Unit 9 Geometry: Solid Shapes
Introduction
In this unit, students will learn to distinguish three-dimensional (or solid) shapes from twodimensional (or flat) shapes. They will learn to identify and name spheres, cubes, cylinders, and
cones—regardless of size, color, and orientation. Students will also attend to features of these
three-dimensional shapes, such as curved and flat faces, as well as corners. They will identify
the flat faces of these three-dimensional shapes as two-dimensional geometric shapes.
Students will learn to describe the relative position of shapes using the terms “in front of,”
“behind,” and “next to.” They will compose basic three-dimensional shapes to make larger
shapes, designs, and simple models.
Materials. The following materials are used throughout the unit.
 Three-dimensional shapes. For this unit, it would be ideal to have wood or foam threedimensional shapes that are perfect spheres, cubes, cylinders, and cones. If you have such
shapes in several sizes and colors, that’s even better. These will be useful in demonstrations
and activities. If you do not have a set of solid shapes, you can use alternatives. For instance,
any perfectly round balls, such as marbles or tennis balls, will work for spheres. Moreover, you
can make your own cubes, cylinders, and cones out of paper and tape using the nets provided
in the BLMs (see BLM Net for a Cube, BLM Net for a Cylinder, and BLM Nets for Cones). To
make a three-dimensional shape from a net, cut out the net, fold the edges and flaps, and then
join the appropriate edges using tape.
The nets from BLM Nets for Cones form cones without a circular “lid.” To add a lid, place the
cone on a blank sheet of paper with the open face down, trace around the bottom of the cone,
cut out the resulting paper circle, and tape it onto the open face of the cone. NOTE: You can
make the cones from this BLM wider or narrower depending on how far you overlap the edges.
 Three-dimensional objects. In addition to perfect three-dimensional shapes, collect in
advance real-world objects that are as close as possible to being perfect spheres, cubes,
cylinders, and cones. For some activities, you will need to collect small objects that are easy
for students to handle. The following are examples of objects that work well for demonstrations
and activities:
Spheres: spherical balls, such as a foam ball, tennis ball, basketball, soccer ball, baseball, golf
ball, or table tennis ball; fruits that are perfect spheres, such as an orange, plum, grape, or
cherry; a toy globe
Cubes: connecting cubes; base ten cubes (ones cube and thousands cube); dice; cubic tissue
boxes; sugar cubes; letter block cubes
Cylinders: cans containing tennis balls, soup, vegetables, or paint; rolls of toilet paper, paper
towels, or wrapping paper (with or without the paper); toy drums; a broom handle; markers with
their lids on; unsharpened pencils; hockey pucks; drinking straws
Cones: certain paper cups; certain ice-cream cones; funnels; traffic cones; certain party hats
Teacher’s Guide for Kindergarten — Unit 9 Geometry
L-1
When showing students examples of real-world objects that are nearly, but not quite, perfect
shapes, you might point out what makes the shape a little bit different from the perfect shape.
For example, for cubes, some dice have rounded corners, some connecting cubes have little
holes in their sides and a linking part that sticks out, cubic beads have a hole in the center, and
ones blocks have one face missing and a linking part that sticks up on the opposite side.
 Bins with labels for sorting. In this unit, students will sort shapes, usually into two different
bins. For example, students will sort shapes that are spheres into one bin and shapes that are
not spheres into another bin. You will need to label the bins in a way that students can
understand. For example, you could tape the picture of a sphere to label a bin for spheres.
Put the picture on each of the four faces of the bin so that students can easily see the label from
any angle.
 Paper shapes. When using paper shapes from BLMs (such as pictures of solid shapes) for
demonstration or display purposes, you might enlarge the shapes so that students can see
them. You can print enlargements of the shapes directly from the BLMs or use the BLMs as a
guide to make your own enlargements. On the other hand, if you wish to use the shapes in the
smaller, actual sizes from the BLMs, you can hold up the shapes and walk around to ensure
that they are visible to all students.
 A chart of shapes for display. Make a chart with four columns that you can display on a
classroom wall throughout the unit. After each lesson about one of the four solid shapes (in
other words, spheres, cubes, cylinders, and cones), fill in a column for that shape as a class.
