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Unit: Word Problems for fifth-graders

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CCSS.MATH.CONTENT.4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2

CCSS.MATH.CONTENT.5.NBT.A.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

CCSS.MATH.CONTENT.5.NBT.A.3.A Read and write decimals to thousandths

CCSS.MATH.CONTENT.5.NBT.A.4 Use place value understanding to round decimals to any place.

CCSS.MATH.CONTENT.5.NF.A.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. 

CCSS.MATH.CONTENT.5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm.

CCSS.MATH.CONTENT.5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths

CCSS.MATH.CONTENT.5.MD.A.1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

Time

Approximately 2.5 hours

Unit Summary

This cross-curricular unit includes a variety of strategies and examples for solving word problems at a fifth-grade level, including division of three-digit numbers, fractions and decimals.

Buffalo Hunts and Division

This lesson begins with a video on long division (optional) or a presentation on uses of division from the playground to the buffalo hunt. Students then watch a short video working long division problems. Finish with practicing long division in Making Camp Dakota. Short videos on Dakota buffalo hunt traditions and related math lessons are also linked.

Watch out for blood-sucking fishes!

This 40-minute lesson introduces new science vocabulary words, teaches about indigenous and invasive species and includes a couple of math problems showing how quickly invasive species multiply. It concludes with students playing the Making Camp Dakota: Past and Present game. Math word problems require finding half of 500 and 10 x 500.

Using Visual Models To Compare Fractions

Students play 2-3 levels of a game that teaches and assesses adding and comparing fractions with different numerators and denominators, with the context of a story from Ojibwe history. They create their own problems using visual models to compare fractions. Students discuss classmates’ problems. The lesson culminates with a video on visualization as a problem-solving strategy. (35-45 minutes)

Decimals, Epidemics & Fly Vomit – It’s science!

Learn decimals while weighing a flies and the food they eat. The lesson begins with a game on decimals and the Aztec smallpox epidemic, then moves to another disease spreader – flies. Students learn the role flies play in our ecosystem, how they eat and reproduce. (75 minutes)

Differentiation

For students who are struggling with word problems, assign these videos directly teaching strategies or watch together in class.

Codex

The Codex in Latin American History and Math

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Standards

CCSS.ELA-LITERACY.RH.6-8.2 Determine the central ideas or information of a primary or secondary source; provide an accurate summary of the source distinct from prior knowledge or opinions.

CCSS.MATH.CONTENT.6.RP.A.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

CCSS.ELA-LITERACY.W.7.1 Write arguments to support claims with clear reasons and relevant evidence.

Technology required

Device with a browser for AzTech Game. Printer for printing codex and related worksheet and activity pages.

Time

4-5 hours

Lesson Summary

This is an augmentation of a lesson from the Library of Congress uses a primary source – the Huexotzinco Codex – as a basis for document analysis, inquiry and applied mathematics. Students analyze pages documenting tribute paid to Spanish administrators, compute the tribute paid, read a one-page overview of the codex and analyze the codex. A presentation is given on connections between Aztec, Mayan and contemporary methods. Students begin or end classes playing a game that includes Mayan history and middle school mathematics.

Lesson

First, some background for the teacher. The Huexotzinco Codex was part of the evidence in a case brought by the Nahuas, Indigenous people of what is now Mexico, against the Spanish administrators, alleging excessive taxation (tribute). This case was won by the Nahuas. In this lesson, students do not learn the full story until the third or fourth class period.

Analyze Documents

Begin with this link to the Library of Congress lesson, “The Huexotzinco Codex”, and have students complete Activity 1, Document Analysis. This should take one class period- approximately one hour.

NOTE TO THE TEACHER: Allow at least 30 minutes before using this lesson the first time, to read through the Library of Congress lesson, download and print out documents for students.

Play a game

Have students sign in and begin the game, AzTech: Meet the Maya. Students should play for about 15 minutes.

Computation – How much was the tribute?

Continue with the second part of Library of Congress lesson, “The Huexotzinco Codex”, and have students complete Activity 2, Computation. After students have completed one tribute sheet and corrected their answers, use this slide presentation to show the connection between the Aztec and Maya codices and our modern system of numbers and graphs. Optionally, have students complete one or two more tribute sheets from the linked lesson. This should take one to two class periods.

Play a Game

At the beginning of class, have students continue the AzTech: Meet the Maya game. Students should play for 15-20 minutes by which time some of the students should have reached the codex activity and explanation in the game.

Write a Narrative Explanation

Continue with the third part of Library of Congress lesson, “The Huexotzinco Codex”, and have students complete Activity 3, Narrative Explanation.

Assessment

Four types of assessments are included; observation of student understanding of historical document analysis in the class discussion, student self-corrected math computation, student written assignments (analysis sheet, observations and scenario outlines) and the math problems in the AzTech game which are scored automatically with data available in teacher reports.

Differentiated instruction (optional)

Advanced Students who complete their assignments early can continue with the AzTech: Meet the Maya game. If they complete this game, they can choose to play AzTech: The Story Begins or AzTech: Empiric Empire.

