2.6 Geometry, Time, and Money

Unit Goals

  • Students reason with shapes and their attributes and partition shapes into equal shares, building a foundation for fractions. They relate halves, fourths, and skip-counting by 5 to tell time, and solve story problems involving the values of coins and dollars.

Section A Goals

  • Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
  • Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.

Section B Goals

  • Partition rectangles and circles into halves, thirds, and fourths and name the pieces.
  • Recognize 2 halves, 3 thirds, and 4 fourths as one whole.
  • Understand that equal pieces do not need to be the same shape.

Section C Goals

  • Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

Section D Goals

  • Find the value of a group of bills and coins.
  • Use addition and subtraction within 100 to solve one- and two-step word problems.
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Section A: Attributes of Shapes

Problem 1

Pre-unit

Practicing Standards:  1.G.A.1

  1. Draw a rectangle and label it A.
  2. Draw a triangle and label it B.

Solution

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Problem 2

Pre-unit

Practicing Standards:  1.G.A.3

  1. Split the circle into 2 equal parts.
    Circle.
  2. Split the rectangle into 4 equal parts.
    Rectangle.

Solution

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Problem 3

Pre-unit

Practicing Standards:  1.MD.B.3

Write the time each clock shows.

  1.  
    Analog clock. Hour hand, ten. Minute hand, twelve.
  2.  
    Analog clock. Hour hand, between five and six. Minute hand, six.

Solution

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Problem 4

Pre-unit

Practicing Standards:  2.NBT.B.5

Find the value of each expression.

  1. \(25 + 25 + 10 + 5\)
  2. \(83 - 42\)
  3. \(37 + 54\)
  4. \(66 - 49\)

Solution

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Problem 5

Here are some shapes.

Assorted shapes.

  1. Find a triangle and label it A. Explain why the shape is a triangle.

  2. Find a pentagon and label it B. Explain why the shape is a pentagon.

Solution

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Problem 6

  1. Diego drew this shape and said that it is a pentagon. Do you agree with Diego? Explain your reasoning.

    Rectangle partitioned into 2 equal parts.

  2. Draw a pentagon on the grid.

Solution

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Problem 7

  1. Draw a quadrilateral that has 3 sides that are 2 inches long.
  2. Draw a different quadrilateral that has 3 sides that are 2 inches long.

Solution

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Problem 8

This image represents a solid shape. Describe this shape.

Cube.

Solution

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Problem 9

Exploration

Priya says this shape is a quadrilateral.

Han says this shape is a pentagon.

Who do you agree with?
Explain your reasoning.

Four-sided shape with five points plotted.

Solution

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Problem 10

Exploration

  1. Can you draw a pentagon with 5 square corners? Use the dots if they are helpful.

  2. Elena says this hexagon has 6 square corners. Do you agree with Elena? Explain your reasoning.

Solution

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Section B: Halves, Thirds, and Fourths

Problem 1

Here is a pattern block shape Lin made.

Shape made of pattern blocks.
  1. Describe the blocks Lin used to make her shape.
  2. Build Lin’s shape using only equal-size shapes.

Solution

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Problem 2

  1. Andre drew this picture and said each part of the square is a fourth. Do you agree with Andre?  Explain.

    Diagram. Square partitioned into 4 equal parts.

  2. Partition the square into 4 equal parts in a different way.

    Square.

Solution

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Problem 3

Diego cut a square into two equal pieces and then cut one of the pieces into two equal pieces. He says the shaded part is a third of the square. Do you agree with Diego? Explain your reasoning.

Diagram. Square partitioned into 3 unequal parts, 1 part shaded.

Solution

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Problem 4

  1. Partition the circle into 4 equal parts.

  2. Shade 3 parts blue and one part red.

  3. How much of the circle is shaded?

    ________________________

Circle.

Solution

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Problem 5

Exploration

Is the square divided into fourths? Show your reasoning.

Diagram. Square partitioned into 4 parts.

Solution

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Problem 6

Exploration

Can you divide the square into equal parts?

  1. 4 equal parts with 3 of the parts different shapes

    Square.

  2. 4 equal parts with 4 of the parts different shapes

    Square.

Solution

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Section C: Time on the Clock

Problem 1

  1. Write the time shown on the clocks using the words half past, quarter past, or quarter till.
    Analog clock. Hour hand, past the three. Minute hand, at three.

    Analog clock. Hour hand, almost to the 8. Minute hand, at 9.

  2. Draw hands on the clock face to show half past 5.

Solution

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Problem 2

Analog clock. Hour hand at 8. Minute hand at 11.

Priya says that the clock shows that it's 7:11. Do you agree with Priya? Explain your reasoning.

Solution

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Problem 3


  1. Analog clock. Hour hand, almost nine. Minute hand, ten.
    The clock shows when Clare went to bed. Write the time, including a.m. or p.m. ____________________

  2. Analog clock. Hour hand, between 7 and 8. Minute hand, at 5.
    The clock shows when Noah got to school. Write the time, including a.m. or p.m. ____________________

Solution

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Problem 4

Exploration

Mai got to school at 7:35 a.m. She left school to go home 375 minutes later. What time did Mai leave to go home? Explain your reasoning.

Solution

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Problem 5

Exploration

Fill out the table with some of the things you do during the day and the time for each activity.

activity time
wake up
leave for school

Solution

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Problem 6

Exploration

This clock only has an hour hand.

What can you say about the time shown on the clock?

Solution

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Section D: The Value of Money

Problem 1

3 dimes. 2 nickels. 4 pennies.
  1. Which coins are shown in the picture?
  2. What is the value of the coins altogether?

Solution

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Problem 2

2 quarters. 3 dimes. 1 nickel. 2 pennies.

  1. Which coins are shown in the picture?

  2. What is the value of the coins altogether?

Solution

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Problem 3

Select 3 collections of coins that show a dollar.

A:
4 quarters.
B:
10 nickels.
C:
Coins. 3 quarters. 3 dimes.
D:
Coins. 3 quarters. 5 nickels.
E:
Coins. 2 quarters. 2 dimes. 3 nickels. 1 penny.
F:
Coins. 3 quarters. 2 dimes. 5 pennies.

Solution

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Problem 4

Mai has 92 cents. She gives Lin 38 cents. How many cents does Mai have now?

Solution

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Problem 5

Diego's bike cost $55.

That's $27 less than Clare’s bike cost. How many dollars did Clare’s bike cost?

Solution

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Problem 6

Exploration

Lin has 7 coins. The value of the coins altogether is 31 cents.

  1. What coins could Lin have?
  2. Can you find more than one possibility?
  3. Can you find more than two possibilities?

Solution

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Problem 7

Exploration

item cost (cents)
notebook 25
colored pencil 18
pencil box 39
glue stick 4

Jada spent exactly one dollar on school supplies. What could Jada have bought? Find 2 different solutions.

Solution

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