Understanding Tens and Ones Unit of Study: Counting and Modeling Numbers to 120 Global Concept Guide: 2 of 4

Content Development  “Making a transition from viewing ten as simply the accumulation of ten ones to seeing it both as ten ones and one ten is an important first step for students toward understanding the structure of the base ten system” (NCTM Standards p. 33)  Until now “ten” has meant 1 more than 9 things…but the singular noun “ten” suddenly becomes one thing.  The ability to view numbers flexibly starts with a firm understanding of tens and ones.  Teachers and students must use precise language in order for students to build conceptual understanding. We must be cognizant that we are not always just saying “17,” but also referring to it as “1 ten and 7 ones” or “10 ones and 7 more ones.” As teachers we need to hold out students accountable for using precise language.

Content Development  Different ways to represent tens and ones will appear throughout this year and years to come. As the class explores ways to represent numbers, create an anchor chart that will document the following ways:

Day 1 Essential Question: How can you group ones to make counting quicker?  The focus of Day 1 is to focus on moving students away from counting every object to recognizing a group of ten and count on from there.  Example:  In this example you would encourage students to recognize the group of ten in the ten frame and begin counting at 10.  10, 11, 12, 13  Providing students with pre-grouped items, such as the ten rod of the base tens blocks, before they conceptually understand making a group of ten can confuse students. Base ten blocks will be introduced in the last part of the unit if ready.  Go Math Lesson 6.3, Engage: Using the Listen and Draw p. 249 in conjunction with the Teach and Talk questions in the margin of your TE manual can be used to probe students to think about the way they count the 12 objects: as 12 single object or a group of 10 and 2 more (10, 11, 12).

Day 1 Continued…  Essential Question: How can you group ones to make counting quicker?  Use this format to record different ways to represent the number 12. This can help students make the connection to addition (expanded form). This would be a good time to start you anchor chart (refer to content development page for example).  You could use the Share and Show p. 250 #s 1-2 to informally assess students understanding. You can use p. 252 for independent practice and p. 251 for remediation (use snap cubes to remediate).  Closure: Have students journal the EQ: How can you group ones to make counting quicker? By the end of Day 1, student should be able to recognize a group of ten and count on (10, 11, 12, etc…).

Day 2 Essential Question: How can you show a number as tens and ones?  Today’s focus is to make the connection from the concrete (manipulative models) to the pictorial.  Students may not know the most efficient way to draw a quick model for their cubes. You may need to model this for your students.  Engage: Write a 2 digit number on the board. Then have students make a concrete model to represent the number. Use the recording sheet (link is on next slide) provided to have students represent the number in additional ways.  Probing questions-How do you know that your drawing represents this number?, How do you determine the number of tens and the number of ones?, How does your model represent the number of tens and ones? Quick Pic

Day 2 Continued… Essential Question: How can you show a number as tens and ones?  Play the Representing Numbers Game! You will show the students a card and they have to represent the number on the recording sheet. (You can have students play in small groups or whole class.)Representing Numbers Game!recording sheet  It is still appropriate on this day for students to use snap cubes to build concrete models.  Closure: Ask and discuss with students “Why is it important to be able to represent numbers in different ways such as standard form, expanded form, word form, pictorial and concrete models?”  Flexible thinking when representing numbers builds a deep and rich understanding of place value for students. This concept is the foundation to future math concepts like mental math computation for all 4 operations. By the end of Day 2, students should be able to represent numbers using concrete models, quick pics, expanded form, standard form and base ten language.

Day 3 Essential Question: How can you represent a number using base ten blocks?  Engage:  Ask children: Which is greater and why? (students may say the snap cubes are greater because they are bigger in size).  Once the class has determined that they have the same value ask students probing questions like: What is the difference between the snap cubes and the base ten blocks? (students may say the snap cubes are bigger, the base ten blocks don’t come apart, etc…)  Building Conceptual Knowledge- Orally present students with two digit numbers greater than 20 to give them the opportunity to represent the number using base ten blocks. Have students share models and explain why it represents the number. You could use white boards to have students represent the number in various forms. (approximately 10 minutes should be spent on this activity)

Day 3 Continued… Essential Question: How can you represent a number using base ten blocks?  Present students with the non-example and have them explain why it is correct or incorrect.  You may use the Share and Show Go Math Lesson 6.6, p. 262 to informally assess students.  You could use Problem Solving p. 264, 268 for independent student practice.  If necessary small group remediation could be done at this time. You may need to remediate by focusing on the connection between snap cubes and base ten blocks.  Closure: Students should select who represented the number correctly and why. Closure By the end of Day 3, students should be able to represent 2 digit numbers using base ten blocks.

Day 4 Essential Question: What are four different ways you can represent a number?  This day should be spent differentiating instruction based on student needs.  Re-teach:  Group Ones to Make a Ten: Students are circling a group of ten and recording the amount of tens and ones. Group Ones to Make a Ten  Tens and Ones: Students will write the number represented by the base ten blocks. Tens and Ones  Core:  Place Value Cover Up: Red die represents the number of tens and the green die represents the number of ones. Roll the both dice, build the number of manipulative, and orally tell your partner the number. Cover the number with a counter and play till 4 counters in a row. Place Value Cover Up  Tens and One Game: Students select a numeral card for the target. Students will roll dice to determine tens and ones. The goal is to regroup ones into tens and reach the target number. This game can be used for core and enrich. Tens and One Game  Dice Game: Students will play a game to practice representing from Dice Game  Enrich:  GO Math Lesson 6.3 TE p 249B – Enrich Activity Performance Task should be given the last minutes of the class.

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