4.MD.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), ... 4.MD.2. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. 4.MD.3. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.
Anchor Standard/Mathematical Practice(s)
MP.2. Reason abstractly and quantitatively. MP.5. Use appropriate tools strategically. MP.6. Attend to precision
Information Technology Standard
Use technology tools and skills to reinforce classroom concepts and activities.
Revised Bloom's Level of thinking
Understanding Applying Evaluating Creating
Learning Target/Task Analysis
4.MD.1 The units of measure that have not been addressed in prior years are pounds, ounces, kilometers, milliliters, and seconds. Students’ prior experiences were limited to measuring length, mass, liquid volume, and elapsed time. Students did not convert measurements. Students need ample opportunities to become familiar with these new units of measure. Students may use a two-column chart to convert from larger to smaller units and record equivalent measurements. They make statements such as, if one foot is 12 inches, then 3 feet has to be 36 inches because there are 3 groups of 12. Foundational understandings to help with measure concepts:
Understand that larger units can be subdivided into equivalent units (partition).
Understand that the same unit can be repeated to determine the measure (iteration).
Understand the relationship between the size of a unit and the number of units needed
(compensatory principal). 4.MD.2 This standard includes multi-step word problems related to expressing measurements from a larger unit in terms of a smaller unit (e.g., feet to inches, meters to centimeter, dollars to cents). Students should have ample opportunities to use number line diagrams to solve word problems. Example: Debbie and 10 friends are planning for a pizza party. They purchased 3 quarts of milk. If each glass holds 8oz will everyone get at least one glass of milk? Possible solution: Debbie plus 10 friends = 11 total people 11 people x 8 ounces (glass of milk) = 88 total ounces 1 quart = 2 pints = 4 cups = 32 ounces Therefore 1 quart = 2 pints = 4 cups = 32 ounces 2 quarts = 4 pints = 8 cups = 64 ounces 3 quarts = 6 pints = 12 cups = 96 ounces If Debbie purchased 3 quarts (6 pints) of milk there would be enough for everyone at her party to have at least one glass of milk. If each person drank 1 glass then she would have 1- 8 oz glass or 1 cup of milk left over. 4.MD.3 Students developed understanding of area and perimeter in 3rd grade by using visual models. While students are expected to use formulas to calculate area and perimeter of rectangles, they need to understand and be able to communicate their understanding of why the formulas work. The formula for area is I x w and the answer will always be in square units. The formula for perimeter can be 2 l + 2 w or 2 (l + w) and the answer will be in linear units. This standard calls for students to generalize their understanding of area and perimeter by connecting the concepts to mathematical formulas. These formulas should be developed through experience not just memorization. Common Misconceptions: 4.MD.1-3 Students believe that larger units will give the larger measure. Students should be given multiple opportunities to measure the same object with different measuring units. For example, have the students measure the length of a room with one-inch tiles, with one-foot rulers, and with yard sticks. Students should notice that it takes fewer yard sticks to measure the room than rulers or tiles and explain their reasoning.
I can...
I can identify the units of measurement within a system. (km, m, cm, kg, g, lb,oz, l, ml, hr, min, sec) I can convert larger units of measurement into smaller units of measurement within the same system. I can create a conversion table showing equivalent units of measures. (inches/feet) I can determine which operation to use when solving word problems involving measurement. I can use the formula for area and perimeter to solve problems.
5000 mL = _ L _ cm = 5 m 6 cups = pints _ quarts = 2 gal
Ask students to represent real-life situations (such as the length of an animal, the weight of a rock, etc.) in different units of measurement (e.g., the rock weighs 2 kg or 2,000 g). Additional Examples with various operations: Division/fractions: Susan has 2 feet of ribbon. She wants to give her ribbon to her 3 best friends so each friend gets the same amount. How much ribbon will each friend get? Students may record their solutions using fractions or inches. (The answer would be 2/3 of a foot or 8 inches. Students are able to express the answer in inches because they understand that 1/3 of a foot is 4 inches and 2/3 of a foot is 2 groups of 1/3.) Addition: Mason ran for an hour and 15 minutes on Monday, 25 minutes on Tuesday, and 40 minutes on Wednesday. What was the total number of minutes Mason ran? Subtraction: A pound of apples costs $1.20. Rachel bought a pound and a half of apples. If she gave the clerk a $5.00 bill, how much change will she get back? Multiplication: Mario and his 2 brothers are selling lemonade. Mario brought one and a half liters, Javier brought 2 liters, and Ernesto brought 450 milliliters. How many total milliliters of lemonade did the boys have? Number line diagrams that feature a measurement scale can represent measurement quantities. Examples include: ruler, diagram marking off distance along a road with cities at various points, a timetable showing hours throughout the day, or a volume measure on the side of a container.
