Day 93: Estimate to Find Percent / Simple Interest

Students in Math 6 received their Topic Six Midpoint Quiz back from Mr. Giomini. Time was spent on looking over the back part of the assessment which is where students struggled. Mr. Giomini then introduced Lesson 6.4: Estimate to Find Percent. This lesson focused on using compatible numbers to help students generate possible "ballpark" answers to percent problems.

 

During Math 6+, students received their Topic Six Midpoint Quiz. A brief discussion was had over a question dealing with percent change. Mr. Giomini then introduced the concept of simple interest to the students. Examples of how simple interest is used was shared: CD deposits, car loans, consumer loans (Best Buy and Home Depot), and discounts on early payments.

Today's Lesson Objective(s):

• Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. (6th Grade)
• Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. (7th Grade)

Day 92: Topic Six Midpoint Quiz

Students in Math 6 and Math 6+ were administered the Topic Six: Percents Midpoint Quiz.

Learning Objective(s) Assessed:

• Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. (6th Grade)
• Generate equivalent fractions, decimals, and percents. (6th Grade)
• Use proportional relationships to solve multi-step ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. (7th Grade)

Day 91: Review

In both Math 6 and Math 6+, Mr. Giomini spent time reviewing concepts from the previous day's lessons in preparation for Friday's Topic 6 Midpoint Quiz.

Today's Learning Objective(s):

• Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. (6th Grade)
• Use proportional relationships to solve multi-step ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. (7th Grade)

Day 90: Percents Greater Than 100 and Less Than 1 / Percent Increase-Decrease

In Math 6 today, students worked with Lesson 6.3: Represent Percents Greater Than 100 and Less Than 1. A percent greater than 100 is equivalent to more than one whole. This is something to thing about as we create an equivalent fraction and decimal. When working with percents less than one, we need to know that the decimal equivalent will have a zero in the ones place.

Students in Math 6+ continued their work with percent change when comparing two numbers.

All classes are going to have a quiz this Friday.

Today's Learning Objective(s):

• Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. (6th Grade)
• Use proportional relationships to solve multi-step ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. (7th Grade)

Day 89: Relate Fractions, Decimals, and Percents / Percent Change

Students in Math 6 worked with Lesson 6.2: Relate Fractions, Decimals, and Percents. During the lesson, students will generate equivalent fractions, decimals, and percents using 100 as the whole as well as dividing fractions. The hope is that students see that fractions, decimals, and percents all represent ways in which to describe parts of a whole.

In Math 6+, students worked with percent change when comparing prices of the same item. Click here for your evening practice. Please only complete the odds and there is an answer key to check your work.

Website for Academic Extension: CLICK HERE

Today's Learning Objective(s):

• Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.               (6th Grade)
• Use proportional relationships to solve multi-step ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. (7th Grade)

Day of Reflection: Martin Luther King Day

Students,

As you sit at home today and enjoy a day of school off, think about why you have today off. Interesting thing about this day is that is is younger than me. President Ronald Reagan signed the holiday into law back in 1983, when I was seven, but it didn't become an observed holiday until 1986.

Dr. King helped facilitate the conversation that allowed us to have a society such as the one we currently live in. Are there still issues that trouble our country? Yes. However, with Dr. King's words as a the motivation to move forward, and young, intelligent people, such as yourself, the country and this world can become a place where all people are viewed as equals. It can be a place where the views and opinions of others can promote change rather than hostility.

Enjoy your day off and think about what you have to offer.

  

Day 88: Understand Percent / Finding a Number When a Percent is Known

In Math 6, students received their Topic Five Post-test back from Mr. Giomini. Look in your email for an answer key should you want to compare your answers to Mr. Giomini's.

Mr. Giomini introduced the next topic, Topic Six: Understand and Use Percents. In Lesson 6.1: Understand Percent, students learned that a percent is a rate in which the first term is compared to 100. The percent is the number of hundredths that represent the part of the whole.

During Math 6+, Mr. Giomini modeled how to convert between fractions, decimals, and percents. Once that was fluent, students worked with finding a number when a percent is known by writing equations for problems such as 98 is 32% of what number.

Lesson Objective(s):

• find a percent of a quantity as a rate per 100. (Math 6)
• solve problems involving finding the whole, given a part and the percent. (Math 6)
• use proportional relationships to solve multistep ration and percent problems. (Math 6+ - 7th Grade)

Day 87: Topic Five Posttest

Students in Math 6 and Math 6+ were administered their respective post-tests for Topic Five: Understand and Use Ratio and Rate.

Skills assessed on the post-test:

1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
2. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. 
3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
4. Solve unit rate problems including those involving unit pricing and constant speed. 
5. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Day 86: Topic Five Review

Students in Math 6 and Math 6+ spent the day using either physical or digital materials to help review for Wednesday's Topic Five Posttest.

