<p>Students will learn how to relate a given number to other numbers, specifically numbers up to ten. At the end of this lesson, students&nbsp;are going to:<br>- perceive an object's relationship to a number as a single when counting.<br>- write numbers in both words and numerals.<br>- depict numbers in a variety of ways, including through the use of images or other models (cubes, links, etc.).<br>- discern the connection between a number and the additional quantities of one and two.<br>- determine how a number relates to the quantities that are one and two less.<br>- identify visual patterns of objects that correspond to a number without counting.<br>- give a set of objects a specified number.<br>- compare and arrange sets of numerals, utilizing cardinal numbers.&nbsp;</p>

<p>- What happens if I combine or divide a set of numbers (objects)?<br>- How does mathematics aid in effective communication?&nbsp;<br>- How do patterns and relationships connect in math?&nbsp;<br>- How can numbers be represented, compared, quantified, and modeled using mathematics?&nbsp;<br>- What does it mean to evaluate or estimate a numerical quantity?&nbsp;<br>- What qualifies a tool and/or strategy for a specific task?&nbsp;<br>- When is it better to estimate rather than calculate?</p>

<p>- Quantity: An amount of an object.&nbsp;<br>- Total: The number of objects all together.</p>

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

<p>- Student understanding will be evaluated through workstations, small-group discussions, and observations made during class activities.<br>- You can use the Random Reporter method to determine&nbsp;if students understand the material. (Preferable) Use Assessment 1 (M-K-1-2_Assessment 1) to assess student mastery in more detail if necessary.</p>

<p>Explicit instruction, modeling, scaffolding, and active engagement<br>W: Explain to the students the connection between quantities shown by sets of counters or other objects and cardinal numbers.&nbsp;<br>H: Lead students through the Counting Students exercise to help them learn that the same quantity can be found and represented in a variety of ways.&nbsp;<br>E: Assist students in practicing the concept of quantity correlation with cardinal numbers by having them participate in the Connecting Cubes activity.&nbsp;<br>R: As students review counting, matching sets to cardinal numbers, and finding sums and differences for quantities, have them work in small groups using workmats and connecting cubes.&nbsp;<br>E: Reconvene students in a sizable group to go over the method they followed and the outcomes in order to assess their progress and comprehension.&nbsp;<br>T: Customize the lesson by incorporating new activities or reducing the amount of free practice that students engage in. Try assigning students to count off or use number cubes in groups, as outlined in the Extension section, for extra practice.&nbsp;<br>O: The objective of this lesson is to transition from representational counting (cubes) to concrete counting (people). Students learn about the more ethereal symbols used to represent numbers through the numeral cards.&nbsp;</p>

