Here is a 15-minute lesson for the Math-Aids Properties of Mathematics Worksheets. The worksheets cover definitions, identifying properties, and working with properties of mathematics. They include the commutative, associative, distributive, identity, inverse, and zero properties.
15-Minute Math Lesson Plan: Understanding Math Properties
Learning Objective
Students will identify common properties of mathematics and use them to simplify expressions and understand why different equations can have the same value.
Materials
-
Pencil and paper
-
Whiteboard or scratch paper
1. Warm-Up (3 minutes)
Write these equations on the board:
-
4 + 7 = 7 + 4
-
5 × 1 = 5
-
9 + 0 = 9
Ask students:
-
What changed in the first equation?
-
Why does multiplying by 1 leave a number unchanged?
-
Why does adding zero leave a number unchanged?
Explain that mathematicians use properties to describe rules that make calculations easier and help us understand equations.
2. Teacher Modeling (4 minutes)
Introduce five important properties.
1. Commutative Property
Changing the order of numbers does not change the answer.
Example:
6 + 8 = 8 + 6
Both equal 14.
2. Associative Property
Changing the grouping of numbers does not change the answer.
Example:
(2 + 5) + 3 = 2 + (5 + 3)
Both equal 10.
3. Distributive Property
Multiply a number by each number inside the parentheses.
Example:
3 × (4 + 2)
= (3 × 4) + (3 × 2)
= 12 + 6
= 18
4. Identity Property
Adding zero or multiplying by one leaves a number unchanged.
Examples:
9 + 0 = 9
9 × 1 = 9
5. Zero Property
Multiplying any number by zero gives zero.
Example:
12 × 0 = 0
Explain that recognizing these patterns helps students solve problems more efficiently.
3. Guided Practice (3 minutes)
Have students identify the property shown in each equation.
Problem 1:
7 × 4 = 4 × 7
Answer: Commutative Property of Multiplication
Problem 2:
(3 + 6) + 2 = 3 + (6 + 2)
Answer: Associative Property of Addition
Problem 3:
5 × (2 + 4) = (5 × 2) + (5 × 4)
Answer: Distributive Property
Problem 4:
15 + 0 = 15
Answer: Identity Property of Addition
Ask students to explain how they recognized each property.
4. Independent Worksheet Practice (3 minutes)
Have students complete a few problems from one of the Math-Aids Properties worksheets.
Choose the worksheet that matches the lesson:
-
Definitions of Properties: Students review the names and rules for different mathematical properties.
-
Identifying Properties: Students examine equations and determine which property is being demonstrated.
-
Working with Properties: Students apply properties to simplify expressions and select correct answers.
Encourage students to look for clues:
-
Are the numbers changing places? Commutative.
-
Are the parentheses changing? Associative.
-
Is a number being multiplied across parentheses? Distributive.
-
Is zero being added or one being multiplied? Identity.
-
Is a number being multiplied by zero? Zero Property.
5. Exit Ticket (2 minutes)
Ask students to identify the property and explain their answer.
Problem 1:
8 + 0 = 8
Answer: Identity Property of Addition.
Problem 2:
4 × (3 + 5) = (4 × 3) + (4 × 5)
Answer: Distributive Property.
Differentiation
Support: Provide a reference sheet with each property name, definition, and one example. Begin with the commutative, associative, identity, and zero properties before introducing the distributive property.
Extension: Introduce the additive inverse and multiplicative inverse.
Examples:
-
7 + (−7) = 0 — Additive Inverse
-
5 × 1/5 = 1 — Multiplicative Inverse
Ask students to explain why each equation is true.
Common Misconceptions
-
Confusing commutative and associative: Commutative changes the order; associative changes the grouping.
-
Confusing identity and zero properties: Adding zero leaves a number unchanged, while multiplying by zero produces zero.
-
Applying the distributive property incorrectly: The outside number must multiply every term inside the parentheses.
-
Thinking subtraction and division are commutative: Changing the order in subtraction or division generally changes the answer.
Assessment
Review students' answers during guided practice, independent worksheet work, and the exit ticket.
Success Criteria: Students can identify common mathematical properties, recognize them in equations, and use them to simplify expressions.
Teacher tip: For a first lesson, I recommend using the Definitions of Properties worksheet as a reference, followed by the Identifying Properties worksheet for practice. The Working with Properties worksheet is a good next step once students recognize the rules.
-----------
Posted 11/14/26
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Back to Geography Lesson Plan
Where Did Foods Originate?
(Foods of the New World and Old World)
Subjects
Arts & Humanities
--Language Arts
Educational Technology
Science
--Agriculture
Social Studies
--Economics
--Geography
--History
----U.S. History
----World History
--Regions/Cultures
Grade
K-2
3-5
6-8
9-12
Advanced
Brief Description
Students explore how New World explorers helped change the Old World's diet (and vice versa).
