Target Learner:

• 6th grade students in a Common Core aligned class.

Assumptions About Prior Learning:

Students are expected to have knowledge in comparing decimal place values and brief overview of operations with decimals using place value and models, as these are 5th grade Common Core math standards. However, students are not expected to be able to perform all four operations with decimals fluently and apply it to solve word problems yet. There will be a pre-survey to get more information on the knowledge levels of the students so that the module can be adjusted based on instructor evaluation.

Anticipated Timeline for this Learning Module:

• 7 school days (recommended: 1-3 days of buffer room if needed)
• It is highly encouraged that instructors offer short office hours (i.e. 15-30 min during dedicated time blocks) to support students who may need additional clarification on the assignments.

Alignment with Common Core Standards:

The following standards will be covered in this learning module. These standards will be referenced in the instructor section of each lesson. 

• CCSS.MATH.CONTENT.6.NS.B.2 Fluently divide multi-digit numbers using the standard algorithm.
• CCSS.MATH.CONTENT.6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
• CCSS.MATH.CONTENT.6.RP.A.3.C 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.
• CCSS.MATH.CONTENT.5.NBT.A.3 Read, write, and compare decimals to thousandths.
• CCSS.MATH.CONTENT.5.NBT.A.3.A Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

(Common Core State Standards Initiative, 2022)

Aligns with Common Core Standards

These are the standards that are covered in this update. 

• CCSS.MATH.CONTENT.5.NBT.A.3 Read, write, and compare decimals to thousandths.
• CCSS.MATH.CONTENT.5.NBT.A.3.A Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

(Common Core State Standards Initiative, 2022)

Rationale

For activating prior knowledge:

This first update aims to activate prior knowledge about decimal place value, which the students had learned last year. This concept is essential in connecting to new content, decimal operations. Research shows that connecting new knowledge to prior knowledge reduces cognitive load and improves learning retention (Myhill & Brackley, 2004). After reviewing and activating their knowledge on place values, students can use this information to understand why it's important to line up the decimal point (and therefore place value) when adding and subtracting decimals in the next lesson. 

For pre-module survey:

The purpose of the pre-module survey is to gauge students’ prior knowledge about decimals and percentages so the teacher can better tailor their lessons to fit the needs of the students. I often administer these pre-module surveys and tell the students to not be stressed if they do not know the answer to the questions. Most of the questions are open-ended to give students more freedom to express what they know and don’t know. After students take the pre-module survey, teachers can analyze the results and take quick notes on any major misconceptions I need to address. You can address the misconceptions as a whole class through making video assignments or holding synchronous discussions. Alternatively, you can also modify the discussion question for the next update to address any major misconceptions if pertaining to the majority of the class. 

Here is a series of screenshots of the pre-module survey for your reference. The survey is built using the survey tool within Scholar. Click post to have the link appear on the student side. 

Screenshots of Pre-Survey

Extra (optional) supplementary resources:

If students struggle with finding real-life applications of decimal place value, one supplementary source you can point them to is the number dyslexia blog (Number Dyslexia, 2022). Alternatively, you can also have students do a mini-reseach session and share out the findings through the updates. 

For real-life applications:

This lesson’s update is focused around making a real life application of decimal place value so students can see what they are learning in the classroom is meaningful to their lives. Additionally, student responses serve as valuable insights for instructors to learn about their interests, experiences. Perhaps best stated by Luukkonen (2003),

“Teachers need to be aware of what the students are doing, listening to, reading, and watching. When we better understand what is going on students’ lives, we can better serve them in our instruction.”

(Luukkonen, 2003)

Aligns with Common Core Standards

These are the standard(s) that are covered in this update.

• CCSS.MATH.CONTENT.6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals

(Common Core State Standards Initiative, 2022)

Rationale:

For video updates:

Flipgrid is used for this lesson’s update to help students make sense of their learning. A six week study was conducted on middle and high school art students. The result showed an increase in student engagement and communication (Johnson & Skarphol, 2018).

Additional notes:

This lesson will follow closely with decimal place value, which was reviewed on the last lesson. Be prepared to hold additional office hours to help with tech related questions around Flipgrid. My experience as a teacher is that most of my students have been able to easily figure out how to record using school computers but there may be a few school devices that require updating or microphone repairs.

