دليل المعلم Volume 2 الرياضيات منهج انجليزي Reveal الصف الثامن الفصل الثاني 2021-2022
IGNiTe
The Ignite! activities, created by Dr. Raj Shah, cultivate curiosity and engage and challenge students. Use these open -ended, activities, located online in the modUe Launch section, to encmrage your students to develop a YOMh mindset towards mathematics a nd problem solving. Use the teacher notes impl ementation suggestions and support for erxouraging productive struggle
Essential Question
At the end of this module, students should be able to answer Essential Ouestim
How can mathematical expressions be represented and Sample answer. Y ou can represent mathematical expressims verbally, numerically, and algebraically. They can be evaluated by applying properties and rules. For example. you can translate a seitence to a numerical or algebraic expression and use the order of operations to simplify or eva luate the expression
What Will You Learn
Prior to begmng this module. have your students rate their knowledge of each item listed. Then. at the end of the module. you be reminded to have your studerts return to these pa ges to rate their knowledge
agan They should see that their know*eØe have meased
DINAH ZIKE FOLDABLES
Focus Students organize their notes about expressions, properties of real numbers, and absolute value
Teach Throughout the module, have students take notes under the tabs of their Foldables while working through each lesson. They should include definitions and key concepts. Encourage students to record examples from each lessn When to Use It Use the tabs as students cover each lesson in this module. Students should add to the vocabulary tab during eadl lessn
Launch the Module
For this module. the Launch the Module video uses online shopping to shmu how algebraic expressions are used in the real Students learn how algebraic expressions are used in the trucking industry. and the importance of order of
What Vocabulary Will You Learn
Introduce the key vocabulary by using the following routine
Define An algebraic expression is a mathematical expression that contains at least one variable
Example 9y — 7x
Ask Is there at least one variatie ? Y es, both 9y and 7x have variables
Are You Ready
Students may need to review the following prerequisite skills to succeed ttis module
• adding and subtracting integers
• multiplying and dividing integers
• adding and subtracting rational numbers
• using order of operations
• naming points on number lines
a ALEKS
ALEKS is an adaptive, personalized learning environrnent that identifies precisely what each student knows and is ready to learn, ensuring student success at all levels
You may want to use the Real Numbers section to ensure student success in this modde
Mindset Matters
Growth Mindset vs. Fixed Mindset
Everyone has a cote belief or mindset about how they leam. People with a growth mindset believe that hard work will make them smarter Those with a fixed mindset believe they can leam new things, but cannot become smarter. When a student changes their mindset, they are more likely to work through challenging problems, leam from their mistakes, and ultimately leam more deeply
How Can I Apply It
Assign students tasks, celebrate mistakes, and provide opportunities for criticwe, revision, and reflection. The Explore activities and discussion prompts are a great tool to begin this jmrney
Explore Order of Operations
Objective
Students explore how to use the order of operations to evaluate numerical expressims
Teaching the Mathematical Practices 4 Apply Mathematics In this Explore, students apply what they know about the order of operations to solving a real- world
Ideas for use
Recommended Use Present the Inquiry Question, or have a student volunteer read it aloud. Have students work in pairs to complete the Explore activity on their deuces. Pairs should discuss each of the
questions. Monitor student progress during the activity. Upon completion of the Explore activity, have student volunteers share their responses to fre Inquiry Question
What if my students don't have devices ? Y ou may choose to project. the activity on a whiteboard. A printable worksheet for each Explore is avadable online. You may choose to print the worksheet so that
individuals or pairs of students can use it to record their observations
Summary of the Activity
Students will be presented with guiding exercises to complete at the end of the activity. Students watch a video setting up the numerical expression for which the order of operations will be used to calculate
Then students will analyze the incorrect work. The guiding exercises will lead students to determine why the work was incorrect and what is the correct sdution path. Then, students wül answer the Inquiry Question (continued on next page)
Learn Writing Numerical Expressions
Objective
Students write numerical expressions by interpreting words as mathematical symbols -
Teaching the Mathematical Practices 6 Communicate Precisely Encourage students to routinely write. or explain their solution methods. Point out that they should use clear definitions when they dscuss their solutions with others
Common Misconception
Students many times do not use parentheses because the verbal sentence does not mention grouping symbols. Remind students that words like sum or difference often need parentheses and to always carefully read verbal sentences to identify relationships that may need grouping symbols
Example 1 T ranslate a Verbal Expression
Teaching the Mathematical Practices I Explain Correspondences Encourage students to explain the relationships between the verbal and numerical expressions in this example
Questions for Mathematical Discourse
Can you tell by the verbal expression what operation is intended to be done frst ? no How could you adjust the verbal expression to indicate addition should be done first ? Sample answer. Add one and eight, and then divide by three
How could you adjust the verbal expression to indicate division should be done first ? Sample answer. Add one to the quotient of eight and three
Go Online
• Find additional teaching notes
• View performance reports of the Checks
• Assign or present an Extra Example
Standard
5 use appropriate tooB stategkany Mathematicany profrient students consider tie aadabe tools when sdving a mahematical These tools inclLÆe pend arui paper. concrete a ruer. a protractM. a a spreadsheet a computer a*ra system. a statistical package. or dynamic gwnetry sdtware. Proficient students are s.fficiently famdiar with tools apptWiate for ttpir grade or course to make swnd decisions abmn when each mese tools be helpful. recovizing both inst to be gained and their Imitations. For example