Use the name and a picture of the shape for the title. In the body of the column, include several
examples of pictures of the shape and pictures of objects with that shape; you can use BLM
Solid Shapes and BLM Solid Objects for these. Show various sizes, colors (using colored
paper or markers), and orientations. Guide students to refer to the chart throughout the unit. The
completed chart might look similar to this example:
Spheres
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Cubes
Cylinders
Cones
Teacher’s Guide for Kindergarten — Unit 9 Geometry In addition to the BLMs provided at the end of this unit, the following Generic BLMs, found in
section R, are used in Unit 9:
BLM Hundreds Chart (p. R-1)
BLM Circles of Different Sizes (p. R-27)
BLM Squares of Different Sizes (p. R-28)
BLM Rectangles of Different Sizes (p. R-29)
BLM Triangles of Different Sizes and Types (p. R-30)
Literature connections. Use picture books and other age-appropriate children’s books that
expose students to shapes. Consider, for example, Cubes, Cones, Cylinders, & Spheres by
Tana Hoban. Reading these books to the whole class and allowing students to look at the books
individually during free time will be valuable.
Recurring activities. The following activity recurs several times in the unit, with variations.
Sorting Examples of a Specified 3-D Shape from Non-examples
Type: Small groups
Objective: To identify examples of a specified 3-D shape (regardless of size or color) and to
distinguish these examples from non-examples
Preparation: In advance, put a collection of 12 to 16 small objects in a box. About half of the
objects should be small spheres (e.g., foam ball, tennis ball, toy globe) and the other half should
be small non-spheres (e.g., die, sponge cube, toy football). Provide each group with one bin
labeled with a picture of a sphere and another bin with no label.
Instructions: Students take turns choosing a shape from the box and saying if the shape is a
sphere. If it is, they put the sphere in the labeled bin; if it is not, they put the shape in the other bin.
Bonus: Students count and say how many spheres there are in the labeled bin, then count and
say how many other objects there are in the unlabeled bin.
Teacher’s Guide for Kindergarten — Unit 9 Geometry
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GK-15
Counting to 90
Page 69
Standards: K.CC.A.1, K.CC.A.2, K.CC.A.3
Goals:
Students count fluently to 90.
Prior Knowledge Required:
Can count to 80
Vocabulary: count, number
Materials:
number cards for 81 to 90
modeling clay (see Activity Center 1)
paint, paintbrushes, and large sheets of paper (see Activity Center 2)
sand table or sandpaper cut into the shape of the number 8 (see Activity Center 3)
counters, at least 90 per student (see Extension 1)
BLM Hundreds Chart (p. R-1, see Extension 1)
Counting practice. Practice counting to 80 as a class (see Introduction, p. A-9). Play “Let’s
Compare” using numbers between 1 and 10.
(MP.7) Learning numbers to 90. ASK: What comes after 30 when we count? PROMPT: We
say 27, 28, 29, 30 …? (31) ASK: What comes after 40? (41) Repeat for 50 (51), 60 (61), and 70
(71). ASK: What do you think comes after 80? (81) What comes after 81? (82) Continue
prompting to 89. ASK: What do you think comes after 89? (90) Clearly say “90.” Practice
counting from 80 to 90 as a class. Add movement to the counting, such as jumping as each
number is spoken.
Counting one at a time. Start at 80. Work through the class and have each student say the
next number until you reach 90. Repeat until everyone has had a turn.
Adding 81 to 90 to the number chart. Make enough number cards for 81 to 90 available so
that each student has one card and you have a set of cards. Distribute a number card to each
student. ASK: Whose number has an 8 and a 1? Direct students who have that number (81) to
hold up their card, and have a volunteer place one of these cards on the number chart. Make
sure the number is oriented correctly. Continue until all of the numbers have been added to the
chart. Have the class say the count sequence from 81 to 90 as you point to each number on the
chart, so that students begin to associate the spoken and written numbers.
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Teacher’s Guide for Kindergarten — Unit 9 Geometry Counting 1 to 90. As a class, count from 1 to 90. You may wish to have one or more students
lead the count, allowing each student to count at least 10 numbers. You may also wish to point
to the numbers on the number chart as everyone counts.
Activity
Play I Start, You Finish (see introduction to Unit 1, p. C-1) for the numbers from 80 to 90 as a
class, then in pairs.
(end of activity)
Preparing for the AP pages. Most students may be able to practice writing 8s directly on
AP Book K.2, Unit 9, p. 69, but students who are still struggling with writing may benefit from
other types of practice first, such as the practice provided in one or more of the following
activity centers.
Activity Centers
For guidance on selecting and using the activity centers, see Introduction p. A-13.
1. Clay Numbers
Type: Individual, creative
Objective: To practice making the number 8 using clay
Preparation: Provide modeling clay.
Instructions: Have students make the number 8 in clay.
2. Painting Numbers
Type: Individual, creative
Objective: To practice painting the number 8
Preparation: Provide paint, a paintbrush, and paper to each student.
Instructions: Have students paint the number 8 on paper.
