<p>Dot cards and number lines are used in this lesson to illustrate skip counting equal groups. Students investigate how multiplication and skip counting relate to one another. Students are going to:<br>- comprehend repeated addition by 2s, 3s, 4s, and 5s to 30 or skip counting.<br>- understand how to&nbsp;skip counting and how&nbsp;equal groups are related.&nbsp;</p>

<p>- How are mathematical representations of relationships made?&nbsp;<br>- How are relationships in mathematical contexts described by patterns?&nbsp;<br>- How do we represent, compare, quantify, and model numbers using mathematics?</p>

<p>- Equivalent: Equal.</p>

<p>- dot cards for 2, 3, 4, and 5, one set for each pair (M-2-4-1_Dot Cards)&nbsp;<br>- large number line for whole-class use, or one that can be placed under a document camera or on an overhead projector (M-2-4_Number Line)&nbsp;<br>- document camera or overhead projector&nbsp;<br>- I Can check-off sheets, one per student (M-2-4-1_I Cans)&nbsp;</p>

<p>- As students play the Equal Groups game, watch them and grade them.&nbsp;<br>- Formative assessments may include the students' self-evaluation on the I Cans sheet (M-2-4-1_I Cans).</p>

<p>Explicit instruction, modeling, scaffolding, and active engagement&nbsp;<br>W: Explain to the class that they will apply their knowledge of addition and skip counting to solve equal-grouping problems.&nbsp;<br>H: Arrange a group of four counters into three sets of 12. See if and how the students arrive at the total number of counters by flashing them.&nbsp;<br>E: After learning what skip counting is on a number line, students will apply that understanding to dot cards before moving on to skip counting without the dots.&nbsp;<br>R: Students will collaborate in pairs to correct each other's misconceptions and compare their ways of thinking.&nbsp;<br>E: As soon as they believe they can complete each task, students will mark their achievements on the I Can sheet.<br>T: Until they feel comfortable working without the visuals, let students utilize dot cards and/or number lines. Once prepared, students can start working in equal groups of up to fifty people.&nbsp;<br>O: In this lesson, students practice using a class number line to count equal groups. Afterwards, they use dot cards without the number line in pairs.&nbsp;</p>

<p><strong>"Today, we will investigate equal groups."</strong>&nbsp;Flash (for approximately 3 seconds) a set of 12 chips arranged in three groups of four. <strong>"How many chips did you see?" </strong>ask students.&nbsp;To find out how many chips a student saw, ask them to explain. Repeat the procedure with six groups of two this time. You can use the set of 12 or 14 arranged in different ways if students are still trying to count by 1 after a few tries.<br><br>Extract the class number line (M-2-4_Number Line) and the dot cards (M-2-4-1_Dot Cards) for the 2s. Set down each dot card as you make your jumps or points on the number line. Say,<strong> "Let's see how many two-person groups we have. 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20."</strong>&nbsp;&nbsp;Next, ask, <strong>"What observations do you have regarding the events that occurred on the numerical line each time I positioned a dot card? How do you interpret the numbers you see?"&nbsp;</strong><br><br>Use the dot cards for 3s and repeat these steps. You can repeat the procedure with 4s and 5s if students require additional practice.<br><br>Inform the students that they will be practicing counting equal groups in pairs. Show the students the sets of 2s, 3s, 4s, or 5s dot cards that each partner group will receive. Encourage students to arrange cards with five on top and five on the bottom, resembling a ten-frame, if you have worked with ten-frames extensively. Allow another student to assist you in modeling the activity. One partner will take as many cards as they each have, up to a maximum of two. They will ask, "How many dots?" after turning them face up. How can you be certain that your response is accurate? (<i>My answer is correct because&nbsp;I counted three rows, and three were in each row, and that makes 9 in total.</i>) Upon achieving fluency, both partners can flip the dot cards over and arrange them, consistently inquiring, "How many dots?"<strong> </strong>Students won't be able to truly count the dots in this instance, which is the only difference. When working with a set of dot cards for 3s, for instance, a partner group should be aware that if they turn four cards face down, it indicates that twelve dots are hidden. On the self-evaluation I Can sheet (M-2-4-1_I Cans), students will track their advancement.<br><br><strong>Extension:</strong><br><br><strong>Routine 1: </strong>Use the overhead or document camera to flash equal groups. Ask&nbsp;the class, <strong>"How many shoes, dots, etc.? How do you know you've got the right answer?"</strong><br><br><strong>Routine 2:</strong> To reinforce the idea of skip-counting, take a few minutes to play the game Cherry Pie during transitions, before or after lunch, etc. (This game is quite similar to Sparkle, the spelling game.)<br><br>Students will form a circle and sit in it. Choose the beginning or ending number (__ to __) and the number the students will count by (2, 3, 4, 5, 10, or 100). The sequence starts with one student saying the first number, then the next student saying the next number. Keep going until you get to the final digit. Assign the students to count from 5 to 100 by 5s, for instance. Around the circle, the first student will say "5," the person next to him or her will say "10," and so on (15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100). The student who comes after the student who says "100" will say "Cherry Pie," and the student who comes after that is out. (If you would rather that students stay in the game, you could assign a challenge to the student who said "Cherry Pie" to keep them in.)<br><br>Practice counting by any number with this game.<br><br><strong>Small Group:</strong> By rolling a number cube twice, students can practice equal groups even further. The first roll represents the number of dots, while the second roll represents the number of groups.<br><br><strong>Expansion:</strong> When students gain confidence, you can work with them to see how they calculate the number of dots while flashing the dot cards.</p>