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How Many?

Lesson Plan

How Many?

Objectives

Students will learn to relate a given number to other numbers, specifically numbers up to ten. They will:

  • see a one-to-one correspondence between objects and numbers when counting.
  • write numbers in words and numerals.
  • represent numbers in different ways, such as with pictures or other models (cubes, links, etc.).
  • recognize the relationship between a number and the quantities which are one and two more.
  • recognize the relationship between a number and the quantities which are one and two less.
  • recognize visual patterns of objects representing a number without counting.
  • create a set with a given number of objects.
  • compare and order sets of numerals using cardinal numbers.

Essential Questions

How can mathematics support effective communication?
How can patterns be used to describe relationships in mathematical situations?
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?
  • What happens when I take a group of numbers (objects) apart or put them together?

Vocabulary

  • Quantity: An amount of an object.
  • Total: The number of objects all together.

Duration

90 minutes

Prerequisite Skills

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

Materials

  • red and yellow (or any two colors) connecting cubes, such as Unifix cubes, approximately 20 of each color
  • ten red cubes and ten yellow cubes for each group
  • two sets of Numeral Cards per small group (M-K-1-2_Numeral Cards.doc)
  • one copy of Workmat 1 for each small group (M-K-1-2_Workmat 1.doc)
  • two six-sided number cubes (two large foam number cubes work well for demonstration)
  • drawing paper
  • colored dot stickers (like those used for garage sales)
  • Ten Black Dots by Donald Crew. Greenwillow, 1968.
  • copies of Assessment 1 (M-K-1-2_Assessment 1.doc)
  • workstation copies of Workmat 2 (M-K-1-2_Workmat 2.doc)
  • crayons or markers
  • pictures or books with pictures of sets containing exactly two types of objects (dogs and cats, baseballs and footballs, etc.)

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.

  • Ten Black Dots by Donald Crew. Greenwillow, 1968.
  • How Many Snails by Paul Giganti, Jr. Greenwillow, 1988.
  • Ten Red Apples by Pat Hutchins. Greenwillow, 2000.
  • The Gummy Candy Counting Book by Amy and Richard Hutchings. Scholastic, 1997.
  • Look and Count by Julie Dalton. Scholastic Library, 2006.
  • How Many, How Many, How Many by Rick Walton. Candlewick, 1996.
  • Ten Little Fish by Audrey Wood. Blue Sky Press, 2004.
  • http://www2.scholastic.com/browse/lessonplan.jsp?id=997 (Lesson Plan for Ten Little Fish)
  • The M & M’s Counting Book by Barbara Barbieri McGrath. Scholastic Inc., 1994.
  • Random Reporter method: https://static.pdesas.org/content/documents/Random%20Reporter.pdf

 


Formative Assessment

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    • Observations during class activities, small-group discussions, and workstations will aid in assessing student understanding.
    • The Random Reporter method may be used to determine whether students comprehend the material.
    • (optional) If more information is needed, use Assessment 1 (M-K-1-2_Assessment 1.doc) to further evaluate student mastery.

Suggested Instructional Supports

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    Scaffolding, Active Engagement, Modeling, Explicit Instruction
    W: Introduce students to the relationship between cardinal numbers and quantities represented by sets of counters or other items.  
    H: Guide students to discover that the same quantity can be found and represented multiple ways by leading them through the Counting Students activity.  
    E: Get students engaged in the Connecting Cubes activity, through which they will practice correlating quantities with cardinal numbers.  
    R: Have students work in small groups using workmats and connecting cubes to review the tasks of counting, matching sets to cardinal numbers, and finding sums and differences for quantities.  
    E: Evaluate student progress and understanding by bringing students back together in a large group to discuss the procedure they used and their results.  
    T: Tailor the lesson by adding onto existing activities or limiting the amount of unguided practice students do. For additional practice, try having students count off or use number cubes in groups, as described in the Extension section.  
    O: This lesson is designed to start with concrete counting (people) and move to representational counting (cubes). The numeral cards expose students to the more abstract symbols used to represent numbers.  