3. Numbers in Sand
Type: Individual
Objective: To practice forming or tracing the number 8
Preparation: Provide a sand table or a sandpaper number 8 to each student.
Instructions: Have students write the number 8 in a sand table or gently trace it with their finger
on sandpaper.
Extensions
1. Distribute at least 90 counters and BLM Hundreds Chart to each student. Have students
place one counter per square, counting as they go, until they reach 90.
2. Have students play I Start, You Finish (see introduction to Unit 1, p. C-1) in pairs, starting
from a number less than 80 and continuing until 90.
Teacher’s Guide for Kindergarten — Unit 9 Geometry
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(MP.6) 3. Counting correctly or incorrectly? Say the count sequence from 80 to 90, but make
a mistake; for example, skip a number or repeat a number. Students should raise their hand or
say “stop” when you make a mistake. Ask them to explain your mistake.
Bonus: Say the entire sequence, sometimes correctly and sometimes making a mistake. When
you reach 90, have students say if you counted correctly or not. NOTE: This extension can be
done in pairs.
4. Put the number cards for 81 to 90 on the board in order but with one adjacent pair reversed.
Ask a volunteer to come to the board and correct the mistake. This is a great exercise for
generating excitement among the class and raising the bar. You can increase the challenge by
making two mistakes or rearranging three cards.
5. Teach students how to count backward from 5 to 1. Begin by writing a row of numbers from 1
to 5 on the board and pointing to them one by one in reverse order, from 5 to 1, as students
count together. Then, keep the numbers on the board, but do not point to the numbers as
students count backward. Finally, erase the row of numbers and have students count backward.
Repeat the process for counting backward from 10 to 1.
(MP.1) 6. Remove the number cards from the hundreds chart for the numbers 11 to 20 and 81
to 90. Place them on the board in two rows, as shown below:
11 12 13 14 15 16 17 18 19 20
81 82 83 84 85 86 87 88 89 90
Remove the 14 card and the 84 card. Hold up one of the two cards, and ASK: Where does this
card belong? Does it belong here (point to the spot for 14)? Does it belong here (point to the
spot for 84)? Students signal thumbs up for yes or thumbs down for no. You might point out that
both number cards end with a 4, and so, students need to look at the other number on the
number card (the 1 or the 8). Point out that all of the number cards in the top line start with a 1,
while all of the number cards in the bottom line start with an 8. After placing the 14 and the 84
back in the correct positions, repeat the exercise with another pair of number cards directly on
top of each other. After repeating several times, increase the challenge by using number cards
that are not vertically aligned (for example, 83 and 17) so that both digits are different. (If all
students are signaling the correct answers, you might wish to try the pair 81 and 18; this could
be very challenging for students, since these numbers involve the same digits.) Then, remove
the number cards from 11 to 20, replace them with the number cards from 21 to 30, and repeat
the exercise.
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Teacher’s Guide for Kindergarten — Unit 9 Geometry GK-16
Spheres and Cubes
Pages 70–74
Standards: K.G.A.1, K.G.A.2, K.G.A.3, K.CC.B.5
Goals:
Students describe real-world spherical and cubic objects, using the words “sphere” and “cube.”
Students name spheres and cubes regardless of color, size, or, in the case of cubes, orientation.
Students distinguish solid shapes (such as spheres and cubes) from flat shapes (such as circles
and squares).
Prior Knowledge Required:
Can identify flat shapes, especially circles and squares
Can count up to 10 objects in various arrangements
Vocabulary: circle, cube, flat, shape, solid, sphere, square
Materials:
tennis ball, basketball, and other objects that are spheres
football and other objects that are not spheres
paper circle the same diameter as the tennis ball
BLM Circles of Different Sizes (p. R-27)
BLM Squares of Different Sizes (p. R-28)
BLM Rectangles of Different Sizes (p. R-29)
BLM Triangles of Different Sizes and Types (p. R-30)
connecting cube and other objects that are cubes
BLM Net for a Cube (p. L-36)
rectangular prism, such as a long, skinny box
paper square the same size as the face of a connecting cube
pictures of spheres and cubes
BLM Solid Shapes (pp. L-37–40)
BLM Solid Objects (pp. L-41–44)
collection of small spheres, cubes, cylinders, and cones
opaque bag per student pair
box and 2 bins (see Activity Centers 2, 3)
modeling clay (see Activity Center 5)
paper and glue (see Extension 2)
Counting practice. Practice counting to 90 as a class by playing I Start, You Finish (see
introduction to Unit 1, p. C-1) for the numbers from 80 to 90, and then from 60 to 90. Play “Let’s
Compare” using numbers between 1 and 10.
