.g., 4372 = 4000 + 300 + 70 + 2).

Duration

90–120 minutes

Prerequisite Skills

Prerequisite Skills haven't been entered into the lesson plan.

Materials

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

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    • Ongoing observation during the “Who Am I” activity and the Group Matching Activity will help in identifying areas of concern.
    • The Lesson 1 Exit Ticket may be used to assess students’ level of understanding.
    • The Number Name Worksheet (M-3-2-1_Number Name Worksheet and KEY.docx) may be used for additional practice or for an additional assessment of student ability to translate between the three different number forms: numeric, word form, and base-ten models.

Suggested Instructional Supports

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    Active Engagement, Modeling
    W: Students will become more familiar with different ways of expressing numbers. After a review of the values and components of base-ten blocks, students practice building numbers with them and identifying numbers built with blocks. Students also practice grouping ten ones to make 10, ten tens to make 100, and so on. 
    H: Students use base-ten blocks and mats to configure various combinations and sums that the teacher suggests. This time will also be used for teacher observation and guidance as necessary.  
    E: Using the “Who Am I?” game, the teacher calls out a combination of blocks, then students arrange them and determine the value. This practice helps students become more proficient at translating between number models and the corresponding numerals. 
    R: The Group Matching Activity cards can be used by small groups of students for additional practice translating between word forms of numbers and numeric forms. If this is too easy for students, they may try the Group Order Activity. If students are having difficulties, use fewer cards. When they are finished, have students choose a few cards and order them from least to greatest and check their work for accuracy. 
    E: For individual assessment of student progress in translating between number forms, the Lesson 1 Exit Ticket may be used. 
    T: To tailor the lesson for a greater challenge, have students play the Group Matching Activity game with more cards. If students need additional practice or are not grasping the concepts as quickly as anticipated, they can use a spinner to play the Greatest Number Place-Value Game and try to create a number greater than their opponents, based on the numbers they spin, to continue learning about place value. 
    O: This lesson is designed to build an understanding of place value and relationships between numbers by practicing ordering numbers and identifying numbers in multiple forms.  

Instructional Procedures

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    “Who remembers what these are called?” Hold up the different types of base-ten blocks. (Possible responses include blocks, cubes, squares, base-ten blocks.) It is important that students are told the proper name “base-ten blocks” if it is not an answer given.

    Hold up a ones cube and ask, “What is the value of this?” (1) Repeat with a tens rod, a hundreds square, and a thousands cube. Some students may not know or remember the value of the hundreds square or thousands cube. “How many ones cubes does it take to make a rod?” (hold up a ones cube and a tens rod) (10) “How many rods does it take to make a square?” (hold up a tens rod and a hundreds square) (10) “How many squares does it take to make a thousands cube?” (hold up a hundreds square and a thousands cube) (10)

    “Today we will be exploring, finding, and comparing numbers and solving problems using base-ten blocks.”

    Hand out base-ten block sets and Base-Ten Block Mats (M-3-2-1_Base-Ten Block Mat.docx) to groups of two to four students. Allow time for exploration.

    “Use three blocks to make 30.” Check mats. “Now make 52.” Check mats and help clarify any confusion or misunderstanding. “What is another way to show 52? Think-pair-share with your neighbor.” Have a student demonstrate another way to get 52.

    “Is there any other way to show 52?” Have students share all the different ways they could show 52. “Use four blocks to make a number greater than 200. How many different ways can you show this using only four blocks?” Students should come to the conclusion that there are many ways to show this.

    “Use four blocks to make a number greater than 200, but less than 400. How many different ways can you show this using only four blocks? Think-pair-share with your neighbor.”

    Ask students to share and record their various ways to use four blocks greater than 200 on the board.

    Make sure students are familiar with the symbols and their meaning. If necessary, use more time to review or instruct.

    “We are going to play a game called ‘Who am I?’ This isn’t a guessing game. Use your blocks to figure out who I am.” Start out with an easy one such as “I am 5 hundreds, 4 tens,
    3 ones”
    (543) to warm up.

    “I am 23 ones and 4 tens. Who am I?” (63)

    “I am 4 hundreds, 12 tens, and 6 ones. Who am I?” (526)

    “I am 30 ones and 3 hundreds. Who am I?” (330)

    “I am 13 ones, 2 hundreds, and 21 ones. Who am I?” (234)

    “If you put 3 more tens with me, I would be 115. Who am I?” (85)

    Use the Group Matching Activity (M-3-2-1_Group Matching Activity.docx). Print and cut out the cards. You can do this in advance of class or have students cut them. You should have one set per group of two to four students. If possible, copy on card stock or laminate for future use. There are twenty-one pairs of matching cards. To begin the game you may want to use fewer pairs and increase the total number of cards as students advance.

