Ordering Rational Numbers and Coordinate Plane Unit 1

Ordering Rational Numbers and Coordinate Plane Unit 1. 2 TEKS 6. 2 A, 6. 2 B, 6. 2 C, 6. 2 D Please read the notes section on each slide for important teacher information.

Greetings! ● Please clear your desk except for the following items: ○ Pencil ○ White Board Marker ○ White Board ○ Math Journal ○ Glue

Day 1 Focus SE 6. 2 B identify a number, its opposite, and its absolute value. Objective The students wil. I use number lines and solve word problems to identify a number and its opposite.

Day 1 Picture it This routine helps students: ● Look for mathematics in their environment ● Apply mathematics concepts to real-world situations ● Pursue solutions with no clear solution ● Reason about number and quantity in the real world ● Refine strategies and ideas about estimation ● Communicate their reasoning to others

Day 1 What to Do 1. 2. 3. 4. 5. 6. 7. 8. 9. Select a picture and a question to ask about the picture. Display the picture and give students a few moments to examine it. Pose the question to students. Give students time to think about an answer to the question. Consider allowing them to capture some thoughts on paper or sticky notes or in their journals. Have students share their solutions and reasoning with a partner. Bring the class back together to share solutions and reasoning. Highlight student ideas during discussion. Honor and explore all reasoning. Be sure to counter both logical and flawed reasoning with questions rather than confirmations of “right” or “wrong”. Consider asking students to think of other questions that they can ask about the picture. These questions could be used in subsequent classes.

Day 1

Numberless Word Problem Notice/Wonder 6 th grade - Unit 1 6. 2 b

What do you notice? What do you wonder?

What do you notice?

What do you notice?

What do you notice?

What point represents the value of ?

Numberless Word Problem 6 th grade - Unit 1 6. 2 b

George wrote an integer. The opposite of George’s integer is a negative number.

George wrote an integer. The opposite of George’s integer is -53. What questions could be asked from this information?

George wrote an integer. The opposite of George’s integer is -53. What is George’s integer? What is the absolute value of George’s integer?

Math Journal Notes Students will Add notes to their journals about: ● ● Absolute Value Opposite numbers

Motivation Math 6. 2 B Students will Complete the Introduction and guided practice- Pages 15 -16.

Day 2 Focus SE 6. 2 B identify a number, its opposite, and its absolute value. Objective The students wil. I use number lines and solve word problems to identify a number and its opposite.

Day 9 Is this the end? This routine helps students: ● Consider how a number relates to another number ● Reason about how two numbers relate to a third ● Develop a sense of relative position and relationship (as the location changes) ● Look for and manipulate patterns and structure within relationships ● Reinforce ideas about friendly numbers or benchmarks ● Practice computation to improve precision ● Develop confidence with quantity and computation ● Communicate their reasoning with others ● Listen actively to the reasoning of others

Day 9 What to Do 1. Draw or project a number line on the board with a known location and unknown endpoints. 2. Give students a value that represents the known location on the number line. 3. Ask students to determine what the endpoints might be for the number line based on the value of the known location. First exposure to the routine can be supported with printed number lines or students journals. In time, the routine can become a mental activity. 4. Have students share their endpoints with classmates in small groups or with partners. 5. Bring the class together. Ask students to share sets of endpoints. REcord the sets of endpoints that students share. Record a host of responses before discussing accuracy and reasoning. 6. After student ideas are collected, discuss the solutions offered by the class. 7. Honor and explore both accurate and flawed reasoning. Highlight how the endpoints are related to the midpoint and possible relationships between sets of endpoints. Here are some questions you might ask: ○ How did you find you endpoints? ○ How do you know the endpoints are accurate? ○ Are there any sets of endpoints that you find surprising? ○ Do you notice any patterns in the endpoints that we created as a class? ○ Is there any set of endpoints that were shared that you are unsure of or that you would like argue?

Is This the End? The arrow is pointing at 1 ½. What are the endpoints?

Task Cards

Day 3 Focus SE 6. 2 A - classify whole numbers, integers, and rational numbers using a visual representation such as a Venn diagram to describe relationships between sets of numbers. (Supporting) Objective The students will use venn diagrams to classify whole numbers, integers, and rational numbers.

