1 Guided Practice
• Materials: Manipulatives, brown paper bags, adhesive tape, index cards, handouts (3).
• Review: An hour is 60 minutes long, and a minute is 60 seconds. The analog clock has
numbers from 1 to 12. The short hand points to the hour and the long hand points to the minutes.
• I do: Motivation.- We already know that 1 hour has 60 minutes, but what happens if I want to
calculate how much time I have in 75 minutes? Then, for this problem I need a solution.
I am observing the clock and I can see there are twelve numbers, and each of them represents 5 minutes
(teacher models counting the numbers in fives). The whole class repeats in chorus.
• Now is time for a movie clip. Pay attention and take notes because we are going to talk about it.
Movie-clip Figuring Out Elapsed Time .-Cyberchase (2:36 duration)
In this video-clip, Matt and Digit compete against Hacker in a Cooking Contest. Digit knows that his best Cybersouffle has to be cooked quietly and exactly in 12 minutes. He calculates that the Cybersouffle will be done by 9:62. His friend Matt says to him that is not possible for there is not such a time...
Questions after the students have watched the movie-clip:
1. The clock is broken, Digit and Matt have now a problem. What they have discovered?
2. How the strip inside the clock looks like?
3. The strip is good to measure what?
4. Is Digit's addition 9:50 plus 0:12 minutes correct?
5. Explain the process Matt uses to solve the problem.
• We do I can see that the clock is a circle (teacher draws circle on chart paper) with numbers and marks,
which reminds me the number line Let’s have some fun laying out one on the floor (teacher uses the
adhesive tape to create the number line with 15 sections, students help to label every section with the index cards).
Now Let’s play jump and count (students jump on the number line while counting in fives.
OK, up to 60 minutes is 1 hour, as you can see there are 3 extra sections with 5 minutes each,
making a total of 75 minutes. However, we know that 60 minutes make an hour. Then, we have
solved the problem because we realize it is 1 hour and 15 minutes(1:15) in 75 minutes.
Students will continue solving problems using the number line in their whiteboards.
• Differentiation: Teacher models for students using manipulatives (beads, legos, or other small objects)
making groups of fives. When they reach 12 groups of fives; they put them on a paper bag labeled "1 hour."
Then, they count a few more that will be the minutes.
You can apply exactly the same operation when you convert seconds to minutes, remember that 1 minute
has 60 seconds. Then if you convert 75 seconds it will be 1 minute and 15 seconds. That was easy!
Ask the students, "which time is longer, an hour, a minute, or a second? Explain
Now, that we know how to convert seconds and minutes, we are going to measure the time with the stopwatches.
Because seconds are smaller than minutes, they can be used to solve problems, and also convert them to minutes
using the stopwatch and the number line. Let's find out how many seconds it will take to do things.
On your marks, get ready! (students have the stopwatches in their hands). Please stand...walk to the front,.. now!...Stop!
Check your stopwatches how many seconds did it take to go to the front. On your marks, move back to your seat...now!
How much time did it take to go to the front and returning to your seats? Explain
Turn and Talk: What other things can we measure with seconds?
Estimate how many seconds you it takes you to walk from the carpet to sit in your seat.
When we press the stopwatch, it stops measuring. Nvertheless, time never stops. It keeps going. Time is continuous.
2 Independent Practice
Students will work in triads to answer the tasks (leader, recorder and timekeeper).
b) Exit ticket:
1. It would take about_______ hours and _______ minutes to watch a movie at the theatre.
2. What unit of time would you use to measure a lap around the block?
3. Did you stop the time or the stopwatch? Write two lines about it.
Key Standards Supported
Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
Prove that all circles are similar.
Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
(+) Construct a tangent line from a point outside a given circle to the circle.
Counting And Cardinality
Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.1
Compare two numbers between 1 and 10 presented as written numerals.
Understand the relationship between numbers and quantities; connect counting to cardinality.
When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.
Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.
Understand that each successive number name refers to a quantity that is one larger.
Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.
Count to 100 by ones and by tens.
Count forward beginning from a given number within the known sequence (instead of having to begin at 1).
Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).
Making Inferences And Justifying Conclusions
Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.
Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
Evaluate reports based on data.
Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?
Measurement And Data
Order three objects by length; compare the lengths of two objects indirectly by using a third object.
Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.
Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.
Tell and write time in hours and half-hours using analog and digital clocks.
Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.
Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.
Estimate lengths using units of inches, feet, centimeters, and meters.
Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.
Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.
Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.
Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put- together, take-apart, and compare problems4 using information presented in a bar graph.
Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.
Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.
Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?
Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
Recognize area as an attribute of plane figures and understand concepts of area measurement.
A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.
A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.
Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
Relate area to the operations of multiplication and addition.
Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
Multiply side lengths to find areas of rectangles with whole- number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.
Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.
Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.
Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.
Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).6 Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.7
Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.
An angle that turns through n one-degree angles is said to have an angle measure of n degrees.
Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.
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), ...
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.
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.
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.
Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.
A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.
Apply the formulas V=l×w×handV=b×h for rectangular prisms to find volumes of right rectangular prisms with whole- number edge lengths in the context of solving real world and mathematical problems.
Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.
Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.3
Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.
Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.