Instructional Procedures

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    “We are going to practice counting from 1 to 10 using numbers, people, and cubes. It is important that we learn to count carefully so that we all get the same answers, or totals. We might find out that there is more than one way to get the same answer.”

    Counting Students Activity

    “Let’s find out more about our class by counting how many boys we have. Would all of our boys come here and stand in a line? Let’s count out loud to find out how many boys are in our class.” Walk behind the boys and point to each as the class counts out loud (this models one-to-one correspondence). On the whiteboard, or some sort of display unit, write the total (____ boys). Repeat the activity by counting all of the girls in the class and write the total: “___ boys and ___ girls.”  “Which do we have more of, boys or girls?”

    Pose the question, “How can we find out how many boys and girls we have all together?” Possible responses may include:

    • Have everyone stand in one line and count them.
    • Add the boys and the girls.
    • Count the boys first and then the girls.

    Choose a suggestion and count to find the total. Try another way. Ask, “Should our totals be the same each time we count? Why?”

    “Does it matter if we count the boys first or the girls first? Why or why not?” Write the total: “___ boys and ___ girls make _____ students.”

    Connecting Cubes Activity

    Give each boy a red connecting cube and give each girl a yellow connecting cube. “Let’s all connect our cubes.” Be sure all students are able to see the final sets of red and yellow cubes.

    “How many red cubes do you think we have?” Choose two or three students to explain their ideas. Repeat this for the yellow cubes. Count the cubes in each set and write the totals under the corresponding boy and girl totals:

    ___ boys and ___ girls make ____ students.

    ___ red and ___ yellow make ____.

    Ask, “How many cubes will we have when we connect the red and yellow cubes together?” Choose students to explain their thinking. Count the red and yellow cubes and write the total for all to see.

    Listen to students to determine if they understand that the number of boys is the same as the number of red cubes, the number of girls is the same as the number of yellow cubes, and both totals should be the same.

    To challenge students who understand quickly, ask:

    • “How many boys would we have if a new one joined our class?”
    • “How many students would we have all together?”
    • “What if one of our girls was not here today, how many girls would we have?”
    • “How many girls would we have if 5 girls were absent today?”
    • “How many students would we have in our whole class?”

    Use the red and yellow cubes to model one more and one less.

    Small-Group Activity

    Choose five or six students to form a group (include boys and girls) to role play the following small-group activity. Provide them with six red and six yellow cubes, two sets of Numeral Cards (M-K-1-2_Numeral Cards.doc), and a copy of Workmat 1 (M-K-1-2_Workmat 1.doc).

    “Count how many boys are in your group. Use the red cubes to show how many boys you have. Find the numeral card that tells how many boys you have, and put it in front of the word ‘boys’ on your workmat. Next count how many girls are in this group, and show how many with the yellow cubes. Now find the numeral card that tells how many girls you have, and put it in front of the word ‘girls.’ How can you find out how many are in your group all together?” Let students discuss the options and guide them to choose one.

    “Find the numeral card that shows your answer, and put it in the last blank space on your workmat.”

    “Let’s read what you found out: ___ boys and ___ girls make ____ students all together.” Answer student questions regarding the instructions.

    Break students into groups of four to six, including some boys and some girls in each group. Give each group the same supplies used for the demonstration (six red cubes, six yellow cubes, two sets of numeral cards 1–6, and a copy of Workmat 1).

    “In your groups, count how many boys and girls you have. Show how many with the cubes. Next choose numbers to tell how many there are of each, and place them on your workmat.”

    Walk around to each group as they are working and ask questions such as:

    • “How many boys/girls are in your group?”
    • “Does your group have more boys or more girls?”
    • “How can you find out how many you have all together?”

    Regroup students and repeat the activity. Group sizes and composition could be selected to meet the needs of students. Smaller groups will be more appropriate for students who can count to five or six; larger groups will challenge students who are able to count to ten or beyond. Have additional cubes and numeral cards (seven to ten) available to meet the needs of groups larger than six.

    Observe the counting strategies used and make note of students who do not yet demonstrate one-to-one correspondence. They will benefit from extended practice in small groups and/or at workstations. Watch for groups that hold their sets side by side to determine which group has more and ask, “How many more (boys than girls/girls than boys) are in your group? How do you know?”

