MEAS1 (3 Instructional Days)

MATH_0382_MEAS1_LES_02

382 Lesson

MEAS1 (3 instructional days)

Real Numbers

Enduring Understandings
The student understands that real numbers can be represented in a variety of ways.
The student understands mathematical relationships and makes connections to geometric formulas.
The student understands that geometry can be used to solve problems.
Vocabulary
irrational number, square root, rational number, Pythagorean Theorem, cylinder, cone, congruent, base, sphere, lateral surface area, total surface area, rectangular prism, triangular prism, diagram, real numbers, set, subset, leg, hypotenuse, scale factor, image, pre-image, integer, natural (counting) numbers, whole numbers, pi, volume, right triangle, area, perimeter, B (area of base), P (perimeter of base), Venn diagram, equivalent, height, composite figure, coordinate plane, number line, integer, whole number, natural or counting number, equation, expression, formula, substitution, approximate, perpendicular, square of a number, exponent, perfect square, 3-dimensional, proportional change
8(2)Number and operations. The student applies mathematical process standards to represent and use real numbers in a variety of forms. The student is expected to:
(A)extend previous knowledge of sets and subsets using a visual representation such as a Venn diagram to describe relationships between sets of real numbers; Supporting
The student will know… / The student will be able to…

the characteristics of various sets of numbers.

Natural/counting numbers
Whole numbers
Integers
Rational numbers
Irrational numbers
Real numbers

determine which set of numbers a number belongs.
construct a graphic organizer to represent the sets and subsets of numbers.
use a graphic organizer to describe relationships between sets of numbers.

8(2)Number and operations. The student applies mathematical process standards to represent and use real numbers in a variety of forms. The student is expected to:
(B)approximate the value of an irrational number, including π and square roots of numbers less than 225, and locate that rational number approximation on a number line; Supporting
The student will know… / The student will be able to…

that an irrational number is a number that cannot be expressed as a ratio of two integers.
appropriate estimation methods for square roots.
that 3.14 is an approximation of pi and is a little less than the actual value of pi.
that the square of a number represents the area of a square.
that the square root of a number represents the side length of a square.

approximate square roots in and out of problem situations.
approximate pi in and out of problem situations.
locate approximate values of irrational numbers on a number line.

8(2)Number and operations. The student applies mathematical process standards to represent and use real numbers in a variety of forms. The student is expected to:
(D)order a set of real numbers arising from mathematical and real-world contexts. Readiness
The student will know… / The student will be able to…

the appropriate real number representations of real-life situations.
that real numbers can be represented in several different forms and still be equivalent.
that real numbers in different forms can be compared and ordered.

locate real numbers on a number line.
write and recognize equivalent forms of real numbers.
convert real numbers to equivalent forms for the purpose of comparing.
convert real numbers to equivalent forms and place in order in mathematical and real-world contexts.

Technology TEKS:

8(3)Research and information fluency. The student acquires, analyzes, and manages content from digital resources. The student is expected to:
(D)process data and communicate results.
8(4)Critical thinking, problem solving, and decision making. The student makes informed decisions by applying critical-thinking and problem-solving skills. The student is expected to:
(C)collect and analyze data to identify solutions and make informed decisions;
(E) make informed decisions and support reasoning;
(F) transfer current knowledge to the learning of newly encountered technologies
8(5)Digital citizenship. The student practices safe, responsible, legal, and ethical behavior while using technology tools and resources. The student is expected to:
(C) practice and explain safe and appropriate online behavior, personal security guidelines, digital identity, digital etiquette, and acceptable use of technology
8(6)Technology operations and concepts. The student demonstrates a thorough understanding of technology concepts, systems, and operations. The student is expected to:
(C) understand and use software applications, including selecting and using software for a defined task;
(J) use a variety of local and remote input sources;
(K) use keyboarding techniques and ergonomic strategies while building speed and accuracy;

ELPS:

(2) Cross-curricular second language acquisition/listening. The student is expected to:

classroom instruction and interactions;