    “We are going to play a game in groups. Each group will get a set of cards.
    Half of the cards have numbers and the other half have the same numbers in words. You are going to match the number cards to the name cards.”
    Divide students into groups of two to four. Hand out one set of cards to each group.

    “I am going to give you the rules for our game now. Shuffle the cards and place them face down in rows, like in the game ‘Memory.’ A player will turn over two cards. If the number and the word on the cards match, you will keep the cards. If the numbers on the cards are not the same, turn the cards back over and have the next player take a turn. The idea is to try and get as many matching pairs of cards as you can. The player with the most matching cards wins.” Allow students enough time to complete the game.

    After students have played the game, have them discuss the difficulties they encountered
    (e.g., words for numbers that were difficult to identify, numbers for words that were difficult to identify, remembering locations of the matching card, etc.).

    “Choose four of the number cards from your set of cards. Put them in order from least to greatest.” Walk around the room and assess how students are doing with the ordering, assist them if necessary. “Who wants to share the numbers you chose and how you ordered them?” Give students an opportunity to share with the entire class or with peers at their table.

    “Now we are going to do another activity that involves ordering numbers. You will each receive a set of numbers, both in word form and number form, and pictures of
    base-ten blocks.”
    Give students cards from the Group Order Activity sheet (M-3-2-1_Group Order Activity and KEY.docx). “You will shuffle the cards and choose four from the stack. Order them from least to greatest. When you are done, share with a partner. Have your partner check that your cards are ordered correctly. If you do not agree, raise your hand and I will help.”

    Give students the Lesson 1 Exit Ticket (M-3-2-1_Lesson 1 Exit Ticket and KEY.docx). “You are going to translate from number form to word form and from word form to number form. As soon as you are finished with your Exit Ticket, bring it to me to have it checked.” Let students who are mastering the skill help others who need guidance. Make sure those students who do not understand receive additional opportunities to learn the material.

    Extension:

    Use the strategies and activities listed below to meet the needs of your students during the year.

    • Routine: If students had difficulty with the Group Matching Activity, have them play the game using fewer pairs of cards. If the cause of their difficulty is remembering the location of the cards, have them group the number cards together and the word cards together in separate areas.

    If students had trouble with the Group Ordering Activity, give them a set of numbers to order starting with two-digit numbers and increasing to four-digit numbers as they improve. Provide base-ten blocks and mats to students who are kinesthetic learners.

    “We are going to use what we have learned about place value to play a game called ‘The Greatest Number.’ We will play in groups of four.” Assign groups ahead of time or put students randomly into groups. Hand out one game spinner sheet and one spinner per group and one recording sheet per person. If spinners are unavailable, show students how to bend a paper clip and spin around the tip of a pen.

    “The object of the game is to have the most points. The way you earn points is by creating the greatest number you can from the numbers that you get on the spinner.” Demonstrate by playing one game with the class using the overhead projector or board to fill in the numbers as a student spins four numbers. As you are playing the game, explain that one person spins the spinner, and everybody places the number in one of the four boxes. Once a number is placed in a box, it cannot be changed.

    After four spins, the student who thinks s/he has the greatest number reads the number aloud. If another student has a greater number s/he reads it. If a student reads the number incorrectly, the student with the next greatest number reads his/her number. Students should be instructed to not say the word “and” when reading a whole number. When a student wins a round, that student earns one point. After a few rounds, students add up their points, and the one with the most points wins. If there is a tie, each student spins a number and the greater number wins.

    “Is this a game of purely guessing or is there a strategy to winning?” If students don’t understand the question, ask: “Why did you choose to put that number in that place?” (Possible response: It was a small number so I put it in the farthest right place or vice versa). It is important to try to get students to verbalize that a number in the thousands place is “worth” more than the same number in the hundreds, and a number in the hundreds place has more value than a number in the tens place, etc. If students grasp this concept, they can also play “The Least Number”.

    • Expansion: Students who demonstrated a proficient understanding during the Group Matching Activity may heighten the challenge by increasing the number of cards up to the full twenty-one sets.

    The Greatest Number Place-Value Game can also be extended by adding more boxes and creating greater numbers.

    If a computer lab is available, introduce students to some math game Web sites (see the Related Resources section).

    This unit is designed to build the understanding of place value, and relations between numbers. The unit begins with students using base-ten blocks and mats to conceptualize that ten in any position makes a single thing (group) in the next position (10 hundreds make 1 thousand) and vice versa. The “Who am I?” activity reinforces the need to regroup numbers using
    base-ten blocks.

    The Group Matching Activity gives students the opportunity to practice in a fun “hands-on” way how to match word form to numbers and numbers to word form and this is assessed with an exit ticket. Then they use the same cards in a new activity where they compare and order numbers.

    The objective of the Greatest Number Place-Value Game is to fine tune the understanding of place value. It also allows you to differentiate instruction by working with small groups of students or individuals who need additional practice.

Related Instructional Videos

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Final 05/10/2013
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