    Bring the small groups back together for a whole-group discussion. Randomly select a student from each group to share his/her findings with the class.

    Ask: “Would you show us the cubes that your group put together and tell us what you found out?” Prompt students if necessary to clarify how the group found how many they had all together. Some responses may include

    • We just knew by looking at the people and then we counted the blocks.
    • We gave each boy a red cube and each girl a yellow cube; then we put them together and counted.
    • We counted the boys first and got that many cubes and then counted the girls.

    Restate the responses that demonstrate good counting strategies such as adding on, counting up, and pointing to each child or cube (one-to-one correspondence).

    Have students complete Assessment 1 (M-K-1-2_Assessment 1.doc). Provide crayons or markers for coloring.

    Extension:

    • Routine: Point out classroom situations throughout the day that encourage counting and comparisons. Emphasize the use of specific vocabulary words from this lesson.
    • Expansion: This activity requires two six-sided number cubes. Begin by seating students in a circle. Have one student roll the number cubes and add the numbers. For example, if the roll was a six and a two, explain that students can count the dots on the first number cube (one, two, three, four, five, six) and then continue where they left off to count the dots on the second cube (seven, eight etc.) while pointing to the dots. Ask students if they have any other counting suggestions (ten-frames, etc.).

    Choose a starting point in the circle and ask children to stand one at a time as they each help count to reach the given number. The first child would stand and say, “one,” the next would stand and say, “two,” and so on until eight are standing. Ask these children to stand as a group off to the side or in the center of the circle. Roll new numbers and repeat the counting activity. Have the new group stand together. Roll again or have the remaining students count themselves and stand together. There will likely be between three and six groups.

    Have each group connect one set of Unifix (or similar) base-ten cubes together to represent their group number. Demonstrate what eight cubes connected together looks like; use six of one color and two of another to represent the values on your number cubes. (Use the numbers from your example roll if it was not eight.) As a class, count out loud from 1 to 8 as you point to each cube in your stack.

     

     

     

     

    Walk around and have individual students (or the whole group in unison) count the number of Unifix cubes in the stack the group created. Have students compare the height of their stack to the other groups’ stacks to see which are largest and smallest.

    Ask the groups to arrange themselves according to which have larger numbers and which have smaller numbers. (They can base this on the numeral used for counting, the size of their group of students, or the height of their cube stack.) If any groups are the same size, help them decide the appropriate place to move their groups. Let students explain how they decided where to stand and have the groups reach a consensus.

    • Small Group: You will want to assemble paper, circle stickers, crayons or markers, and the book Ten Black Dots by Donald Crew. Read the book Ten Black Dots and discuss the different ways dots are used to represent numbers.

    If this book is not available, use another alternative counting book. (Several book choices are listed in the Related Resources at the end of the lesson.) Prepare one or two dot examples to model for students. Do this by using from one to ten black dots to create simple pictures. Give each student a piece of drawing paper. Have students choose a number between 1 and 10 and write it on their paper. Instruct them to use the same number of dot stickers as their number to make their own picture. At the bottom of their pictures, students will write “_____ dots can make a _____.” Save the pages to create a class Dot book.

    • Workstation 1: Have available at the station several copies of Workmat 2 (M-K-1-2_Workmat 2.doc), two colors of cubes, and numeral cards (M-K-1-2_Numeral Cards.doc). Students will need a picture showing a set of two different types of mixed objects (dogs and cats, cars and boats, etc.). Either provide specific pictures of your choice or have students find pictures in a set of picture books at the station. Have students use the color cubes to represent how many of each of the two items are in their set and place the corresponding numerals on their workmat. Students should be able to explain how many of each object they found, how many objects there are in total, and how they found them.
    • Workstation 2: For students who need practice with one-to-one correspondence, set up this workstation with ten cubes of one color and numeral cards 1 to 10. Have students make sets of cubes to match numbers on the cards. Limit the cards to five for students who need more practice counting beyond five.

Related Instructional Videos

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Instructional videos haven't been assigned to the lesson plan.
Final 4/18/14
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