Counting Strategies Lesson 2

  • Counting to 10 with Cubes

    Lesson 2 of 2
    Kindergarten

    45 minutes

    Description

    Students make comparisons of given numbers to the benchmark number of 5 to develop a conceptual understanding of the relative size of numbers and their relationship to one another.

    Materials

    Introduce

    Give students crayons and a piece of paper large enough to trace both of their hands. Instruct students to fold the paper in half (and keep it folded) and trace a hand.

    Have students trace one hand with their fingers outstretched. Students can help one another if they are struggling to trace. Ask students to write the numeral that represents the total number of fingers in their drawing. [5.] Also ask, "How can we verify that our total is correct?" [Count.] To verify, count out loud the number of fingers in their tracings.

    Finally, ask students to create a tower of 5 using the same colored snap cubes. Both the tracing and the tower will now be used as visual benchmarks. Make sure to keep these tracings for use in future lessons.

    Explore

    Distribute 5 cubes to each group of students, and show the numeral card 5. Have students demonstrate they recognize this amount by placing the correct number of cubes, one per finger, on the tracing they just made.

    • How many snap cubes should each student have? [5 - Allow the students to place the cubes on their own fingers to verify the amount.]
    • How do you know we have exactly 5 cubes? [Answers will vary. Sample answer: We filled up one hand, which we know has 5 fingers.]

    Show students the numeral card 6. Say the number together. Ask students to place a cube on each of their six fingers. [They should realize that they do not have enough fingers to place cubes on.] Ask students what this means. [We need more fingers for more than 5 cubes.] Ask, "If we traced our other hand how could this help us?" [We can now place all cubes on our fingers.] Have them unfold their papers and trace their other (or same) hand. After doing so, they should be able to place the six cubes on a finger.

    Tell students to look around the room and describe what they notice about the cubes on their friends' fingers.

    • Some students may not fill one hand before starting on another.
    • They may have placed the 6th counter on a finger other than the thumb of the right hand.
    • They may not have filled in their fingers left to right.

    If any of the above is mentioned, have a discussion on what they think is the best method to go about placing the cubes on each finger. The class should come to a consensus that working left to right is the most organized method of counting. Utilize a number line if needed.

    Conversation about representing 6 as 5 and one more needs to be the focus. There are other representations for 6 (i.e. 3 and 3), but the goal of this lesson is establishing 5 as a benchmark.

    Talk about this representation for 6 and relate this representation for 6 back to 5 and talk about how 6 is different than 5 and vice versa.

    • Do we have a total of five cubes? [No.]
    • Is six more or less than 5? [More.]
    • How do we know? [Answers will vary. Sample answer: We counted past 5.]
    • What do we need to do to have 5 cubes? [Remove or take away 1.]

    Have students take out their tower of 5 for reinforcement. Next, have students create a tower with their 6 cubes.

    • I need a volunteer to use their tower and show me the fifth cube.
    • I need a different volunteer to use their tower and show me the sixth cube.
    • Which is more five or six ? By how much? [6 (At this point, you can call 6 a neighbor of 5); 1.]
    • What is another neighbor of 5? [4.]

    Show students the numeral card 4. Say the number together. Ask students to place a cube on each of their fingers. Have them also build a tower of 4. and compare it to their tower of five.

    Repeat the guided questions above changing the focus to numbers that are less than five.

    When students can comfortably talk about how 6 and 5 are related as well as how 4 and 5 are related, give each student (or pair of students) a numeral card between 0 and 10 (inclusive). Ask them to create a new tower that is the height of their new number. Have them build their tower and then trade towers with another student (or pair of students). Each pair then counts their cubes, compares their tower to their tower of five, and talks about how the numbers relate to each other. Listen to how students are justifying the amount that they have and elicit conversation about using 5 as a benchmark.

    Students can continue this conversation by using the Ten Frame interactive, games 1-3. They can even put the cubes on their fingers to match the scenarios posed in the app. Stress that the first row represents 5 cubes and is analogous to five fingers.

    You can have students apply their learning by using the Okta's Rescue interactive on the Very Easy setting. They can count small numbers of objects, count the total number of objects rescued, and represent that number on the number line.

    Synthesize

    Bring the class back together and distribute a numeral card (between 0–10) to each student (or pair of students). Have them place the number of cubes on their hand tracing that equals their numeral card, then instruct them to turn their card upside down. Also have them create a tower with their cubes that represents this amount. Engage students in a Counting Gallery Walk. With a partner or individually, students will visit somebody else's construction. Have them decide if what they see is more or less than five. To verify what they think, have them count how many, say the number of cubes they see, and flip over the card to verify their conjectures.

    Rotate and repeat. As students are walking around viewing each other's work, observe student thinking, noticing if they are counting all, or if they just know how many. Then have students return to their own hand placemat. During this summary, conduct your formative assessment while circulating the room.

    Assessment

    Optional

    During the Gallery Walk (and throughout the lesson), take a quick inventory of students' strategies for counting.

    Extension

    Optional

    Grouping and Grazing—Make sure the setting is for "Count by 5s." In this app, students can practice counting by 5s and grouping the cows together. They will get a sense that they can count a large number of objects through grouping.

    Teacher Reflection

    • Which students could count to 10? What experiences are necessary for those who could not?
    • Which students are able to identify the numerals to 10? Which could write and/or identify all of them? What practice is needed for those who cannot identify them?
    • Which students recognize the relationship of a given number to 5? What sorts of remediation tools could you implement to help struggling learners?
    • How did students grapple with the idea of using 5 as a benchmark number?
    • What were some struggles students had with number relationships?
    • What adjustments will I make the next time I teach this lesson?

    Leave your thoughts in the comments below.

    Related Material

    Teaching Children Mathematics, Julia Schnur-Laughlin

    Teaching Children Mathematics, Julie Schwerdtfeger, Angela Chan

    Other Lessons in This Activity

    Lesson 1 of 2

    Students use snap cubes and the number line to count how many they have in various configurations and make connections between numerals and quantities.

  • Comments

  • 4 Comments

    • Avatar

      I agree that unifix worked great for this lesson! I also made and used preprinted hands and this helped a lot. I also had only explicitly taught numbers 0-5 so I began by only using those numbers. Overall this was a great lesson - loved the hands on andmore» visuals of this lesson.«less

    • Avatar

      In my kindergarten class at Erma Siegel Elementary, I used pre-made laminated number lines for each student and when students were pulling numbers from a baggie to compare to their tower of 5, students placed their 5 tower on their number line & thenmore» placed their new built tower on the number line. It was a great visual for what represents as more /less on the number line.«less

    • Avatar

      I agree, unifix cubes work best. Things I modified, I had tracings of hands premade and folded. On materials it would be beneficial to know how many cubes each student should have. Also, based on where you are in teaching numbers I wouldn't pass outmore» number cards to 10. For example, I have only taught numbers 0-4 explicitly and 5 and six through the previous lesson one. So I only passed out cards 0-6 after this lesson.«less

    • Avatar

      One idea is to use unifix cubes with kindergarten instead of pop cubes. It is much easier for the students to manipulate.

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  • Essential Question(s)

    • How does a given number relate to 5?

    Standards

    CCSS, Content Standards to specific grade/standard

    • K.CC.A.3 Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).
    • K.CC.B.4.c Understand that each successive number name refers to a quantity that is one larger.
    • K.CC.B.7 Compare two numbers between 1 and 10 presented as written numerals.

    CCSS, Standards for Mathematical Practices

    • SMP 2 Reason abstractly and quantitatively.

    PtA, highlighted Effective Teaching Practice and/or Guiding Principle CCSS

    • Use and connect mathematical representations.