Way To WeighWay To Weigh

Fourth Grade MathematicsFourth Grade MathematicsStandard Units of MeasurementStandard Units of Measurement

Unit’s GoalBy the end the unit students should be able todemonstrate the following:Measure the weight of an object using appropriate

units (gram, kilogram, pound).Know some familiar referents for various weight unit.Solve problems involving the conversion of gram,

kilogram and pound.Estimate weight using gram, kilogram and pound.

StandardsStandardsCommon Core States Standard

CCSS.Math.Content.4.MD.A.1

Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36),

Standards Cont’dStandards Cont’d

Standards For Mathematical Practice

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.3. Model with mathematics.4. Use appropriate tools strategically5. Attend to precision6. Look for and make use of structure.

Lessons and ContentLessons and Content

1. Let’s Set The Standardo Understand and use a standard unit of

measure (gram)2. What’s My Weight?o Estimate and weigh items using grams and

Kilograms 3. How Much Is A Pound?o Understand and use pound as a measure of weight

Lesson 1: Let’s Set The Lesson 1: Let’s Set The StandardStandard

TaskUnderstand and use a standard unit of

measure (g)Background knowledgeStudents should know how to measure mass

using a balance scale, have experience measuring and comparing weight using a balance scale, and understand the difference between standard and non-standard units in measurement.

Metric PrefixesMetric Prefixes

Grams

(g)

Hecto- gram

(h)

Deca-gram(da)

Kilo-gram(kg)

Deci-gram

(d)

Centi-gram

(c)

Milli-gram(m)

1,000 100 10 1 1/10 1/100 1/1000

Essential QuestionsEssential Questions

What are the difference between a gram and a kilogram?

What is weight/mass?Why do we measure weight?What happen to a unit when we change units?Objective: Students will be able to:Recognize the difference between standard and

non-standard unit of measurement.know how to use standard unit of measurement

MaterialMaterialFor each Group:Balance ScaleSet of small items (paperclips etc.)Set of gram weights (1g, 5g, 10g, 20g)For each Student:Student worksheetSandwich size ziploc bagFor the ClassPieces of fruit, potatoes, 5lbs. gravelPacket of macaroni, salt and teaComputer with high speed internetOne 2-gallon Ziploc bag (to create a 1 kilo bag)

Time: Time: 45 minutes45 minutesClass size:Class size: 20 (12 girls & 8 boys) 20 (12 girls & 8 boys)

Motivation:Let’s talk about weight..... (class discussion)When do you need to measure weight?What kinds of tool do you use to measure

weight?What units do you use to measure

weight/mass?

ProcedureProcedureStudent will transition from non-standard to a standard unit

of measure (grams). They will use grams to measure the mass of the pieces of fruit. (The word mass is used because students will measure the weight of their fruit using a balance scale).Teacher will:

Show gram weights, introduce its name and symbol and describe standard unit of weight.

Ask students to use balance scale to compare 1 Gram (1g) to the paper clips.

Show the other gram weights (5g, 10g, 20g) and have students estimate and measure how many paper clips would equal each weight.

Ask students to discuss their findings.

Procedure Cont’dProcedure Cont’d

When discussing the weight of the fruit teacher will: Guide students to suggest making new units (100g) weight. Allow students to show how they can create these (using

zippered bag and gravels) Allow students to determine how they will combine their

weights sets to get a total of 100g on one side of the balance scale, and then measure an equivalent amount of gravel to balance scale.

Measure fruits using the old and new weights, encourage students to use the metric roots and prefixes from prior knowledge.

Teacher will: Allow students to make (10) 100g bags, and place them

in a large zippered plastic bag. Ask students to figure out how  much this new unit

 weighs (1000g). Guide students to the term kilogram.Students’ Task:

Students will follow the directions below from the “Let’s Set The Standard,” student worksheet.