Differentiation
Intervention:
DPI Classroom Strategies Blackline Master p.58-59 Students can use Block Boy & Block Girl to calculate area and/or perimeter of the various body parts. Draw quadrilaterals with sidewalk chalk and have them measure around with precut yarn to determine the area or perimeter. http://daretodifferentiate.wikispaces.com/Choice+Boards Grid paper, Classroom objects for manipulation, Calculator, ELL/EC students’ vocabulary list ahead of time. Post words with visuals on word wall and in vocabulary notebooks. DPI Classroom Strategies Blackline Master p.58-59 Students can use Block Boy & Block Girl to calculate area and/or perimeter of the various body parts. Geoboards Students can bring in empty cereal, shoe or cracker boxes from home. They work in partner/groups to measure the length and width of the object. They would then calculate the area and/or perimeter. They could use 1” square tiles or 1” die cut squares to check the area and see if they calculated correctly. Draw quadrilaterals with sidewalk chalk and have them measure around with precut yarn to determine the area or perimeter.
Enrichment:
Write a poem, jingle or rap to help them remember the formulas for area and perimeter. Students create and solve real world word problems. Scavenger Hunt Have students work in small groups to follow a map of the school to find the area & perimeter of predetermined items or places. DPI Classroom Strategies p.79-Letter J Give students the NC placemats and have them measure and estimate the perimeter of the shape of NC. Have students use grid to draw parallel, perpendicular, & intersecting lines. Scavenger Hunt
Common Core Standards
4.MD.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), ...4.MD.2. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
4.MD.3. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.
Anchor Standard/Mathematical Practice(s)
MP.2. Reason abstractly and quantitatively.MP.5. Use appropriate tools strategically.
MP.6. Attend to precision
Information Technology Standard
Use technology tools and skills to reinforce classroom concepts and activities.Revised Bloom's Level of thinking
UnderstandingApplying
Evaluating
Creating
Learning Target/Task Analysis
4.MD.1The units of measure that have not been addressed in prior years are pounds, ounces, kilometers, milliliters, and seconds. Students’ prior experiences were limited to measuring length, mass, liquid volume, and elapsed time. Students did not convert measurements. Students need ample opportunities to become familiar with these new units of measure. Students may use a two-column chart to convert from larger to smaller units and record equivalent measurements. They make statements such as, if one foot is 12 inches, then 3 feet has to be 36 inches because there are 3 groups of 12.
Foundational understandings to help with measure concepts:
- Understand that larger units can be subdivided into equivalent units (partition).
- Understand that the same unit can be repeated to determine the measure (iteration).
- Understand the relationship between the size of a unit and the number of units needed
(compensatory principal).4.MD.2
This standard includes multi-step word problems related to expressing measurements from a larger unit in terms of a smaller unit (e.g., feet to inches, meters to centimeter, dollars to cents). Students should have ample opportunities to use number line diagrams to solve word problems.
Example:
Debbie and 10 friends are planning for a pizza party. They purchased 3 quarts of milk. If each glass holds 8oz will everyone get at least one glass of milk?
Possible solution: Debbie plus 10 friends = 11 total people
11 people x 8 ounces (glass of milk) = 88 total ounces
1 quart = 2 pints = 4 cups = 32 ounces
Therefore 1 quart = 2 pints = 4 cups = 32 ounces
2 quarts = 4 pints = 8 cups = 64 ounces
3 quarts = 6 pints = 12 cups = 96 ounces
If Debbie purchased 3 quarts (6 pints) of milk there would be enough for everyone at her party to have at least one glass of milk. If each person drank 1 glass then she would have 1- 8 oz glass or 1 cup of milk left over.
4.MD.3
Students developed understanding of area and perimeter in 3rd grade by using visual models. While students are expected to use formulas to calculate area and perimeter of rectangles, they need to understand and be able to communicate their understanding of why the formulas work. The formula for area is I x w and the answer will always be in square units. The formula for perimeter can be 2 l + 2 w or 2 (l + w) and the answer will be in linear units.