<p><strong>"We're going to practice counting to ten with cubes, people, and numbers. We must learn to count carefully so that we all get the same answers or totals. More than one method may exist to arrive at the same answer."</strong><br><br><strong>Counting Student Activity</strong><br><br><strong>"Let's learn more about our class by counting the number of boys in it. Would all our boys gather here and form a line?"</strong> Let us count aloud to determine the number of boys in our class.<strong>"As the class counts aloud, follow the boys and point to each one to represent one-to-one correspondence. Write the total (____ boys) on the whiteboard or another type of display unit. After counting every girl in the class, repeat the exercise and record the total: "___ boys and ___ girls." &nbsp;"Is it more common to have boys or girls among us?"</strong><br><br>Ask:<strong> "Is there a way to find out how many boys and girls we have together?" </strong>Possible answers could be:<br><br>Make everyone line up and count them.<br><br>Incorporate the girls and boys.<br><br>Count the boys first, then the girls.<br><br>To determine the sum, select a suggestion and count. Try a different approach. Question: <strong>"Should we always count to the same total each time? Why?"</strong><br><br><strong>"Is it important to count the boys or the girls first? Why and why not? Put the sum here: "Students are made up of ___ boys and ___ girls."</strong><br><br><strong>Connecting Cubes Activity</strong><br><br>Assign a red connecting cube to every boy and a yellow cube to every girl. <strong>"Combine all of our cubes."</strong> Ensure that all students can see the final sets of red and yellow cubes.<br><br><strong>"How many red cubes do you think we have?" </strong>Select two or three pupils to present their ideas. For the yellow cubes, repeat these steps. Count the cubes in each set and record the totals under the boy and girl totals:<br><br>___ boys and ___ girls combine to form ____ pupils.<br><br>Red and yellow together make ____.<br><br>Ask the question,<strong> "How many cubes will we have when we connect the red and yellow cubes?"</strong> Select students and ask them to share their thoughts. Count the red and yellow cubes and write the total on the board for everyone to see.<br><br>Ask students to repeat back to you the information that the number of boys equals the number of red cubes, the number of girls equals the number of yellow cubes, and both sums should equal one.<br><br>To test quick learners, pose the following question:<br><br><strong>“How many boys would we have if a new one joined our class?”</strong><br><strong>“How many pupils would we have in total?”</strong><br><strong>“How many girls would we have if one of our girls wasn't here today?”</strong><br><strong>“If five girls weren't here today, how many girls would we have?”</strong><br><strong>"How many students would there be in our entire class?"</strong><br><br>Use the red and yellow cubes to represent one more and one less.<br><br><strong>Small-Group Activity</strong><br><br>Form a group of five or six students, including boys and girls, to role-play the following small-group exercise. Give them two sets of numerical cards (M-K-1-2_Numeral Cards), a copy of Workmat 1 (M-K-1-2_Workmat 1), and six red and six yellow cubes.<br><br><strong>"Count the number of boys in your group. To display the number of boys you have, use the red cubes. Place the numerical card indicating the number of boys you have in front of the word "boys" on your workmat. Next, use the yellow cubes to indicate how many girls are in this group by counting them. Place the numerical card indicating the number of girls you have in front of the word "girls." How do you find out the total number of people in your group? " </strong>Allow students to deliberate over the choices and assist them in making a decision.<br><br><strong>"Select the numerical card displaying your solution and place it in the final empty area on your workmat."</strong><br><br><strong>"Let's read what you discovered: ___ boys and ___ girls combined make up ____ students."</strong> Address any inquiries from the students about the guidelines.<br><br>Divide the class into groups of four to six people, with a mix of boys and girls in each group. Assign the same materials to each group that were used in the demonstration: two sets of numeral cards 1-6, six red cubes, six yellow cubes, and a copy of Workmat 1.<br><br><strong>"Count the number of boys and girls in each of your groups. Count the number using the cubes. Next, select numbers to indicate each item's quantity and arrange them on your workmat."</strong><br><br>As you observe each group at work, approach them and pose inquiries like these:<br><br><strong>“How many girls and boys make up your group?”</strong><br><strong>“How many boys and how many girls are in your group?”</strong><br><strong>"How do you determine how many in total you have?"</strong><br><br>Regroup students and carry out the task once more. It is possible to choose group sizes and makeup to better suit the needs of the students. Students who can count to five or six will do better in smaller groups; those who can count to ten or more will find larger groups challenging. For larger groups than six, keep extra cubes and numeral cards (seven to ten) on hand to accommodate their needs.<br><br>Take note of the counting techniques employed and the students who do not yet exhibit one-to-one correspondence. Extended practice in small groups and/or at workstations will be beneficial. Ask,<strong> "How many more (boys than girls or girls than boys) are there in your group?" </strong>when you see groups holding their sets side by side to see which group has more. <strong>"In what way are you aware?"