Find the weight of each object using 1 gram (1 g) weights

Students TasksStudents Tasks

Students’ Task Cont’dStudents’ Task Cont’d

Record the weights in the chart below. Place a piece of fruit in your balance scale. Talk

with your group about how you would measure the fruit using metric units. Record your thoughts below.

Create a three-column chart similar to the worksheet. Label the first column Object Name, the second column Measurement in Grams (g), and the third column Measurement in kilogram (kg). Find the weight of each object and record it in your chart. Students may weigh more than one piece of fruit to have at least one kilogram.

HomeworkHomeworkStudents will: Look around their home for 10 items that

weighs less than 100g; and for 10 items weighs more than 100g or 1 kilogram.

Students will record their findings in their math journals, and share their findings with the class.

Formative Assessment QuestionsFormative Assessment Questions

What is the difference between a standard and non-standard unit of measurement?

How can you use gram weights and a balance scale to measure the weight of an object?

What happens when the unit is too small to measure an object?

What is the difference between units in the same system of measurement?

DifferentiationDifferentiation Extension: Ask students to look around the classroom for objects, find

the weight of the objects using different units, such as hectograms and dekagrams.

Seeing students had already measured the mass of 1 apple, 1 banana, and 1 orange, ask students to estimate how many apples would be needed to make one kilogram? How many bananas? How many oranges?

Intervention: Make the relationship between kilogram and gram (1kg =

1,000g) explicit. Give students a second recording sheet, allowing the

student to focus on measurement, not creating a chart.

TechnologyTechnology

http://www.youtube.com/watch?v=KuXbwWtF-uM This tutorial about the mass of objects can be used for remediation purposes.

http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/weigh/index.htm This activity is a problem solving activity which uses a set of scales and a variety of shapes. It can be used for additional practice or remediation purposes.

Lesson 2: What’s My Weight?Lesson 2: What’s My Weight?

Time: 2 days/45 minutes each day

BACKGROUND KNOWLEDGE Students need to be familiar with the terms gram

and kilogram, metric units used to measure the mass of an object. One kilogram is equal to 1,000 grams. One gram weighs about as much as a large paper clip or a packet of sweetener, and one kilogram is the weight of a textbook and is equal to about 2.2 pounds.

MaterialsMaterials What’s My Weight-Worksheet (Part 1) What’s My Weight-Worksheet (Part 2) Large paper clip Gram weight Balance scales 1 kg reference weights Spring scales Liter bottle, gravel, water Dried Peas Computer with high speed internet access.

Grouping: Grouping: Students will work in small Students will work in small groups.groups.

Motivation: King Henry Drinking Chocolate Milkhttp://www.flocabulary.com/metric-system/

Students will receive copy of the song, so they can sing along.

Essential QuestionsEssential Questions

How are grams and kilograms related?What objects around us weighs about a gram? About

a kilogram?When should we measure with grams? Kilograms?What happens to a measurement when we change

units?Objective:Students will be able to make conversion between

grams and kilogram.

ProcedureProcedure

First PartTeacher will fill a one liter bottle with water. This

weighs about one kilogram. Teacher and students will work together and fill bags with, gravel, and dried beans.  Teacher will compare the weight of the bottle of water with the bags and tell students that the bags weigh about 1 kilogram each. Student can use these “reference weights” to compare weights when looking for items that weigh one kilogram.

Procedure: First Part cont’dProcedure: First Part cont’dTo introduce this part of the lesson teacher will:Hold up a large paper clip and explain that it weighs

about one gram.Pass large paper clips around to the students, so that

they can get an idea of how much a gram is. Involve the class in a discussion about what might be

appropriate to measure in grams.Ask the class for a few suggestions, and allow

students to list things in the classroom they think they could weigh using grams.

Ask students to record their items in the table on their worksheet, “Worth the Weight, Part 1 – Grams.”