(2) Cross-curricular second language acquisition/listening. The student is expected to:

(D) monitor understanding of spoken language during classroom instruction and interactions and seek

clarification as needed;

(3) Cross-curricular second language acquisition/speaking. The student is expected to:

(E) share information in cooperative learning interactions;

(5) Cross-curricular second language acquisition/writing. The student is expected to:

rules with increasing accuracy as more English is acquired;

Materials:

Markers/Colored Pencils
Glue/Tape
Scissors
1 piece of grid paper per student (Day 1)
1 copy of Perfect Squares and Square Roots Foldable per student (Day 1)
1 copy of Investigating Irrationals per student (Day 1)
1 copy of Real Numbers Graphic Organizer per student (Day 2)
Real Numbers
Rational Numbers
Integers
Whole Numbers
Natural/Counting Numbers
Irrational Numbers
1 copy of Super Sets per student (Day 2)
1 white board, marker, and eraser per student (Day 3)
1 copy of Order Matters per student (Day 3)

Procedure:

Day 1:
Use the MATH_0382_MEAS1_ MAT_REALNUMPRESENT1_02 notebook file to guide this lesson.
Use the Grid Paper and Perfect Squares and Square Roots Foldable for this lesson’s ISN entry.
/ Slide 1: Title Slide
/ Slide 2: Lesson Hook
This slide gives students instructions on creating squares on their grid paper.
Students will come back to this activity later in the lesson.
/ Slide 3: This slide gives students the mathematical definition of perfect squares and square roots.
Pull out the “perfect square” icons to reveal the information. /
/ Slide 4: Teacher Led Example

/ Slide 5: On this slide, students connect the “perfect squares” they created in their hook to perfect squares and square roots. Students should add the “What Does It Mean” section to the empty space on the bottom of their grid paper.
/ Slide 6: This slide shows students how to set up their ISN.
The reminders and descriptions they should add to the page are on the next slide.
/ Slide 7: Perfect Squares and Square Roots Description.
Click on each of the colored boxes to reveal what students should add to their ISN page.
/ Slide 8: This slide shows students how to finish setting up their ISN.
/ Slide 9: This slide provides students with a description of irrational numbers and introduces estimating the value of irrational numbers. /
/ Slide 10: Teacher Guided Example
Pull out each colored star to reveal a step in estimating irrational numbers.
Have students call out responses as you record their answers on the smartboard.
/
/ Slide 11: Teacher Guided Example
Follow the same instructions as in slide 10.
/
/ Slide 12: Teacher Guided Example
Follow the same instructions as in slide 10.
/
Assign students Investigating Irrationals as independent practice/homework.

Procedure:

Day 2:
Use the MATH_0382_MEAS1_MAT_REALNUMPRESENT2_02 notebook file to guide this lesson.
Use the Real Numbers Graphic Organizer for this lesson’s ISN entry.
/ Slide 1: Title Slide
/ Slide 2:
This slide shows students how to set up their ISN entry for this lesson.
/ Slide 3:
This slide provides examples of Natural Numbers.
Have students copy the definition into the section of the graphic organizer, Natural Numbers. /
/ Slide 4:
This slide provides examples of Whole Numbers.
Have students copy the definition into the next section of the graphic organizer, Whole Numbers. /
/ Slide 5:
This slide provides examples of Integers.
Have students copy the definition into the next section of the graphic organizer, Integers. /
/ Slide 6:
This slide provides examples of Rational Numbers.
Have the discussion with students that even though is a square root, the number is simplified to 12 which would go inside the inner most, natural number subset. Have students the definition into the next section of the graphic organizer, Rational Numbers. /
/ Slide 7:
This slide provides examples of Irrational Numbers.
Have students copy the definition into the next section of the graphic organizer, Irrational Numbers. /
/ Slide 8:
This slide provides examples of Real Numbers.
Have students copy the definition into the next section of the graphic organizer, Real Numbers. /
/ Slide 9:
Review each subset and have the students write the examples in their organizer.
/ Slide 10: This slide provides examples for students to practice on the left side of their notebook.
Students can write their examples on a post-it note, and then write which sets of numbers they belong to underneath the post-it.
Click on each of the examples to reveal the sets of numbers they belong to.
/ Slide 11: Teacher guided example.
Answer: D /
/ Slide 12: Teacher guided example.
Answer: B /
/ Slide 13: Teacher guided example.
Answer: D /
Assign students Super Sets as individual practice/homework.