English learners can play the AzTech : Meet the Maya and AzTech: The Beginning games in English or Spanish.

Recommended Related Lesson

Counting ropes and rational numbers

Decimals, Epidemics & Fly Vomit – It’s science!

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📖Standards

CCSS.MATH.CONTENT.5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths

CCSS.MATH.CONTENT.5.MD.A.1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

CCSS.ELA-LITERACY.L.6.6 Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression.

Technology

Students will need a phone or tablet to play the game.

Time

75 minutes

Lesson Summary

Learn decimals while weighing a flies and the food they eat. The lesson begins with a game on decimals and the Aztec smallpox epidemic, then moves to another disease spreader – flies. Students learn the role flies play in our ecosystem, how they eat and reproduce.

Lesson

1. Play a game

Play AzTech: Empiric Empire to learn basic conversions from fractions to decimals. Empiric Empire is available free for iPad or iPhone and for Android phones. As an added bonus, students will also learn about epidemics. It’s worth mentioning that the smallpox epidemic was spread by viruses but a lot of other diseases are spread by flies.

Note: For summer learning, you may want to just copy the paragraph above into your Google classroom for students to download the games to their phones.

2. Watch a video

I pasted in a link starting after the first minute because that is mostly telling you to like/ subscribe and comment. Ah, YouTube!

Bell Ringer – What if flies went extinct ?  This 7:33  minute video discusses flies as agricultural pests and disease vectors, but also their benefits as scavengers eating up decaying carcasses, pollinators and animal feed.

Here is the link if you’d like to post in your Google classroom or other CMS for students to watch at home. https://youtu.be/80Iqp6bqc-0?t=76

3. Read about flies & perform a demonstration

Recommended reading: Eat like a house fly. Houseflies and barf

What really happens when a house fly lands on your food? Print out this page from Science World – Canada , include the link in your Google classroom or other CMS for students to read, or just read the page to students during class. The demonstration requires vinegar, jello and a turkey baster – things many people have around the house or can pick up easily at a local store. It also includes a list of vocabulary words and definitions, which fits perfectly with our philosophy of direct teaching of academic language.

4. Complete word journal

This lesson provides the opportunity for students to learn many words, in the reading, in the videos and possibly in the Empiric Empire game as well. Students add words or terms with which they are unfamiliar to their word journal. Some teachers call it a personal dictionary, to others it’s a word journal. Regardless, the goal is the same, for students to record new words, give a dictionary definition and “make the word their own”. This can be done by rewriting the definition in their own words, using the word in a sentence or including an illustration of the word.

Two dictionary sites to recommend for definitions are below. An added bonus to mention to students is that they can hear words pronounced.

Since students often ask for an example, here is an example you can link in your lesson. 

The personal dictionary assignment, with all links, can be found here. Feel free to copy and paste into your Google classroom or other site, or print out for your class.

5. Presentation on Decimals in Science (Fly Experiment)

Give this presentation on using decimals to weigh flies, their containers and the food they eat to answer the question, “Do flies really eat 10 times their weight each day?”

Watch a second video

I recommend watching the first 5 1/2 minutes of the Facts About Flies – Secret Nature video  to give the students some idea about both flies as vectors of disease but also important scavengers consuming decaying material. The full documentary is 49 minutes, which I personally found to be more about flies than I wanted to know.

Assessment

Three types of assessment are included in this lesson.

  1. The Word Journal assignment is completed individually and submitted.
  2. Math questions answered within the Empiric Empire game are scored automatically with immediate feedback and student results can be viewed in the teacher reports.
  3. Math questions posed within the presentation can be answered as a whole class, having students hold up a card with their answer or with individual students responding and asking the rest of the class to agree or disagree.


Differentiated instruction

Review of Decimal Addition

One-minute step-by-step video from TeacherTube on Adding Decimals may be helpful for students who need a review of decimal addition.

Watch the whole video

For students who are extremely interested in insects, watching the entire 49 minute video of Facts about Flies will satisfy their curiosity

Experiments with fly larva

Hungry Hungry Hermetia

For teachers who want to do a deep dive into the role flies in consuming food waste, the experiment above uses 100 black soldier fly larvae. I am extremely impressed with this lesson because not only does it include a link to where to buy maggots (on Amazon, of course) but also answers the obvious question of what do you do with 100 fly larvae after your experiment is over. The answer is that you feed these to your class reptile. Would I bring 100 maggots into my classroom? Not in a million years, but that is why I am not an entomologist.

You DO have a class snake, don’t you?

Counting ropes and rational numbers

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Contributed by Lori Hieresrich

📖 Standard

CCSS.MATH.CONTENT.7.NS.A.1
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

📃 Summary

The lesson begins with a discussion of record keeping methods in Indigenous cultures. Students will watch video on Incan counting ropes. Students will create their own number line counting rope. Students watch another video on number lines. Students will use their number line to find Absolute Value of an integer. Students will demonstrate understanding of adding and subtracting integers on number line.

