Mission 2 Summary
Mission 2 Summary
Embedded Files
Learning Objectives
Students will be able to:
Express metric length, mass and capacity measurements in terms of a smaller unit
Model and solve addition and subtraction word problems involving metric length, mass and capacity.
Know and relate metric units to place value units in order to express measurements in different units.
Use addition and subtraction to solve multi-step word problems involving length, mass, and capacity
Metric unit conversion involves changing a measurement from one unit to another within the metric system. Lets see how
Units of measurement:
Length→1m = 100cm and 1km = 1000m
Capacity →1L = 1000 ml
Mass → 1kg = 1000g
Strategy:
1. Practice place value by breaking down numbers into smaller part
Example 1: 347 = 300 + 40 + 7
Example 2: 543 = 500 + 40 + 3
2. Solve simple problems using addition and subtraction of metric units.
Example 1: 500 g + 300 g = 800 g
Example 2: 700 ml - 200 ml = 500 ml
3. Choose to convert mixed and single units before or after doing the calculations.
Example 1: 1kg + 500g
= 1000g + 500g
= 1500g
Example 2: 1km + 150m
= 1000m + 150m
= 1,150m
4. Connect what you know about metric units and place value to learn conversions.
Example: 1 meter = 100 centimeters, etc
5. Adding/subtracting mixed units of length using the algorithm or simplifying strategies:
Understanding these conversions will help with addition, subtraction and later when we need to multiply and divide metric units as well.
Example 1:
Meter and Centimeter Number Bonds
Number bonds show how a number can be divided into parts.
Example: For the number 10, the number bonds could be:
1 + 9
2 + 8, etc
Similarly, for 150cm, the number bonds could be:
1m + 50cm i.e 100cm + 50cm
They help us see how numbers add up and how we can break down numbers for subtraction.
To add and subtract meters and centimeters/any metric units:
Convert metric length units in the context of addition and subtraction problems involving mixed units.
On some occasions, we can convert from a smaller unit to a larger unit.
This can be done by creating a connection between units of measures related to place value, as it serves as a natural guide for moving between larger and smaller units. Answers in smaller units are mostly acceptable.
Consider the connections and similarities between the following equalities:
Unit Counting
Unit counting in math means counting each individual item as one unit.
Count by 50 cm in the following sequence.
Example
• 50 cm, 100 cm, 150 cm, 200 cm, 250 cm, 300 cm, 250 cm, 200 cm, 150 cm, 100 cm, 50 cm.
• 50 cm, 1 m, 150 cm, 2 m, 250 cm, 3 m, 250 cm, 2 m, 150 cm, 1 m, 50 cm.
• 50 cm, 1 m, 1 m 50 cm, 2 m, 2 m 50 cm, 3 m, 2 m 50 cm, 2 m, 1 m 50 cm, 1 m, 50 cm.
Working with mixed units of meters and centimeters will help understand other mixed units like liters and milliliters, kilometers and meters, kilograms and grams, and whole numbers and fractions.
Noting the patterns
Example: Metric Units:
1 L = 1,000 × 1 mL
1 kg = 1,000 × 1 g
1 km = 1,000 × 1 m
1 m = 100 × 1 cm
Place Value:
1 thousand = 1,000 × 1 one
1 hundred = 100 × 1 one
Relate Units of Measurement to Units of Place Value
Breaking Down Measurements:
1. 1,200 milliliters = 1 liter 200 milliliters
2. 1,200 = 1 thousand 200 ones
Example:
Renaming 15,450 milliliters, kilograms, and ones similarly:
1. 15,450 mL = 15 L 450 mL
2. 15,450 kg = 15 tons 450 kg
3. 15,450 ones = 1 ten thousand 5 thousand 450 ones
Compare Metric Units Using Place Value Knowledge and a Number Line
Conversions:
1. 724,706 milliliters = 724 liters 706 milliliters
2. 72 liters = 72,000 milliliters
Number Line:
1. 0 kilometers to 2 kilometers
2. 1 kilometer = 1,000 meters
3. 2 kilometers = 2,000 meters
Example:
Comparing Measurements:
To compare the measurements, we first need to convert both measurements to the same unit.
For example: In the below case, we'll convert them to liters and milliliters for easier comparison.
724,706 ml with 72 L 760 ml
724,706 ml = 724 L 706 ml
724,706ml ________________ 72L 760ml
724,706ml > 72L 760ml
724 > 72
Placing on Number Line:
1. 7,256 m between 7,250 m and 7,260 m
2. 7 km 246 m between 7 km 240 m (7,240 m) and 7 km 250 m (7,250 m)
Order of Measurements
From least to greatest:
1. 7 km 246 m < 7,256 m < 725,900 cm
Word problems
Solving word problems by adding and subtracting metric units, will make it better at thinking about parts and wholes. This helps to prepare for working with bigger numbers and fractions in the future. Using tape diagrams and number lines help to solve these word problems using standard methods.
Lets see the steps: using addition and subtraction to solve word problems with multiple steps involving length, weight, and capacity.
Step 1: Model the problem.
Review the following questions before solving the problem.
• Can you draw something?
• What can you draw?
• What conclusions can you make from your drawing?
Step 2: Calculate to solve
Step 3: Write a statement.
Step 4: Assess the solution for reasonableness.
For example:
Example 1: Sarah has 250 grams of apples and 300 grams of bananas. How many grams of fruit does she have?
Step 1: Model the problem through tape diagram
Step 2: Calculate to solve
250g + 300g = 550g
Step 3: Write a statement.
She has 550g of fruits.
Step 4: Assess the solution for reasonableness.
Recheck your answer by subtraction: 550g - 250g = 300g
Thus, the solution of 550 grams of fruit is reasonable.
Example 2: Tom had 2 meters of ribbon. He used 75 centimeters. How much ribbon is left?
125 centimeters of ribbon is left
2 m = 200 cm
200 cm - 75 cm = 125 cm
Reasonableness/check work by addition:
125 cm + 75 cm = 200 cm
Thus, the solution of 125 cm is reasonable.
New or Recently Introduced Terms
• Convert
Express a measurement in a different unit; rename units
• Kilometer
km, a unit of measure for length
• Mass
The measure of the amount of matter in an object
• Milliliter
ml, a unit of measure for liquid volume
• Mixed units
Different units combined together
E.g., 3 m 43 cm
Familiar Terms and Symbols
• =, <, > - Equal to, less than, greater than
• Algorithm - A step-by-step procedure to solve a particular type of problem
• Capacity - The maximum amount that something can contain
• Distance -The length of the line segment joining two points
• Equivalent -Equal
• Kilogram (kg), gram (g) Units of measure for mass
• Larger or smaller unit Used in a comparison of units
• Length The measurement of something from end to end
• Liter (L) Unit of measure for liquid volume
• Measurement Dimensions, quantity, or capacity as determined by comparison with a standard
• Meter (m), centimeter (cm) Units of measure for length
• Mixed units E.g., 2 tens 4 ones, 2 kilometers 34 meters
• Simplifying strategy- A mental math or recorded method for making a problem easier to solve
• Table- Used to represent data
• Times as much as E.g., 1 hundred is 10 times as much as 1 ten
• Weight The measurement of how heavy something is
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