mathematically profrieM school studems analyze furutiom and sdLRions generated a wapNng calculator. Thw detect possble stratecaUy using estimation and Other mathematical knowledge. When making mathnatical mo«s. they know that techneogy can enable ttwn to visualize the. results of varyig assumptims. explore conseq. ences. and compare with ta. Mathematically students at various wade levels are able to identity relevant external mathematical resources. SLRh as cmtent located on a website. use them to pose They are le to use tools to eVore ard deepen their understandng 6 Anatd Mattpmatically profkiert students try to precisely to others. They try to use dear dibms Oscussion with others and in their reasming. They state mearing the synbds they choose, Kluding using the equal sign consistently and apmomiately. They are careful about mits of measure. and labeling axes to clarity the with quantities in a They calculate accurately and efficiently. express turnerical answers with a Of precision for probem context. In me elementary students give caretuuy formulated explanatms to each Other. By the tine they reach scmol they have learned to examuw daims and make explicit use
Student Mindset
Mindset Matters tips located in each rnodule provide specific examples of how Reveal Math Integrated content can be used to promote a growth mindset in all students. Another feature focused on promoting a growth mindset is Ignite Activities developed by Dr. Raj Shah to spark student curiosity about why the
math works. An Ignite! delivers problem sets that are flexible enough so that students with varying background knowledge can engage with the content and motivates them to ask questions. solve complex problems. and develop a can do attitude toward math
Mindset Matters
Growth vs. Fixed Mindset
Everyone has a core beåef mindset about how they leam. Pegle with a growth miMset believe that hard work will make them smarter. Those with a fixed mindset believe that they can learn new things, but can't become smarter. When a student changes their rnindset they are nwe likely to work through challenging learn their mistakes, aM ultimately learn more deeply
How Can I Apply It
Assign students tasks. such as the Explore activities, ttut can help them to intelligence. Let them know that each time they learn a new idea an electric current fires that connects Mferert parts of
ttE brain
Teacher Edition Mindset Tip
Formative Assessment
The key to reaching all learners is to adjust instruction based. on each student's understanding. Reveal Math Integrated offers. powerful formative assessment tools that help teachers to efficiently and effectively differentiate instruction for all students
Math Probes
Each module includes a Cheryl Tobey Formative Assessment. Math Probe that is focused on addressing student misconceptions about key math topics. Students can complete these probes at the beginning. middle. or end of a module. The teacher support includes a list of recommended differentiated resources that teachers assign based on students' responses
Example Checks
After multiple examples. a formative assessment Check that students complete on their own allows teachers to gauge students' understanding of the concept or skill presented. When students complete the Check online. the teacher receives resource recommendations which can be assigned to students
Example 2 T ranslate a Verbal Expression
with Grouping Symbols
Teaching the Mathematical Practices 1 students to explain he between the verbal and numerical in this example
Questions for Mathematical Discourse
What mrd phrase represents divisim? divided
What word phrase indicates need symbols sun on
Could a that does not use by of stil result in the sarne numerical expression ? If so. an euTWe_ Yes: s.ame answer: half the sum of five and nine
Common Error
SD-idents often treat tte words sum and Metence Eke regular a"tim sa_btaction words. even though they rewire the use parentEE Encurage students to undertim or sum or ditference as a to treat them dfferently when translating
Example 3 Write a Numerical Expression
Teaching the Mathematical Practices 2 Create Guide stLdents to Mte a numerical expression that models the situatim this example
Questions for Mathematical Discourse
What three operatims are present in the verbal subtractim, m uttiicatiom and division
What synols should be used in expression? parentheses and a tractim bar
Why is subtractm 200 — 170 instead of 170 — 200
Sample answer: The average is subtracted 200. so 200 gæs first and he average next
DIFFERENTIATE
Reteaching Activity
IF studerts have &fficulty trmslatng fran verbal expressions to mmerkal expressims, THEN have them make cards with words on me be operation on the other side
Enrichrnent ktMty E
Pablo and Martin both Miting a numero for the phrase three thes sun of four squæed and foe. Pablo writes + 5) Martin writes ) + 5. Who is correct Pauo Or Martin ? Explan reasmng. Pablo: answer: Pablo included parenfreses around the sum: Martin did not
Example 6 Write and Evaluate a Numerical
Expression
Teaching the Mathematical Practices
5 Use a Source Guide students to fnd external information to answer the questions posed in the Use a Source feature
Questions for Mathematical Discourse
What mathematical operation will b used when combining the points earned from the three different point levels ? additio
The problem states the value for each ball Mellie rolled What mathematical operation represents the point values when translating to a numerical operation ? multiplication
How would the expression change if Mellie also rolled one ball into the 100-point hole ? The expression would be 2(30) + 4(20) + 3(50) + 1000)
Common Error
Students may not know W'hat understood math operations are attached to the words triple and ±ub/e, and may try to add. Remind students that these words represent multi cation
Essential Question Follow- up
Students have begun applying the order of operations when evaluating numerical expressions is order important when evaluating numical expressions
Sample answer: Order matters because otherwise multiple answers codd be found for one problem. when only one answer is actually correct
DIFFERENTIATE
Reteaching Activity
IF students struggle remembering the order of operatims, THEN have students write PEMDAS in their foldable with Parentheses, Exponent. Multiplication, Division, Addition. and Subtraction written by each letter. Have students draw an arrow above MD and AS to remind thern to work from left to right
Enrichment Activity
Using the numbers 2, 3, 4, and 8 only once and any operation or grouping symbols, write a numerical expression evaluating to 8
.