Day 3 That’s a fact This routine helps students: ● Develop their understanding of the magnitude of numbers ● Develop a sense of reasonableness ● Make better sense of their world as it is described with numbers and measurements ● Justify and communicate their reasoning ● Consider the reasoning and strategies of others

Day 3 What to Do 1. Create four numeric or statistical statements about topics of interest. Trivia books, books of records, or internet searches can be quite helpful for finding and creating these statements. Note that the number of statements can be adjusted due to the amount of time allotted for the routine in class. 2. Remove the values from the statements. 3. Present the statements separate from the values. Include additional incorrect values. 4. Charge small groups of students to discuss and agree on the likely values for each statement with a justification for their selection. 5. Once students arrive at solutions, discuss group ideas about the solutions. Highlight student reasoning during discussion. Honor and explore both accurate and flawed reasoning. 6. Reveal solutions to the statements and discuss possible surprises.

Day 3

Numberless Word Problems Same/Different Notice/Wonder 6 th grade - Unit 1 6. 2 a

What do you notice? What’s the same? What’s different?

What do you notice? What’s the same? What’s different?

What do you notice? What do you wonder?

The Venn diagram shows the relationship among different sets of numbers.

The Venn diagram shows the relationship among different sets of numbers. Which number would be located in the shaded part of the diagram?

The Venn diagram shows the relationship among different sets of numbers. 2 3 -1. 7 -8 10 Which number could be located in the shaded part of the diagram?

What do you notice? What do you wonder?

What do you notice? What do you wonder?

Which graphic organizer correctly groups the following numbers? 3. 4 -1. 2 -2 3

Which graphic organizer correctly groups the following numbers? 3. 4 A C -1. 2 -2 B 3 D

Motivation Math 6. 2 A Students will Complete the Introduction and guided practice- Pages 7 -8.

Day 4 Focus SE 6. 2 A - classify whole numbers, integers, and rational numbers using a visual representation such as a Venn diagram to describe relationships between sets of numbers. (Supporting) Objective The students will determine if statements about classifying whole numbers, integers, and rational numbers are always true, sometimes true, or never true.

Always, Sometimes, or Never? High Yield Strategy Instructional Steps Always/Sometimes/ 1. Teacher creates content statement cards that include Never (2015) true and false statements. Statements should be based on student misconception. 2. Students discuss content statement cards to determine if the statement is “always true, ” “sometimes true, ” or “never true. ” 3. Student groups will debate those statements for which they disagree. Thinking (Process TEKS Rigor) • Compare/Contrast • Summarize • Analyze • Justify Arguments • Communicate Mathematical Ideas

Always, Sometimes, or Never? If a number is an Integer, then it is a Rational Number.

Always, Sometimes, or Never? If a number is a negative decimal, then it is a Integer.

Always, Sometimes, or Never? If a number is positive, then it is a Whole Number.

Always, Sometimes, or Never? If a number is a Rational Number, then it is also an Integer and a Whole Number.

Always, Sometimes, or Never? If a number is negative, then it is a Whole Number.

Always, Sometimes, or Never? Fractions are Rational Numbers.

Always, Sometimes, or Never? If a number is a Whole Number, then it is an Integer.

Always, Sometimes, or Never? If a number is a Whole Number, then it is also an Integer and Rational Number.

Always, Sometimes, Never Cut and Paste Activity ● ● ● Cut out the cards. Determine if the statement is always true, sometimes true, or never true. Glue the statement in the correct place on the table.

Day 5 Focus SE 6. 2(c) - locate, compare, and order integers and rational numbers using a number line. (Supporting) Objective Use number lines to locate, compare, and order integers and rational numbers.

Two columns This routine helps students: ● Estimate values and solutions to expressions ● Consider efficient methods for finding results ● Communicate their reasoning to others ● Develop confidence in their reasoning and computations ● Consider the reasoning and strategies of others ● Enhance their ability to determine reasonableness of answers or solutions ● Develop computational fluency ● Compare their ideas to the reasoning of others ● Look for and make use of number relationships and patterns within operations pg. 73

What to Do 1. Select two or three sets of expressions to compare. Keep in mind that the routine should be completed in 5 to 7 minutes, so one set of expressions may be enough to compare for some classes. 2. Compare each before sharing with students to anticipate what students might do. 3. Direct students to compare each row of expressions, deciding which expression is greater. 4. Remind students that this is a mental mathematics activity and that exact answers aren’t required, though they can use exact figures if they are able to find them. 5. Provide time for students to reason and compare. 6. Direct students to share their findings and reasoning with a partner. 7. Facilitate a discussion about how students compared the expressions. 8. Optional: Record student strategies on the whiteboard or document camera. Doing this can help other students see classmates’ reasoning. 9. Optional: Find exact solutions after discussion about estimates and reasoning. 10. Honor and explore both accurate and flawed reasoning.

Motivation Math 6. 2 C Complete the introduction and guided Practice Pages 23 -24

Task Cards 6. 2 C

Day 6 Focus SE 6. 2(d) - order a set of rational numbers arising from mathematical and real-world contexts. (Readiness) Objective Order rational numbers in in real world contexts.

Day 9 Is this the end? This routine helps students: ● Consider how a number relates to another number ● Reason about how two numbers relate to a third ● Develop a sense of relative position and relationship (as the location changes) ● Look for and manipulate patterns and structure within relationships ● Reinforce ideas about friendly numbers or benchmarks ● Practice computation to improve precision ● Develop confidence with quantity and computation ● Communicate their reasoning with others ● Listen actively to the reasoning of others

Day 9 What to Do 1. Draw or project a number line on the board with a known location and unknown endpoints. 2. Give students a value that represents the known location on the number line. 3. Ask students to determine what the endpoints might be for the number line based on the value of the known location. First exposure to the routine can be supported with printed number lines or students journals. In time, the routine can become a mental activity. 4. Have students share their endpoints with classmates in small groups or with partners. 5. Bring the class together. Ask students to share sets of endpoints. REcord the sets of endpoints that students share. Record a host of responses before discussing accuracy and reasoning. 6. After student ideas are collected, discuss the solutions offered by the class. 7. Honor and explore both accurate and flawed reasoning. Highlight how the endpoints are related to the midpoint and possible relationships between sets of endpoints. Here are some questions you might ask: ○ How did you find you endpoints? ○ How do you know the endpoints are accurate? ○ Are there any sets of endpoints that you find surprising? ○ Do you notice any patterns in the endpoints that we created as a class? ○ Is there any set of endpoints that were shared that you are unsure of or that you would like argue?

Here are the low temperatures (in Celsius) for one week in Juneau, Alaska: Monday Tuesday Sunday 5 -1 Wednesday -6 Thursday -2 Friday Saturday 3 7 0 Arrange them in order from coldest to warmest temperature.

On a winter day, the low temperature in Anchorage was 23 degrees below zero (in degrees Celsius) and the low temperature in Minneapolis was 14 degrees below zero (in degrees Celsius). Sophia wrote, Minneapolis was colder because -14 < -23 Is Sophia correct? Explain your answer.

The lowest temperature ever recorded on earth was -89 degrees Celsius in Antarctica. The average temperature on Mars is about-55 degrees Celsius. Which is warmer, the Lowest temperature on earth or the average temperature on Mars? Write an inequality to support your answer.

Motivation Math 6. 2 D Complete the introduction and guided Practice Pages 31 -32.

Day 7 Focus SE 6. 2(c) - locate, compare, and order integers and rational numbers using a number line. (Supporting) 6. 2(d) - order a set of rational numbers arising from mathematical and real-world contexts. (Readiness) Objective Students will complete task cards and a classification coloring sheet as a review for the test.

Switcharoo This routine helps students: ● Consider how problems are posed and numbers are related ● Find various solutions to the same problem ● Critique the reasoning of others ● Attend to the precision of their calculations ● Develop confidence with calculations and combinations ● Build understanding of the relationship between contexts, representations, and operations pg. 85

What to Do 1. Create one or more computation or word problems. 2. Use the solution(s) from step 1 as the prompt for the routine. 3. Give students time to create situations or calculations with the intended result. Adjust the number of situations presented so that students work independently for approximately 2 minutes. 4. Have students share their creations with partners. 5. Bring the class together to discuss. See the notes section for some questions you might ask. 6. Consider having students share solutions before having a class discussion. 7. Consider exploring solutions to one of the problems first before moving on to the next. 8. Consider skipping a conversation about one of the questions or the second value and its questions if time becomes limited due to discussion. 9. Remember to honor student thinking. 10. Inject new ideas if students feature common approaches. For example, if all students create addition equations that add a decimal less than 1 to find 15. 73 (e. g. , 15. 23 + 0. 5, 15. 63 + 0. 1, 15. 5 + 0. 23), give an example that adds a decimal greater than 1, such as 14. 63 + 1. 2.

Test Review Integer Task Cards 6. 2 B, C, D