Students Tasks Students Tasks Students will follow the directions below from the

“What’s My Weight- Grams” worksheet. Teacher:  Think about how heavy a paper clip is. Find

five objects that you think should be weighed using grams. Do not use a scale to check yet! After you have found five objects:

Write the name of the objects in the chart below.Make an estimate for each item and record it in the

chart below.Weigh each item using the scale provided and record

it in the chart below.

Students Task cont’dStudents Task cont’d

Students will answer the following questions:

How did you make your estimates?Why are the items you choose appropriate

to measure in grams?Be ready to share your thinking with the

class.

What’s My Weight? Part 2What’s My Weight? Part 2To complete the second part of the lesson

teacher will:Pass the kilogram referents around to the students.Ask the class for a few suggestions of classroom

items for which kilograms would be an appropriate unit of measure.

For each item on their chart, students should first hold the item to estimate its weight (more than, less than, or about 1 kilogram), measure its weight using a spring scale, and write down the actual weight of each item. When students are finished, hold a class discussion about what objects are appropriate to weigh in grams and what students learned from this part of the lesson.

Students TaskStudents Task Students will follow the directions below from the “What’s My Weight”  Part 2

- Kilogram worksheet. Teacher: Students, you and your partner are going on a kilogram scavenger

hunt! Use one of the reference weights to get an idea of how heavy one kilogram is. Then find items around the room that weigh less than, about, and more than one kilogram.

List the items in the table below. Predict whether each item is more than, less than, or about 1 kilogram. Weigh each item with a spring scale. Weigh each item with a spring scale. Remember: 1 kg = 1,000 grams

Formative Assessment QuestionsFormative Assessment QuestionsWhy is it important to associate items with

a weight?When would you use grams and kilograms

in your everyday life?What are your predictions for which

objects will weigh about a gram? Why?What are your predictions for which

objects will weigh about a kilogram? Why?

DifferentiationDifferentiation

Extension:Have students find ten items around their house

that they would measure using grams or kilograms. 5 items for grams and 5 items for kilograms. (estimate items weight)

Have students estimate how many kilograms five different people weigh (family members)

Intervention:Each week, have a ten minute discussion about

units of weights. Choose an item from the classroom, discuss the appropriate unit to use to measure the weight, and then estimate the weight of the object.

TechnologyTechnology http://www.sheppardsoftware.com/mathgames/measurement/

MeasurementGrams.htm This website can be used for remediation http://www.ixl.com/math/grade-4/compare-and-convert-metric-units This

website is great for re-teaching measurement concept.

 Homework Assuming that students have access to a working computer with high

speed internet, students will write a 1 page research paper on how the Ancient Egyptians measured weight.

Lesson 3: What’s In A Pound?Lesson 3: What’s In A Pound?Time: 2 days/45 mins.

Grouping: Students will work in small groups.

Motivation: Teacher: (Class discussion) If you want to know  your weight what are you going to use? What about another objects such as tomatoes, and potatoes. How can I know the weight of these things? Where can you see a balance? Why we use a balance? What are you doing if there is no balance in your home or in the world, how can you measure the weight of objects?

Objective: Objective: Students will be able to explain and use pound as a measure of Students will be able to explain and use pound as a measure of weight.weight.

BACKGROUND KNOWLEDGEStudents should know how to use a scale and

have heard the term pound as a unit of weight measurement. Teacher will begin the lesson with a brainstorming session of when they have heard the term “pound” used in real life. This will give teacher an understanding of what students know about the measurement.

MaterialsMaterials “What’s in a Pound?, Part 1 – Worksheet “What’s in a Pound?, Part 2 – Worksheet Five (1 lb) weight 1 cloth or paper bag for each group 5 lbs. of sand, gravel, blocks, cubes, beans, etc. for

students to fill bags Items in the classroom that weigh about one pound Spring scale Computer with high speed internet

Essential Questions: Why are units important in measurement? What units are appropriate to measure weight?