Day 85: Relate Customary and Metric Units

Students in Math 6 and 6+ worked with Lesson 5.10: Relate Customary and Metric Units. The goal of this lesson is for students to see how to convert, using unit rate and conversion factors, between customary and metric units of measure. During the lesson, students work with equivalent rates and dimensional analysis to convert between the systems.

Lesson Objective(s):

• use ratio reasoning and conversion factors to convert between customary and metric units of measure. (6th)

Day 84: Convert Metric Measurements

In Math 6 and Math 6+, students were introduced to and practiced skills from Lesson 5.9: Ratio Reasoning - Convert Metric Units. This lesson took yesterday's skills with dimensional analysis and applied it to the metric system. A cheat sheet was provided to the students to help them their metric conversions. It was placed into their math notebook.

Lesson Objective(s):

• Use ratio reasoning and conversion factors to convert units of measure. (6th)

Day 83: Convert Customary Units

In Math 6 and Math 6+, students were introduced to and practiced skills from Lesson 5.8: Ratio Reasoning - Convert Customary Units. During this lesson, students worked with units of measure similar to the ones in the table below to solve multi-step problems involving measurement conversion with units typically used in the United States.

Lesson Objective(s):

• Use ratio reasoning and conversion factors to convert units of measure. (6th)

Day 82: Solve Unit Rate Problems

Students in Math 6 and Math 6+ worked with Lesson 5.7: Solve Unit Rate Problems. This lesson extends our unit rate work from yesterday to include constant speed.

Lesson Objective(s):

• Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger." (6th)
• Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? (6th)

Day 81: Compare Unit Rates

Students in Math 6 and Math 6+ worked with Lesson 5.6: Compare Unit Rates. This lesson extends the student's understanding of rates and unit rates to comparing such items.

Lesson Objective:

• Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger." (6th)
• Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? (6th)

Day 80: Quiz Review

Students in Math 6 and Math 6+ received their Topic Five Midpoint Quiz back from the previous day. Mr. Giomini clarified any questions that the students might have had regarding their assessment.

The evening practice from the previous day was also discussed due to misunderstandings on some of the questions.

Day 79: Topic Five Midpoint Quiz

Today in Math 6 and Math 6+, students completed the Topic Five Midpoint Quiz.

Items assessed:

1. Make tables of equivalent ratios relating quantities with whole-number measurements. (6th)
2. Find missing values in the tables. (6th)
3. Plot the pairs of values on the coordinate plane. (6th)
4. Use tables to compare ratios. (6th)

Day 78: Understand Rates and Unit Rates

Students in Math 6 and Math 6+ worked with Lesson 5.5: Understand Rates and Unit Rates. This lesson lends itself well to shopping and having students understand what they, or their parents, are paying for an item in the store.

A rate is a special type of ratio that compares two quantities with unlike units of measure, and that unit rates compare a quantity to one unit of another quantity. 

Lesson Objective:

• Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger." (6th)
• Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? (6th)

Day 77: Graph Ratios - Write and Solve Proportions

In Math 6 today, Mr. Giomini modeled and explained how students can utilize ratios to create tables and eventually graphs. Once Mr. Giomini presented the information, students had the opportunity to practice the skill with a colleague.

Math 6+ students continued their work with writing and solving proportions from word problems. Students worked in a small group setting and under a time constraint to complete multiple word problems. 

Lesson Objective(s):

• Make tables of equivalent ratios relating quantities with whole-number measurements. (6th)
• Find missing values in the tables. (6th)
• Plot the pairs of values on the coordinate plane. (6th)
• Use tables to compare ratios. (6th)
• Represent proportional relationships by equations. (7th)
• Use proportional relationships to solve multi-step ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. (7th)

Snow Day

No school today, snow day. This gives me time to winterize my lawn.

Day 76: MAPs Testing - Proportions

In Math 6 today, all classes were administered the Winter MAP. These scores are compared to the Fall MAP to check for student growth.

Students in Math 6+ reviewed comparing ratios and then progressed into solving proportions.

Lesson Objectives:

• represent proportional relationships by equations. (7th grade)

Congratulations to these students for solving the problem pictured below:

Day 75: Compare Ratios

Students in Math 6 and Math 6+ worked with Lesson 5.3: Compare Ratios. During this lesson, students analyzed tables of information to generate and compare equivalent ratios using multiplication and division. Throughout the lesson, students worked with comparing ratios using a common term and then applied this understanding to solve real-world and mathematical problems.

Here is another equivalent ratio game - Ratio Stadium.

Lesson Objectives:

1. use ratio tables to compare ratios.
2. compare ratios to solve problems.