</strong><br><br>Reconvene the small groups for a discussion as a whole. Choose a student at random from each group to present his or her research to the class.<br><br><strong>"Would you show us the cubes that your group assembled and share your findings with us?"</strong> If needed, ask students to explain how the group determined how many they had in total. Among the possible answers are:<br><br>We just looked at the people and counted the blocks.<br><br>We distributed red and yellow cubes to each boy and girl, stacked them, and counted.<br><br>Before counting the girls, we counted the boys and obtained that many cubes.<br><br>Summarize the answers that show effective counting techniques, like adding to, counting up, and pointing to each child or cube in a one-to-one manner.<br><br>Students should finish the first assessment (M-K-1-2_Assessment). Give coloring pencils or markers.<br><br><strong>Extension:</strong><br><br><strong>Routine:</strong> Throughout the day, identify classroom scenarios that promote counting and drawing comparisons. In this lesson, emphasize the use of specific vocabulary words.<br><br><strong>Expansion:</strong> Two six-sided number cubes are needed for this exercise. Divide the class into circles to start. Roll the number cubes and have one student add the numbers. Explain that students can count the dots on the first number cube (one, two, three, four, five, and six), for instance, if the roll was a six and a two. They can then pick up where they left off and count the dots on the second cube (seven, eight, etc.), pointing to the dots. Find out if the students have any more ideas for counting (ten frames, for example).<br><br>Decide on a starting point for the circle and instruct kids to stand one at a time, counting with you until you reach the designated number. When the first child stood up and said, "one," the next one stood up and said, "two," and so on until eight children were standing. As a group, ask the children to stand in the middle of the circle or to the side. Roll new dice and repeat the counting exercise. Get the new group to take a united stance. Roll the dice again, or have the remaining students count themselves and stand in unison. There will probably be three or six groups.<br><br>To symbolize their group number, have each group join one set of base-ten Unifix (or comparable) cubes. Use six of one color and two of another to represent the values on your number cubes, and show what eight cubes connected look like. (If it wasn't eight, use the numbers from your example roll.) While pointing to each cube in your stack, have the class count aloud from 1 to 8.<br><img src="https://storage.googleapis.com/worksheetzone/test-upload/1707118106847.jpeg" width="392" height="233"><br>Have each student count the number of Unifix cubes in the stack the group assembled, either individually or collectively as a group. Ask students to determine which stacks are the biggest and smallest by comparing the heights of their stacks to those of the other groups.<br><br>Request that the groups sort themselves into larger and smaller groups based on the numbers. (They can base this on the height of their cube stack, the size of their student group, or the counting numeral.) Help them choose the best location for their groups to move to if any are the same size. Encourage groups to come to a consensus and ask students to explain how they chose where to stand.<br><br><strong>Small Group: </strong>Get paper, circle stickers, crayons, markers, and Donald Crew's book Ten Black Dots ready. Discuss the various ways that dots are used to represent numbers after reading the book Ten Black Dots.<br><br>Use a different counting book if this one isn't available. (Several recommended books are listed in the lesson's Related Resources section.) Get ready to present the students with one or two dot examples. To accomplish this, make simple pictures with one to ten black dots. Assign a piece of drawing paper to every student. Students should select a number between 1 and 10 and write it on their paper. Give them instructions to create their picture using the same number of dot stickers as their own. Students will write, "_____ dots can make a _____," at the bottom of their pictures. To make a class Dot book, save the pages.<br><br><strong>Workstation 1: </strong>Provide multiple copies of Workmat 2 (M-K-1-2_Workmat), two different colored cubes, and numeral cards (M-K-1-2_Numeral Cards) at the station. Students will require an image that displays a pair of distinct mixed-object types (e.g., dogs and cats, cars and boats, etc.). Students can either locate pictures in a set of picture books at the station or you can provide them with specific pictures of your choosing. Students should place the matching numerals on their workmat after using the color cubes to indicate how many of each of the two items are in their set. Students should be able to explain how many of each object they discovered, the total number of objects discovered, and how they discovered them.<br><br><strong>Workstation 2: </strong>Arrange ten cubes of the same color and numeral cards numbered 1 through 10 in this workstation for students who need practice with one-to-one correspondence. Students should build cube sets that correspond to the numbers on the cards. For students who require additional practice counting beyond five, limit the number of cards to five.</p>