Connecting Quantities and Numerals
Lesson 1 of 2
Kindergarten
45 minutes
Description
Students use snap cubes and the number line to count how many they have in various configurations and make connections between numerals and quantities.
Materials
Introduce
Gather students together and read a counting book of your choice. See these suggestions:
- Mother Goose Numbers on the Loose by Leo and Diane Dillon
- The Grapes of Math by Greg Tang
- One Was Johnny: A Counting Book by Maurice Sendak
- Olivia Counts by Ian Falconer
- Anno's Counting Book by Mitsumasa Anno
- Mouse Count by Ellen Stoll Walsh
- Mouse Count / Cuenta de raton (bilingual edition) by Ellen Stoll Walsh
- Ten Little Ladybugs by Melanie Gerth
- Ten Black Dots by Donald Crews
- 10 Little Rubber Ducks by Eric Carle
- My Little Sister Ate One Hare by Bill Grossman
Ask students to say the number aloud (as you read the book), and then write that numeral. Use index cards to display the numeral stated.
If students need assistance with writing numerals, refer to a different writing suggestion in the writing guide.
After finishing the book, introduce the idea of how we use numerals to represent the number of objects we count and how the last numeral stated is the one that tells the total number of objects counted.
Explore
Place a container of snap cubes at each table. Display a numeral less than 11 (e.g., 4) and ask the students to count out that many snap cubes. Once they have the appropriate number of cubes ask the students to count out loud as they snap each individual cube together to make a train. Once a train is completed, reinforce the idea of counting each individual cube to discover the total amount. Additionally, focus on the last numeral stated, identifying this as the total amount of objects. Repeat several times until all 10 numerals are created.
- What does the last number that we said counted out loud as we counted tell us?
[It tells us the total amount.]
- If we rearrange the cubes and count again, what will happen to the total? [The total amount does not change.]
- What would happen if we took all the cubes off the desk? How would you describe the total amount now? Let's draw this numeral. [There wouldn't be any; students often say no. Guide them to recognizing that we call this amount zero; have students write this numeral.]
Engage in a discussion about how the trains are organized (randomly) and ask students to think about if this is the manner in which we count [No.]. Have several students model the way we normally count (1,2,3,4...).
If students have trouble understanding this, provide an example by counting the number of fingers on one hand. Provide additional opportunities for students to count objects as needed.
Once students can answer, "No," then ask them to organize their trains in the manner in which we count. Students can organize their trains from shortest to tallest or vice versa. Doing so elicits conversation about counting forward as well as backward.
Assign individual students a numeral. Hold up number card and ask the student that has the train that represents that number to hold up the corresponding train. Engage in discussion that allows opportunities for students to count both forward and backward. Discuss how these numbers are related to one another.
- What number is one more than this? How do you know?
- What number is one less than this? How do you know?
After a student responds, ask the class to show the number with their cubes and/or fingers and decide if they agree that the number is 1 more than/less than the given number.
Have students consider and make conjectures about how zero would be represented and where it would appear on the number line.
Now select two numbers less than 10 and ask students to represent these amounts with their cubes by building towers they can compare. Building cube towers will provide an assessment of students' understanding of the relationship between numbers and quantities and compare two numbers. The Building Towers Activity Sheet allows teachers the flexibility to choose two numbers that will be appropriate for their students.
Synthesize
To summarize the lesson, gather the students in a circle and bring a variety of interesting objects for counting (ex: snap cubes, bear counters, shells). Put a collection of 10 or less items in the middle of the circle. Then pose the question, "About how many objects do you think we have in our collection?"
To include estimation skills, prompt with "Do you think we have more or less than 2? More or less than 5? More or less than 10?
Then, ask "What can we do to figure this out? [Count them.] Can we use any of the same strategies for counting these objects that we used for counting the snap cubes?" [Have multiple students demonstrate their ideas.]
To assess student understandings close with conversation that addresses comprehension, for example:
- What is the connection between the last number name said and the number of objects counted? [The last number name said is the total number of objects.]
- Does the arrangement or the order in which objects are counted affect the number of objects? [No.]
- Write the numeral ____ in the air with your finger (choose a numeral between 0 and 10).
[Answers will vary.]
- Stand under the number ____ on the number line.
[Answers will vary.]
Assessment
Optional
Assessment 1 (Technology Option)
Have pairs of students play the game Concentration against each other using a computer or tablet.
Assessment 2
Spill and Count
Remove the bins of cubes and give each pair of students a cup of cubes (between 4–10).
Depending on available resources, students could simply grab a handful of cubes from a bin to bring back to their station.
If a particular student is showing proficiency, then you may wish to give them an empty cup.
Explain to students that everyone has cups of cubes, but they have different quantities at each desk. They are going to start with their own cup and then move onto other groups' cups (or trade cups with another table). Instruct them to do the following:
- Spill the cubes.
- Count the cubes to determine the total.
- Snap cubes together to create a train and bring it up to the number line to find its corresponding numeral.
- Write the numeral that represents the total number of cubes.
- State a number that is greater than your number and less than your number.
Make note of the strategies that students are using.
Teacher Reflection
- Which cardinal (counting) number words were students familiar with when the lesson began? How could you use this as a benchmark?
- How did students cope with the notion of zero and how to record the numeral 0?
- Which numeral did students struggle with the most? What practice would be good for remediation?
- How did students grapple with 100 (if you used that specific guiding question)? Were they more or less comfortable with it than the number 20?
- What were some struggles that students had in connecting the visual model, written numeral, and placement on the number line?
- When writing the numerals, which ones did students struggle with the most?
- What adjustments will I make the next time I teach this lesson?
Leave your thoughts in the comments below.