This standard calls for students to generalize their understanding of area and perimeter by connecting the concepts to mathematical formulas. These formulas should be developed through experience not just memorization.
Common Misconceptions: 4.MD.1-3
Students believe that larger units will give the larger measure. Students should be given multiple opportunities to measure the same object with different measuring units. For example, have the students measure the length of a room with one-inch tiles, with one-foot rulers, and with yard sticks. Students should notice that it takes fewer yard sticks to measure the room than rulers or tiles and explain their reasoning.
I can...
I can identify the units of measurement within a system. (km, m, cm, kg, g, lb,oz, l, ml, hr, min, sec)I can convert larger units of measurement into smaller units of measurement within the same system.
I can create a conversion table showing equivalent units of measures. (inches/feet)
I can determine which operation to use when solving word problems involving measurement.
I can use the formula for area and perimeter to solve problems.
Essential Vocabulary
kilometer, meter, centimeter, kilogram, gram, pound, ounce, liter, milliliter, hour, minute, second, equivalent, distance, time, liquide volumes, mass, money, rectangles, area, perimeter, formulaSample Assessments
5000 mL = _ L
_ cm = 5 m
6 cups = pints
_ quarts = 2 gal
Ask students to represent real-life situations (such as the length of an animal, the weight of a rock, etc.) in different units of measurement (e.g., the rock weighs 2 kg or 2,000 g).
Additional Examples with various operations:
Division/fractions: Susan has 2 feet of ribbon. She wants to give her ribbon to her 3 best friends
so each friend gets the same amount. How much ribbon will each friend get?
Students may record their solutions using fractions or inches. (The answer would be 2/3 of a foot
or 8 inches.
Students are able to express the answer in inches because they understand that 1/3 of a foot is 4
inches and 2/3 of a foot is 2 groups of 1/3.)
Addition: Mason ran for an hour and 15 minutes on Monday, 25 minutes on Tuesday, and 40
minutes on Wednesday. What was the total number of minutes Mason ran?
Subtraction: A pound of apples costs $1.20. Rachel bought a pound and a half of apples. If she
gave the clerk a $5.00 bill, how much change will she get back?
Multiplication: Mario and his 2 brothers are selling lemonade. Mario brought one and a half liters,
Javier brought 2 liters, and Ernesto brought 450 milliliters. How many total milliliters of lemonade
did the boys have?
Number line diagrams that feature a measurement scale can represent measurement quantities.
Examples include: ruler, diagram marking off distance along a road with cities at various points, a
timetable showing hours throughout the day, or a volume measure on the side of a container.
Differentiation
Intervention:
DPI Classroom Strategies Blackline Master p.58-59Students can use Block Boy & Block Girl to calculate area and/or perimeter of the various
body parts.
Draw quadrilaterals with sidewalk chalk and have them measure around with precut yarn to determine the area or perimeter.
http://daretodifferentiate.wikispaces.com/Choice+Boards
Grid paper, Classroom objects for manipulation, Calculator, ELL/EC students’ vocabulary list ahead of time.
Post words with visuals on word wall and in vocabulary notebooks.
DPI Classroom Strategies Blackline Master p.58-59
Students can use Block Boy & Block Girl to calculate area and/or perimeter of the various body parts.
Geoboards
Students can bring in empty cereal, shoe or cracker boxes from home. They work in partner/groups to measure the length and width of the object. They would then calculate the area and/or perimeter. They could use 1” square tiles or 1” die cut squares to check the area and see if they calculated correctly.
Draw quadrilaterals with sidewalk chalk and have them measure around with precut yarn to determine the area or perimeter.
Enrichment:
Write a poem, jingle or rap to help them remember the formulas for area and perimeter.Students create and solve real world word problems.
Scavenger Hunt Have students work in small groups to follow a map of the school to find the area & perimeter of predetermined items or places.
DPI Classroom Strategies p.79-Letter J
Give students the NC placemats and have them measure and estimate the perimeter of the shape of NC.
Have students use grid to draw parallel, perpendicular, & intersecting lines.
Scavenger Hunt
Instructional Resources
http://www.jmathpage.com/JIMSMeasurementpage.htmlFill it to Capacity
Notes and Additional Information