Day 74: Ratios - Proportions - Equivalent Ratios

In Math 6 - 1° students worked with Lesson 5.1: Understand Ratios. Students begin to understand that ratios compare quantities. We discussed ratios that compare part to part and part to whole.

Students in Math 6+ began work with writing and solving proportions.

During Math 6 - 3/7°, students worked with Lesson 5.2: Generate Equivalent Ratios. Here, students learn the procedural method of generating equivalent ratios by multiplying and dividing the original terms of a ratio by the same nonzero number.


Here is a game to play for finding equivalent ratios: Math Playground - Alien Ratios

Lesson Objective(s):

1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
2. Use tables to compare ratios.
3. Make tables of equivalent ratios relating quantities with whole numbers.

Day 73: Understand Ratios - MAP Testing

Students in Math 6 received a new workbook today in class which they will use the remainder of the year. Mr. Giomini introduced Lesson 5.1:Understand Ratios. Ratios can be used to describe the relationship between two different quantities similar to the example below.

During Math 6+, students were administered the Winter MAP exam in Mathematics.

Lesson Objective(s):

1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

Day 72: Topic 1 - 4 Cumulative Assessment

In all Math 6 classes, students completed Part II of the Topic 1 - 4 Cumulative Assessment.

Due to Mock Trial, Math 6+ had a fraction of its students. Those students who remained worked on Khan or other tasks with Mr. Giomini.

Items assessed on this cumulative assessment include:

• use substitution to determine whether a given number in a specified set makes an equation or inequality true.
• solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for which cases in which p, q, and x are all nonnegative rational numbers.
• use variables to represent two quantities in a real-world problem that change in relationship to one another.
• write equations to represent the relationships between variables.
• write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem.
• analyze the relationship between the dependent and independent variables using graphs, tables, and relate them to the equation.
• write and evaluate numerical expressions involving whole-number exponents.
• write expressions that record operations with numbers and with letters standing for numbers.
• identify parts of an expressions using mathematical terms.
• view one or more parts of an expression as a single entity.
• evaluate expressions at specific values of their variables.
• understand that positive and negative numbers are used to describe quantities having opposite directions of values.
• use positive and negative numbers to represent quantities in real-world contexts.
• find and position integers and other rational numbers on a horizontal or vertical number line.
• position pairs on integers and other rational numbers on a coordinate plane.
• interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.
• fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
• find the greatest common factor of two whole numbers less than or equal to 100.
• find the least common multiple of two whole numbers less than or equal to 12.

Day 71: Topic 1 - 4 Cumulative Assessment

In all Math 6 and Math 6+ classes, students were in some stage of working on the Topic 1 - 4 Cumulative Assessment.

Items assessed on this cumulative assessment include:

• use substitution to determine whether a given number in a specified set makes an equation or inequality true.
• solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for which cases in which p, q, and x are all nonnegative rational numbers.
• use variables to represent two quantities in a real-world problem that change in relationship to one another.
• write equations to represent the relationships between variables.
• write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem.
• analyze the relationship between the dependent and independent variables using graphs, tables, and relate them to the equation.
• write and evaluate numerical expressions involving whole-number exponents.
• write expressions that record operations with numbers and with letters standing for numbers.
• identify parts of an expressions using mathematical terms.
• view one or more parts of an expression as a single entity.
• evaluate expressions at specific values of their variables.
• understand that positive and negative numbers are used to describe quantities having opposite directions of values.
• use positive and negative numbers to represent quantities in real-world contexts.
• find and position integers and other rational numbers on a horizontal or vertical number line.
• position pairs on integers and other rational numbers on a coordinate plane.
• interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.
• fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
• find the greatest common factor of two whole numbers less than or equal to 100.
• find the least common multiple of two whole numbers less than or equal to 12.

Day 70: Topic Three Review

Students in Math 6 spent their last day prepping for the Topic 1 - 4 Cumulative Assessment. Mr. Giomini created example problems on index cards that he posted along the hallway for students to complete as part of a Gallery Walk.

Math 6+ students had the option of beginning their Topic 1 - 4 Cumulative Assessment in class or continue with review.

Lesson Objectives: The student will be able to...

• write and evaluate numerical expressions involving whole-number exponents.
• write expressions that record operations with numbers and with letters standing for numbers.
• identify parts of an expressions using mathematical terms.
• view one or more parts of an expression as a single entity.
• evaluate expressions at specific values of their variables.

Day 69: Topic Two Review

Today in Math 6, students reviewed concepts from Topic Two: Integers and Rational Numbers. Mr. Giomini reviewed with students how to compare and order rational numbers using a number line. Students were then given time to work on the online assessment piece for Topic Two to help prepare for the assessment.

For the next two days, students will review skills from the previous topics in preparation for the Topics 1-4 Cumulative Assessment which takes place on Wednesday, December 7th.