Procedure: Procedure:

In this lesson, students will be involved in a kinesthetic activity that helps them experience how heavy a pound is and develop a conceptual understanding of a pound. Students will then use that experience to estimate the weight of everyday items.

Part 1:Part 1: Teacher will:Teacher will:

Introduce this lesson, and pass a one pound weight around to the students.

Ask each student to hold the one pound and try to remember how heavy it feels.  (Bags of materials can be made ahead of time and be used as referents for this task. Bags may contain sand, gravel, beans, etc.)

Ask Student to empty and refill their bags at least three times, even if they were very close to one pound on their first or second attempt.

Use and encourage students to use mathematical words to describe whether the bag weighs more than, less than, or equal to a pound. This is an important part of this activity.

Students’ TaskStudents’ Task Students will follow the directions below from the “What’s in a Pound? Work sheet.

Think about how heavy the pound weight felt. Now create a bag that you think will weigh about 1 pound. Do not use a scale to create your bag! After you have made your 1 pound bag, weigh your bag using the scale provided.

Does your bag weigh less than a pound? More than a pound? Exactly one pound? Determine if your bag weighs more than, less than, or equal to one pound. Record your

results in the chart below. 2.      List common items from school or home that could be measured using pounds. 3.      Think, could the same items be measured using kilograms? Record your thinking

below.

Students Task Cont’dStudents Task Cont’dDetermine if your bag weighs more than, less

than, or equal to one pound. Record your results in the chart below.

List common items from school or home that could be     measured using pounds.

Think, could the same items be measured using kilograms? Record your thinking below.

Part 2: What’s In A Pound?Part 2: What’s In A Pound? To begin the lesson, the pound referents are passed

around, so students can be reminded of what a pound feel like.

Ask the class for a few classroom items for which pounds would be an appropriate unit of measure.

For each item that students give, let student first hold the item to estimate its weight (more than, less than, or about 1 pound), measure its weight using a spring scale, and write down the actual weight of each item in their math journals

When students are finished, hold a class discussion about the objects, and what students learned from this.

Use the results from the students’ work to generate a list of items in the classroom that weigh approximately one pound.  

Students TaskStudents TaskStudent, you and your partner are going on a

pound scavenger hunt! Use one of the reference weights to get an idea of how heavy one pound is. Then find items around the room that weigh less than, about, and more than one pound.

List the items in the table below.Predict whether each item is more than, less

than, or about 1 pound.Weigh each item with a spring scale.Record the weight in the last column.

Formative Assessment QuestionsFormative Assessment Questions When could you use a pound in your everyday routines? How could you estimate and/or measure an item without using a scale?

Differentiation Extension Create picture cards of items and separate cards with corresponding

weights in pounds. Have students match the items with their weights and use a self-checking system on the back of the cards. Understanding how much items in their own world weigh will assist in overall understanding of the unit.

TechnologyTechnology http://www.youtube.com/watch?v=vbglZ9qw0hU ·This

tutorial video about converting measures of weight can be used for remediation purposes.

http://www.mathsisfun.com/measure/ This is a tutorial resource which discusses converting customary units of weight. It can be used for remediation purposes.

Homework Students will estimate their weights in pounds and the

weights of some of their family members, and convert the pounds to kilograms. Write the steps in your math journals.

SummarySummary There are two basic systems of measurement. When measuring

in these systems, a comparison is made to some unit recognized as a standard. The system used in the United States is called the customary system of measurement. The other basic system of measurement is called the metric system. Within the metric system, the gram is the fundamental unit of mass. The metric system is a base-ten system. Prefixes are used to designate 10 times (deka-), 100 times (hecto-), and 1,000 times (kilo-) the unit. The prefixes deci-, centi-, and milli- are used to designate the unit, respectively. Converting units within the metric system is much simpler than within the customary system. Because the metric system is a base-ten system, students simply need to multiply or divide by powers of ten to convert. They can look up the equivalencies in the tables provided in their math book.