Aligns with Common Core Standards

These are the standards that are covered in this update.

• CCSS.MATH.CONTENT.6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals
• CCSS.MATH.CONTENT.6.NS.B.2 Fluently divide multi-digit numbers using the standard algorithm.

Extra supplementary resources:

If students struggle with long division of whole numbers from previous years, here is a resource that may help them, in addition to inviting them to office hours to help them fill the gaps that they may have developed from the last few years.

Video 6. Long Division with Whole Numbers (Math Antics, 2013)

Rationale:

The purpose of this update is to help students connect decimal multiplication and division to whole number multiplication and division.

As mentioned before, connecting new knowledge to prior knowledge improves learning outcomes (Myhill & Brackley, 2004).

This week’s update intentionally provided students with two choices of update prompt as well as two choices of presentation. Study conducted with 207 high school students showed that students reported higher intrinsic motivation and performed better on unit tests when they were given a choice in homework assignment selection (Patall et al., 2010).

Aligns with Common Core Standards

These are the standards that are covered in this update.

• CCSS.MATH.CONTENT.6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals

(Common Core State Standards Initiative, 2022)

Teacher Resources:

Answer key and student samples for Vending Machine Activity available below. Note that each student vending machine (Task 5) may be slighlty different depending on which items they selected in the project. This will lead to a variety of possible answers to help the class see that decimals can be applied in many context in real life. If time permits, it may be fun to do a virtual gallery walk or post sample student projects from the class to help peers learn from the broader community. 

Teacher Key Vending Machine Activity PDF (Congruent Math, 2022)

Aligns with Common Core Standards

These are the standards that are covered in this update.

CCSS.MATH.CONTENT.6.RP.A.3.C 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.

(Common Core State Standards Initiative, 2022)

Rationale:

This update also aims to connect percentages to prior knowledge of decimals to help enhance learning. The video explored the similarities of both percentages and decimals as part of a whole. 

Aligns with Common Core Standards

These are the standards that are covered in this update.

CCSS.MATH.CONTENT.6.RP.A.3.C 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.

(Common Core State Standards Initiative, 2022)

Rationale:

When students create their own number and word problems, they connect math concepts to their background knowledge and lived experiences. Building this connection with the students is essential for meaningful learning (Luukkonen, 2003).

Below is an example of how a student may create and present a math problem related to content standard. This video showed lower grade levels but the same concept and rationale is applied when designing this week’s update.

Video 9. Creating Our Own Math Story Problems (Meredith Phelan, 2017)

Aligns with Common Core Standards

These are the standards that are covered in this update.

• CCSS.MATH.CONTENT.6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals
• CCSS.MATH.CONTENT.6.RP.A.3.C 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.

(Common Core State Standards Initiative, 2022)
 

Rationale

The peer review project is a great summative assessment to gauge the mastery of content standards around percentages and decimals. This peer review project is interesting because shopping during sales is a relatable experience for most of my students. Deciding between deals to save money is a practical skill. In order to find the best deal, students need to find a percentage of a number and then perform decimal subtraction to find the value of the first coupon. For the second coupon, they would need to perform whole number subtraction to find the sale price. Lastly, they would need to compare the two decimals to determine the better deal.I think the questions in the project will stretch their critical thinking and application skills.

Students then receive feedback and comments from two peers, which gives them opportunities to fill in any gaps in their understanding and improve their final work. The rubrics provide a generalized expectation list that will set students up for success.

Here are screenshots of the peer assessment rubric that the student would be able to see when they are in the peer review project tab.

Screenshots of Peer Review Rubric

After the peer review project, the teacher can choose to discuss any further confusions or misconceptions (if they noticed any) if needed. The teacher can also target specific student groups for reteaching through the data collected from this peer review project. They may send struggling students an invitation to join small-group office hours or study sessions to help fill in the gaps needed. During the office hours, students can receive more support on misconceptions. Teacher could then give them another way to demonstrate mastery and then reassess from there.

Here are screenshots of the post-survey for your reference: