Lesson 2

• Groups of 2
• Display image.
• “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
• 1 minute: quiet think time

• “Discuss your thinking with your partner.”
• 2–3 minutes: partner discussion
• Record responses.

• “How does each image show pairs of socks?” (Sample responses: A shows 4 pairs side-by-side, but they don’t match. B shows 3 pairs of socks that are the same color and right next to each other. C shows socks in 2 rows. The matching pairs are above and below each other. D shows matching pairs side-by-side.)

The purpose of this activity is for students to separate objects into groups of 2 and identify numbers of objects that can be split into pairs with “no leftovers” and numbers of objects that can be split into pairs with “one leftover.” In the synthesis, create a t-chart with students that lists the numbers that belong to each category. Students share what they notice and wonder about each group of numbers. Save the t-chart for use in the lesson synthesis.

When recording student responses in the synthesis, record how students counted to find the total number of counters by drawing pairs in rows (see activity synthesis). This helps students see the groups of 2 and prepares them for analyzing arrays in future lessons.

This activity uses MLR8 Discussion Supports. Advances: speaking.

• Each group of 2 needs a container of 4 to 15 counters.
• Create a t-chart on a large piece of chart paper to display in the activity synthesis.
• Use “Making Pairs” as the title.
• Label the t-chart with “no leftovers” and “one leftover” as the categories.

• Groups of 2
• Give each group a bag of counters.

• “Work with your partner to make as many pairs of 1 red and 1 yellow counter that you can. Represent your counters with a drawing or symbols in the first column.”
• “Record the total amount of counters and the number of counters left over, after you have made pairs.”
• “When you finish pairing the counters in one bag, pack up the counters and trade with another group.”
• 10 minutes: partner work time

• “How does your arrangement show a pair of counters that has 1 red and 1 yellow?”
• “How could you rearrange your counters to show pairs?”

• Display t-chart labeled “Making Pairs” with “no leftovers” and “one leftover” as the categories.
• Invite students to share a total amount and whether they made pairs with no leftovers or pairs with a leftover.
• Record the total on the chart.
• “How did you count the counters to find the total?” (I counted each pair by 2.)
• Represent how the student counted by drawing dots in rows. If students count by 2, represent this by drawing two dots at a time and count by 2.
  • For example:

    

    

• “Look at the numbers in each group. What do you notice? What do you wonder?” (All of the numbers show pairs. The numbers in the leftover group have only 1 leftover, the rest make pairs. I wonder what other numbers go in these groups. I wonder if these are the same numbers we found had 1 leftover yesterday.)

• Before students share, remind students to use words such as pairs, equal groups, and leftovers.
• 1 minute: quiet think time
• 1-2 minutes: partner discussion
• Share responses.
• If needed, “How many leftovers did each number have?”

The purpose of this activity is for students to determine whether a group of people (16–20) can be organized into groups of 2 without any person left alone or any groups of 3. They begin to reason about whether a group of objects is even or odd by using what they know about counting or adding by 2 (MP7, MP8). Students should be given access to counters, but may use other representations, including equations.

• Groups of 2
• Give students access to connecting cubes or counters.
• Have students pair up to find a new partner or line up in pairs.
• “Does everyone have a partner?”
• “When we need a partner for an activity, are we always able to have only groups of 2?” (No. When ___ was absent, we had to make a group of 3.)

• “Let’s show whether all students in different class sizes can be paired up to make only groups of 2.”
• “Do the first question on your own.”
• 3 minutes: independent work time
• “Compare your thinking with your partner. Then answer numbers 2 and 3 together.”
• 8 minutes: partner work time
• Monitor for different ways students show pairs for 19 students to share in the synthesis.

• Draw or display:

• “How could we use this representation to show whether everyone in Noah’s class will have a partner?” (There are 18 circles and you can see they are in pairs. 19 is one more than 18. So, one circle would be left out).
• Share responses. Include reasoning from previously selected students.