(MP.2) Introduce spheres. Hold up a tennis ball and ASK: What is this? (a tennis ball)
SAY: This is a tennis ball. Repeat with other spherical balls (e.g., basketball, soccer ball,
Teacher’s Guide for Kindergarten — Unit 9 Geometry
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baseball, golf ball, table tennis ball). SAY: All of these balls have a perfectly round shape.
Hold up a football. ASK: What is this? (a football) SAY: This is a football. ASK: Does a football
have a perfectly round shape, just like the tennis ball? (no) SAY: A football is a kind of ball, but it
does not have a perfectly round shape. Repeat with fruits or vegetables that are spheres (i.e.,
have a perfectly round shape like a tennis ball), and fruits or vegetables that are not spheres
(i.e., do not have a perfectly round shape like a tennis ball).
SAY: A perfectly round shape like a tennis ball is called a sphere. Have students say the word
“sphere” several times. Show more examples of spheres (such as a wood or foam sphere or a
globe), examples of objects that are obviously not spheres (such as cubes), and examples of
objects that are closer to being spheres (such as a football, an egg, or other egg-shaped
objects). Each time you hold up an object, ASK: Is this a sphere? Students signal thumbs up for
yes or thumbs down for no. You can prompt students by asking whether the object is perfectly
round like a tennis ball. For the objects that are closer to spheres, ask students to explain how
they look different from spheres. For example, for a football, students might say the football is a
little pointy at the ends. Eventually have students call out the answers (sphere or not a sphere)
rather than signaling with their thumbs, so they get used to using the word “sphere.”
Spheres can be different sizes and colors. SAY: Spheres can be large or small. Spheres can
be different colors. They can be green like a tennis ball or orange like a basketball. Point out the
different sizes and colors of spheres already shown. Hold up a tennis ball in one hand and, one
by one, hold the other spheres in your other hand. Each time, ASK: Is this sphere larger than
the tennis ball, smaller than the tennis ball, or about the same size? What color(s) is the
sphere? (answers will vary)
Flat and solid shapes. In one hand, hold up a paper circle about the same size as the tennis
ball and ASK: What is this shape called? (a circle) Hold up the tennis ball in the other hand.
ASK: How are the tennis ball and the circle the same? (they are both round) How are they
different? (the tennis ball sticks out, the circle doesn’t) Are they the same shape? (no)
Place the tennis ball on a table in such a way that it stays put and does not roll. For example,
put it on an upside-down bottle lid. Place the paper circle flat on the table near the tennis ball.
Have all students come to the table in groups of five and crouch so that they can just barely see
over the table. ASK: Can you see the tennis ball? (yes) Can you see the circle? (no) SAY: The
circle is flat. When you place a flat shape on a table, it doesn’t stick up. The tennis ball is solid.
When you place a solid shape on a table, it sticks up. Hold up some other examples of solid
shapes (such as spheres, cubes, and other objects around the classroom) and flat shapes
(such as paper circles, squares, rectangles, and triangles from BLM Circles of Different Sizes,
BLM Squares of Different Sizes, BLM Rectangles of Different Sizes, and BLM Triangles of
Different Sizes and Types). Each time, ASK: Is this shape solid or flat?
(MP.2) Introduce cubes. Hold up a connecting cube and ASK: What is this? (a connecting
cube) SAY: A shape like a connecting cube is called a cube. Cubes can be large or small.
Cubes can be different colors. But, all cubes have the same shape. One at a time, hold up some
other cubes, such as a die, a tissue box, or a sugar cube, and ASK: What is this shape? (a
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Teacher’s Guide for Kindergarten — Unit 9 Geometry cube) Is this cube larger or smaller than the connecting cube? (answers will vary) What color is
the cube? (answers will vary)
Cubes are cubes no matter how you turn them. In advance, make a cube using the net cut
from BLM Net for a Cube. Write the numerals 1 to 6 on the faces of the net before assembling
it. Show the cube to the class and then turn the cube so that students see each of the different
numbers on it. ASK: Which number do you see on the cube now? Keep turning until students
have seen each face of the cube. Then, hold the cube so that only one corner points down to
the ground. ASK: Is this still a cube, even when I hold it like this? (yes) Hold the cube in several
different orientations and repeat. SAY: It doesn’t matter which way you turn a cube, it’s still a
cube. Repeat with a different cube, such as a letter block cube.
Distinguishing cubes from other 3-D shapes. Hold up a tennis ball and ASK: Is this tennis
ball a cube? (no) What shape is this tennis ball? (a sphere) Hold up different objects, some that
are cubes and some that are not cubes, such as spheres and other objects in the classroom.
