Students will work with different representations of square and cube roots. They understand the terms “rational” and “irrational,” and how to best approximate irrational numbers on a number line using what they know about rational numbers. Students will engage in proving and algebraically manipulating the Pythagorean Theorem. They specifically utilize the Pythagorean Theorem to estimate distances on a coordinate grid, prove a triangle is a right triangle and find missing sides of a triangle in a given context.

PACING = 4 weeks

Essential Learning Outcomes (ELO)

⊡ Students will identify and compare rational and irrational numbers.  (8.NS.1, 8.NS.2) (MP.1, MP.2) 

Learning Targets:

• I can identify rational numbers as numbers that can be written in the form of a fraction. (8.NS.1)

• I can write non-terminating, repeating decimals with a repeating symbol that highlights the repeated pattern. (8.NS.1)

• I can identify irrational numbers as any non-repeating, non-terminating decimal. (8.NS.1)

• I can recognize that any number that is not irrational is rational. (8.NS.1)

• I can compare the value of numbers by stating which is bigger or smaller. (8.NS.2)

⊡ Students will reason quantitatively to show that decimal expansion for rational numbers eventually repeats.  (8.NS.1, 8.NS.2) (MP.1, MP.2, MP.5, MP.6) 

Learning Targets:

• I can write any rational number as a decimal expansion that repeats. (8.NS.1)

⊡ Students will approximate and locate irrational numbers on a number line.  (8.NS.2) (MP.4) 

Learning Targets:

• I can round decimals to the nearest whole number or given decimal place value. (8.NS.2)

• I can correctly place rational numbers on a number line. (8.NS.2)

• I can approximate any decimal between two whole numbers or between tenths of a number. (8.NS.2)

• I can use rational numbers to approximate irrational numbers. (8.NS.2)

• I can place irrational numbers on a number line to the closest approximation. (8.NS.2)

∎ Students will be able to state, rearrange, and prove the Pythagorean Theorem.  (8.G.6, 8.G.7) (MP.8) 

Learning Targets:

• I can state the Pythagorean Theorem. (8.G.6)

• I can rearrange the Pythagorean Theorem as needed. (8.G.7)

• I can explain a proof of the Pythagorean Theorem and its converse. (8.G.6)

∎ Students will apply the Pythagorean Theorem and its converse as a mathematical model to a variety of real-world and mathematical problems.  (8.G.7, 8.G.8) (MP.4) 

Learning Targets:

• I can determine if a triangle is a right triangle using the length of the sides. (8.G.7)

• I can determine whether a missing side of a right triangle is a hypotenuse or leg, and then find its length. (8.G.7)

• I can use the Pythagorean Theorem to determine the distance between two points on a coordinate grid. (8.G.8)

• I can solve word problems with the Pythagorean Theorem. (8.G.7, 8.G.8)

∎ Major Content           ⊡ Supporting Content           🌕 Additional Content

Computational Number Talks/Strings (minimum 3 days a week) to work on computational strategies.

Use your Daily Math Fluency kit (Hand2Mind)  *This kit was part of the Essential Learning PD week.

This kit has math talks (one problem to collect all of your students' strategies - formative assessment to see if they have efficient strategies) and number strings (pose one problem at a time from a series that is building/practicing ONE strategy, so do NOT collect all strategies).  

*The computational strategies that you practice during number talks does NOT have to align with the core math content.  Number talks are meant to practice fluency strategies, not teach new content.

CAN DO / Additional Resources:

Prior knowledge/Just in Time support     &     Enrichment RTTB   Lesson 25: That's So Irrational

Nearpod Math lessons Open Middle tasks

Interactive manipulatives

CAN DO / Additional Resources:

Prior knowledge/Just in Time support     &     Enrichment RTTB   Lesson 27: Spiral of Theodorus

Nearpod Math lessons Open Middle tasks

Interactive manipulatives