Objectives
Students will
learn about changes that occurred in the New World and Old World as a result of early exploration.
use library and Internet sources to research food origins. (Older students only.)
create a bulletin-board map illustrating the many foods that were shared as a result of exploration.
Keywords
Columbus, explorers, origin, food, timeline, plants, map, New World, Old World, colonies, colonial, crops, media literacy, products, consumer
Materials Needed:
library and/or Internet access (older students only)
outline map of the world (You might print the map on a transparency; then use an overhead projector to project and trace a large outline map of the world onto white paper on a bulletin board.)
magazines (optional)
Lesson Plan
The early explorers to the Americas were exposed to many things they had never seen before. Besides strange people and animals, they were exposed to many foods that were unknown in the Old World. In this lesson, you might post an outline map of the continents on a bulletin board. Have students use library and/or Internet resources (provided below) to research some of the edible items the first explorers saw for the first time in the New World. On the bulletin board, draw an arrow from the New World (the Americas) to the Old World (Europe, Asia, Africa) and post around it drawings or images (from magazines or clip art) of products discovered in the New World and taken back to the Old World.
Soon, the explorers would introduce plants/foods from the Old World to the Americas. You might draw a second arrow on the board -- from the Old World to the New World -- and post appropriate drawings or images around it.
Adapt the Lesson for Younger Students
Younger students will not have the ability to research foods that originated in the New and Old World. You might adapt the lesson by sharing some of the food items in the Food Lists section below. Have students collect or draw pictures of those items for the bulletin board display.
Resources
In addition to library resources, students might use the following Internet sites as they research the geographic origins of some foods:
Curry, Spice, and All Things Nice: Food Origins
The Food Timeline
Native Foods of the Americas
A Harvest Gathered: Food in the New World
We Are What We Eat Timeline (Note: This resource is an archived resource; the original page is no longer live and updated.)
Food Lists Our research uncovered the Old and New World foods below. Students might find many of those and add them to the bulletin board display. Notice that some items appear on both lists -- beans, for example. There are many varieties of beans, some with New World origins and others with their origins in the Old World. In our research, we found sources that indicate onions originated in the New and sources that indicate onions originated in the Old World. Students might create a special question mark symbol to post next to any item for which contradictory sources can be found
Note: The Food Timeline is a resource that documents many Old World products. This resource sets up a number of contradictions. For example:
Many sources note that tomatoes originated in the New World; The Food Timeline indicates that tomatoes were introduced to the New World in 1781.
The Food Timeline indicates that strawberries and raspberries were available in the 1st century in Europe; other sources identify them as New World commodities.
Foods That Originated in the New World: artichokes, avocados, beans (kidney and lima), black walnuts, blueberries, cacao (cocoa/chocolate), cashews, cassava, chestnuts, corn (maize), crab apples, cranberries, gourds, hickory nuts, onions, papayas, peanuts, pecans, peppers (bell peppers, chili peppers), pineapples, plums, potatoes, pumpkins, raspberries, squash, strawberries, sunflowers, sweet potatoes, tobacco, tomatoes, turkey, vanilla, wild cherries, wild rice.
Foods That Originated in the Old World: apples, bananas, beans (some varieties), beets, broccoli, carrots, cattle (beef), cauliflower, celery, cheese, cherries, chickens, chickpeas, cinnamon, coffee, cows, cucumbers, eggplant, garlic, ginger, grapes, honey (honey bees), lemons, lettuce, limes, mangos, oats, okra, olives, onions, oranges, pasta, peaches, pears, peas, pigs, radishes, rice, sheep, spinach, tea, watermelon, wheat, yams.
Extension Activities
Home-school connection. Have students and their parents search their food cupboards at home; ask each student to bring in two food items whose origin can be traced to a specific place (foreign if possible, domestic if not). Labels from those products will be sufficient, especially if the products are in breakable containers. Place those labels/items around a world map; use yarn to connect each label to the location of its origin on the map.
Media literacy. Because students will research many sources, have them list the sources for the information they find about each food item. Have them place an asterisk or checkmark next to the food item each time they find that item in a different source. If students find a food in multiple sources, they might consider it "verified"; those foods they find in only one source might require additional research to verify.
Assessment
Invite students to agree or disagree with the following statement:The early explorers were surprised by many of the foods they saw in the New World.
Have students write a paragraph in support of their opinion.