In Math 6+, Mr. Giomini distributed the graded Topic Four Posttest back to students. Some of the more highly missed questions were then discussed again. A quiz dealing with writing equations is going to be administered tomorrow to help assess if students are better comprehending the skill.

Students were then given time to work on the online assessment piece for Topic Two to help prepare for the assessment.

Lesson Objectives: The student will be able to...

• understand that positive and negative numbers are used to describe quantities having opposite directions of values.
• use positive and negative numbers to represent quantities in real-world contexts.
• find and position integers and other rational numbers on a horizontal or vertical number line.
• position pairs on integers and other rational numbers on a coordinate plane.

Day 68: Topic One Review

Today in Math 6, students received their Topic Four Posttest back from Mr. Giomini. Students were encouraged to ask question pertaining to the assessment that needed clarification. Mr. Giomini then reviewed Topic One: Use Positive Rational Numbers.

For the next three days, students will review skills from the previous topics in preparation for the Topics 1-4 Cumulative Assessment which takes place on Wednesday, December 7th.

In Math 6+, Mr. Giomini distributed the Topic Four Posttest back to the students. He then posted an answer key, with detailed work for each problem to help generate discussion pertaining to questions that students may have head regarding the assessment.

Lesson Objectives: The student will be able to...

• interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.
• fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
• find the greatest common factor of two whole numbers less than or equal to 100.
• find the least common multiple of two whole numbers less than or equal to 12.

Day 67: Topic Four Posttest

Students in Math 6 and Math 6+ completed the Topic Four Posttest.

Assessment Objectives: The student will be able to...

• use substitution to determine whether a given number in a specified set makes an equation or inequality true.
• solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for which cases in which p, q, and x are all nonnegative rational numbers.
• use variables to represent two quantities in a real-world problem that change in relationship to one another.
• write equations to represent the relationships between variables.
• write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem.
• analyze the relationship between the dependent and independent variables using graphs, tables, and relate them to the equation.

Day 66: Last Review

Students in Math 6 played Jeopardy in class today to help review for tomorrow´s Topic Four Posttest. 

During Math 6+, students completed a Gallery Walk to help with their test preparation.

CLICK HERE for Google Slide Show for Math 6+ Gallery Walk questions.

Lesson Objectives: The student will be able to...

• use substitution to determine whether a given number in a specified set makes an equation or inequality true.
• solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for which cases in which p, q, and x are all nonnegative rational numbers.
• use variables to represent two quantities in a real-world problem that change in relationship to one another.
• write equations to represent the relationships between variables.
• write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem.
• analyze the relationship between the dependent and independent variables using graphs, tables, and relate them to the equation.

Day 65: Review Lessons 4.5 - 4.8

Students in Math 6 and Math 6+ reviewed skills from Lessons 4.5 - 4.8 which dealt with inequalities.

Video for Math 6+

Video for Math 6+

Lesson Objectives: The student will be able to...

• use substitution to determine whether a given number in a specified set makes an equation or inequality true.
• solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for which cases in which p, q, and x are all nonnegative rational numbers.
• use variables to represent two quantities in a real-world problem that change in relationship to one another.
• write equations to represent the relationships between variables.
• write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem.
• analyze the relationship between the dependent and independent variables using graphs, tables, and relate them to the equation.

Day 64: Review of Lessons 4.1 - 4.4

Students in Math 6 and Math 6+ reviewed skills from Lessons 4.1 - 4.4. These lessons deal with solving equations both one step and multi-step using addition, subtraction, multiplication, and division. Mr. Giomini also had the students focus on writing equations from word problems and then solving.

Lesson Objectives: The student will be able to...

• use substitution to determine whether a given number in a specified set makes an equation or inequality true.
• solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for which cases in which p, q, and x are all nonnegative rational numbers.
• use variables to represent two quantities in a real-world problem that change in relationship to one another.
• write equations to represent the relationships between variables.
• write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem.
• analyze the relationship between the dependent and independent variables using graphs, tables, and relate them to the equation.

Day 63: Review

Students in Math 6 and Math 6+ discussed the different skills in Topic Four: Represent and Solve Equations and Inequalities. Mr. Giomini encouraged students to ask questions about each lesson in the topic as he briefly went through all ten lessons in an attempt to provide students with a more focused plan for studying over Fall Break.

Finally, a Quizzizz was used to review skills from our current topic of study.

Lesson Objectives: The student will be able to...

• use substitution to determine whether a given number in a specified set makes an equation or inequality true.
• solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for which cases in which p, q, and x are all nonnegative rational numbers.
• use variables to represent two quantities in a real-world problem that change in relationship to one another.
• write equations to represent the relationships between variables.
• write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem.
• analyze the relationship between the dependent and independent variables using graphs, tables, and relate them to the equation.