⏰ Time

45- 60 minutes

📲 Technology Required

The videos can be watched on any computer, phone or tablet. Not technology, but each student needs 2 yards of cord. ( As long as needed for all the knots with even spaces between.) Thicker cord is better to make it more tactile. Cord that works could be hemp, leather strips, or twine.

📚Lesson

Start with this PowerPoint presentation. Also available as a Google Slides presentation.

NOTE: If you are using it as a PowerPoint presentation, download it before making any changes. Making changes to the PowerPoint in Google Drive will delete the animations and one of the embedded videos and you don’t want to do that.

The first five slides introduce the topic of how people from different Indigenous cultures in the Americas measured time and other quantities.

2. Watch this video on Quipu accounting

3. Make a counting rope

Students make their own counting ropes using rope, string or twine. Instructions to give students are provided in the PowerPoint.

4. Use the counting rope to solve math problems

Students follow along in the presentation to solve problems using positive integers , fractions and negative integers. The concept of absolute number is introduced, as well as the fact that adding the same number but with the opposite sign will always equal zero. If students are learning at home, they can complete the problems on their own.

Assessment

In addition to the problems completed as a class in the presentation, students complete this worksheet with problems on using a number line with positive and negative integers and absolute value. Only print the first page. The second page is the answer key.

Number line and absolute value – word doc

Number line and absolute value – pdf

Differentiated instruction (optional)

Knots on a counting rope video or the children’s book by the same name give other examples of using a rope to count. This would be appropriate for younger children or those in the class who are at a lower grade level in reading proficiency.

Recommended Related Lesson

The Codex in Latin American history and math

What is a statistical question?

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📖 Standard

CCSS.MATH.CONTENT.6.SP.A.1 Recognize a statistical question as one that anticipates
variability in the data related to the question and accounts
for it in the answers

📲 Technology Required

Computer with projector, for students learning in class. For students learning at home, materials can be accessed on any device with a browser and application to read PDF files or can be printed out and sent home with students.

⏰ Time Required

2 hours (We recommend doing this over two class periods)

📃 Summary

Teachers begin the lesson with a Google slides presentation explaining the requirements for a statistical question. Students complete an assignment identifying whether or not a question qualifies as a statistical question. After class discussion, students complete a second assignment using a small data set shown on a map. In Part 3, students write and answer their own statistical questions using a data set provided, giving an explanation for their answers. Optionally, students can complete a more challenging assignment drawing conclusions from a graph and/or play a game and identify statistical questions.

📚 Lesson

Before you begin, you should have printed out or added to your Google classroom and shared with students the STUDENT handout from the U.S. Census Bureau, “What is a statistical question?” The student version is 11 pages. If you are short on printer paper, you can skip printing page 1. Also, pages 7 and 8 are an optional activity.

You should also print or download the TEACHER version of the Census Bureau handout, “What is a statistical question?” which includes answers to questions in the first two assignments and explanations why each answer was or was not a statistical question.

Introduce students to definition of a statistical question

Begin with the Google Slides presentation, “What is a statistical question?” which breaks down the two components of a statistical question – it must be answered by data and the data must vary.

Students complete assignment on identifying a statistical question

Have students complete Part 1 of the handout “What is a statistical question?” After all students have answered the questions in Part 1, discuss their answers in small groups or as a class.

Students complete Part 2, assignment on identifying a statistical question using real data

Have students complete Part 2 of the handout “What is a statistical question?” After all students have answered the questions in Part 1, discuss their answers in small groups or as a class.

Then, continue with the Google slides presentation and have students complete Part 2 of the student handout from the U.S. Census Bureau (linked above). Have students discuss their answers with one another.

Either correct the answers as a class or collect these to correct yourself. Remember, the teacher handout, linked above, has the correct answers.

We recommend you end the first day’s lesson here and begin the next lesson after students have had the assignments from Part 1 and Part 2 corrected.

Students complete part 3, creating their own statistical questions from data.

Students complete Part 3 of the handout on “What is a statistical question?”

Discuss students’ answers in class. Provide feedback on whether a question really is a statistical question and whether students’ answers to their questions are correct. Allow students time to explain their conclusions.

Optional: Students Complete Part 4

First, use the Google slides presentation, starting on Slide 24, to explain how to read an area chart.

Next, have students complete Part 4 from the student handout, “Drawing conclusions from a graph.”

AzTech: Empiric Empire

Optional: Play Empiric Empire

After students have completed Parts 1 to 3 of the student handout (and, optionally, Part 4), have them play the game Empiric Empire. As an additional optional assignment, ask students to identify statistical questions asked and answered during the game.

If students do not have phones but have Chromebooks, they can play Disaster Deduction Detectives instead – available June, 2022.

Assessment

For assignments in Parts 1 and 2 the teacher version of the handout has correct answers and explanations. For assignments in Parts 3 and 4 of the student handout, examples of correct responses are given but these will vary as students provide their own statistical questions.

For the Empiric Empire game, the teacher reports show student responses to questions. It should be noted that this game does begin with fractions and decimals, which are a prerequisite to statistics.