Procedure:

Day 3:
Use the MATH_0382_MEAS1_MAT_REALNUMPRESENT3_02 notebook file to guide this lesson.
/ Slide 1: Title Slide
Have students use white boards during this lesson to record their work and order the numbers.
/ Slide 2: Transition Slide
/ Slide 3: Students will use their estimation skills to decide which number is larger.
They can designate their answer on their whiteboard.
By clicking on the answer on the smartboard, it will reveal if that answer is correct or incorrect. /
Classflow link

/ Slide 4: Students will use their estimation skills to decide which number is smaller.
They can designate their answer on their whiteboard.
By clicking on the answer on the smartboard, it will reveal if that answer is correct or incorrect. /
/ Slide 5: Students will use their estimation skills to decide which number is larger.
They can designate their answer on their whiteboard.
By clicking on the answer on the smartboard, it will reveal if that answer is correct or incorrect. /
/ Slide 6: Students will use their estimation skills to decide which inequality statement is correct.
They can designate their answer on their whiteboard.
By clicking on the answer on the smartboard, it will reveal if that answer is correct or incorrect. /
/ Slide 7: Transition Slide
/ Slide 8: This slide contains multiple examples for students to work on. These examples include ordering numbers on a number line and ordering a list of numbers.
Numbers can be moved until students hit submit. Once they hit submit they will be told if they are correct or incorrect.
Allow students 1 – 2 minutes per example to work on their individual whiteboard before having students come to the board and order numbers. /
Assign students Order Matters as individual practice/homework.

Determine which two ingeters the following irrational numbers are between.

is between ______and ______.

- is between ______and ______.

- is between ______and ______.

is between ______and ______.

is between ______and ______.

- is between ______and ______.

Place the following irrational numbers on a number line.

Determine which two integers the following irrational numbers are between.

is between ______and ______.

- is between ______and ______.

- is between ______and ______.

is between ______and ______.

is between ______and ______.

- is between ______and ______.

Place the following irrational numbers on a number line.

MATH_0382_MEAS1_LES_02

Real Numbers Graphic Organizer – Real Numbers

All ______and ______numbers.

Real Numbers Graphic Organizer – Rational Numbers

Any number that can be expressed as the ______
of two ______. / Any number that can be expressed as the ______
of two ______.

MATH_0382_MEAS1_LES_02.docx

Real Numbers Graphic Organizer – Integers

______numbers and their
______. / ______numbers and their
______.
______numbers and their
______. / ______numbers and their
______.

Real Numbers Graphic Organizer – Whole Numbers

______numbers and ______. / ______numbers and ______.
______numbers and ______. / ______numbers and ______.
______numbers and ______. / ______numbers and ______.

Real Numbers Graphic Organizer – Natural Numbers

______numbers / ______numbers / ______numbers / ______numbers
______numbers / ______numbers / ______numbers / ______numbers
______numbers / ______numbers / ______numbers / ______numbers
______numbers / ______numbers / ______numbers / ______numbers
______numbers / ______numbers / ______numbers / ______numbers

Real Numbers Graphic Organizer – Irrational Numbers

Any number that ______be expressed as a ______
of two ______. / Any number that ______be expressed as a ______
of two ______. / Any number that ______be expressed as a ______
of two ______. / Any number that ______be expressed as a ______
of two ______.

Use the graphic organizer for questions 1 – 5.

Which set(s) of numbers does -87 belong to? (circle all that apply)