Lesson Plan Source
Education World
Submitted By
Gary Hopkins
National Standards
LANGUAGE ARTS: EnglishGRADES K - 12NL-ENG.K-12.2 Reading for UnderstandingNL-ENG.K-12.8 Developing Research SkillsNL-ENG.K-12.9 Multicultural UnderstandingNL-ENG.K-12.12 Applying Language Skills
SOCIAL SCIENCES: EconomicsGRADES K - 4NSS-EC.K-4.1 Productive ResourcesNSS-EC.K-4.6 Gain from TradeGRADES 5 - 8NSS-EC.5-8.1 Productive ResourcesNSS-EC.5-8.6 Gain from TradeGRADES 9 - 12NSS-EC.9-12.1 Productive ResourcesNSS-EC.9-12.6 Gain from Trade
SOCIAL SCIENCES: GeographyGRADES K - 12NSS-G.K-12.1 The World in Spatial TermsNSS-G.K-12.2 Places and Regions
SOCIAL SCIENCES: U.S. HistoryGRADES K - 4NSS-USH.K-4.1 Living and Working together in Families and Communities, Now and Long AgoNSS-USH.K-4.3 The History of the United States: Democratic Principles and Values and the People from Many Cultures Who Contributed to Its Cultural, Economic, and Political HeritageNSS-USH.K-4.4 The History of Peoples of Many Cultures Around the WorldGRADES 5 - 12NSS-USH.5-12.1 Era 1: Three Worlds Meet (Beginnings to 1620)NSS-USH.5-12.2 Era 2: Colonization and Settlement (1585-1763)NSS-WH.5-12.6 Global Expansion and Encounter, 1450-1770
TECHNOLOGYGRADES K - 12NT.K-12.1 Basic Operations and ConceptsNT.K-12.5 Technology Research Tools
Find many more great geography lesson ideas and resources in Education World's Geography Center.
Click here to return to this week's World of Learning lesson plan page.
Updated 10/11/12
Having a tough time finding the right words to come up with "areas for improvement" comments on your students' report cards? Check out our helpful suggestions to find just the right one!
The following statements will help you tailor your comments to specific children and highlight their areas for improvement.
Be sure to check out our 125 Report Card Comments for positive comments!
Needs Improvement- all topics
is a hard worker, but has difficulty staying on task.
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needs to be more respectful and courteous to his/her classmates.
needs to listen to directions fully so that he/she can learn to work more independently.
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gives up easily when something is difficult and needs extensive encouragement to attempt the task.
gets along with his/her classmates well, but is very disruptive during full group instruction.
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is having a difficult time with math. Going over _____ at home would help considerably.
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needs to practice reading at home every day to help make him/her a stronger reader.
needs to practice his/her sight words so that he/she knows them on sight and can spell them.
needs to work on his/her spelling. Practicing at home would be very beneficial.
can read words fluently, but has a difficult time with comprehension. Reading with ______ every day would be helpful.
could benefit from working on his/her handwriting. Slowing down and taking more time would help with this.
is having difficulty writing stories. Encouraging him/her to tell stories at home would help with this.
has a difficult time knowing when it is appropriate to share his/her thoughts. We are working on learning when it is a good time to share and when it is a good time to listen.
needs to work on his/her time management skills. _______is able to complete his/her work, but spends too much time on other tasks and rarely completes his/her work.
needs reminders about the daily classroom routine. Talking through the classroom routine at home would be helpful.
is having a difficult time remembering the difference between short and long vowel sounds. Practicing these at home would be very helpful.
is struggling with reading. He/she does not seem to enjoy it and does not want to do it. Choosing books that he/she like and reading them with him/her at home will help build a love of reading.
frequently turns in incomplete homework or does not hand in any homework. Encouraging _______to complete his/her homework would be very helpful.
does not take pride in his/her work. We are working to help him/her feel good about what he/she accomplishes.
does not actively participate in small group activities. Active participation would be beneficial.
has a difficult time remembering to go back and check his/her work. Because of this, there are often spelling and grammar mistakes in his/her work.
does not much effort into his/her writing. As a result, his/her work is often messy and incomplete.
is struggling to understand new concepts in science. Paying closer attention to the class discussions and the readings that we are doing would be beneficial.
is reading significantly below grade level. Intervention is required.
does not write a clear beginning, middle and end when writing a story. We are working to identify the parts of the stories that he/she is writing.
is struggling to use new reading strategies to help him/her read higher level books.
is wonderful at writing creative stories, but needs to work on writing nonfiction and using facts.
has a difficult time understanding how to solve word problems.
needs to slow down and go back and check his/her work to make sure that all answers are correct.
is not completing math work that is on grade level. Intervention is required.
is struggling to understand place value.
is very enthusiastic about math, but struggles to understand basic concepts.
has a difficult time remembering the value of different coins and how to count them. Practicing this at home would be helpful.
would benefit from practicing math facts at home.
is very engaged during whole group math instruction, but struggles to work independently.
is able to correctly answer word problems, but is unable to explain how he/she got the answer.
is having a difficult time comparing numbers.
Related: 125 Report Card Comments for positive comments!
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