Each time, ASK: Is this a cube? You can prompt students by asking whether the object looks
like the connecting cube. Hold the cubes in various orientations.
(MP.3) Hold up a rectangular prism that is not a cube, such as a long, skinny cardboard box.
ASK: Does this shape look just like a cube? (no) Holding a cube in one hand and the long
skinny box in the other, ASK: How is this shape different from a cube? (it’s stretched, it’s long
and skinny)
Cubes and squares. Hold up a paper square that is about the same size as the faces of a
connecting cube. ASK: What is this shape called? (a square) Place the cube and the paper
square flat on a table. ASK: Does the cube stick up when we place it on the table? (yes) Is the
cube solid or flat? (solid) Does the square stick up when we place it on the table? (no) Is the
square solid or flat? (flat)
Pictures of spheres and cubes. Show students several pictures of spheres and cubes, such
as may be found in children’s books (see unit introduction for a recommendation). Students
should be able to recognize actual spheres and cubes (solid, three-dimensional objects) as well
as pictures or photos of spheres and cubes (solid objects represented on a flat surface). Be
sure to include all of the cubes from BLM Solid Shapes (2), which shows cubes in different
orientations.
(MP.3) Distinguishing pictures of spheres from other shapes and objects. One at a time,
post pictures of spheres and other shapes on the board. Use pictures from BLM Solid Shapes
and BLM Solid Objects. Each time, ASK: Is this a sphere? Students signal thumbs up for yes
or thumbs down for no.
(MP.3) Distinguishing pictures of cubes from other shapes and objects. Repeat the above
exercise for cubes. Include all of the cubes from BLM Solid Shapes (2), which shows cubes in
different orientations.
Teacher’s Guide for Kindergarten — Unit 9 Geometry
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Counting spheres. On the board, post pictures of spheres from BLM Solid Shapes (1) and
BLM Solid Objects (2). Write the numerals 1 to 10 below the spheres, as shown below:
1
2
3
4
5
6
7
8
9
10
SAY: Let’s count the spheres together. Set the pace by pointing to the spheres one at a time as
students count together. ASK: How many spheres are there? (5) SAY: Let’s decide what
number we write for 5. As I point to each number, signal thumbs up if it is 5. Signal thumbs
down if it is not 5. After the class identifies the correct numeral, circle the “5,” and SAY: There
are five spheres. Repeat for various examples of 1 to 10 spheres in different arrangements (you
can make duplicates of the spheres from the BLMs for larger numbers).
Include examples of shapes that are not spheres (for example, four spheres and three cubes).
Point to each shape and have students signal thumbs up for a sphere or thumbs down for not a
sphere. Remove the shapes that are not spheres. As a class, count the spheres, as before.
Counting cubes. Repeat the above exercise for cubes.
NOTE: In advance, collect small spheres, cubes, cylinders, and cones for students to explore
during the activities and activity centers.
Activities 1–2
1. Comparing spheres and cubes by touch. Have students hold spheres and cubes in their
hands and discuss how these solids feel different from each other. Students might say that the
cubes have many pointy edges and corners that feel sharp, while the spheres feel very smooth.
2. Identifying spheres and cubes by touch. Provide each pair of students with an opaque bag
that contains two spheres and two cubes. Partner 1 holds the bag while Partner 2 reaches into
the bag and feels the shapes with her eyes closed. When Partner 2 thinks she knows which
shape she is holding, she pulls out the shape and says “sphere” or “cube.” She then opens her
eyes to see if she is correct. Partner 2 continues until she has identified all of the shapes in the
bag. Then, players switch roles and play again. For an extra challenge, increase the number of
spheres and cubes in the bag.
(end of activities)
Preparing for the AP pages. For Questions 1–3 on AP Book K.2, Unit 9, pp. 70–71, make
sure students understand that they are supposed to count or color all the spheres in each
question, including colored spheres and objects shaped like spheres, such as a basketball.
Similarly, for Questions 4–8 on pp. 72–74, students must count or color all cubes and objects
shaped like cubes, such as a letter block cube.
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Teacher’s Guide for Kindergarten — Unit 9 Geometry Activity Centers
(MP.2) 1. Finding Spheres and Cubes in the Classroom
Type: Pairs, active
Objective: To find spheres and cubes in the classroom
Preparation: Place objects around the classroom that are spheres and cubes.
Instructions: Tell students to walk around and find spheres and cubes. Students then tell their
partners about what they found.
(MP.6) 2. Sorting Examples of a Specified 3-D Shape from Non-Examples (see unit
introduction, p. L-3)
(MP.6) 3. Sorting Examples of a Specified 3-D Shape from Non-Examples (see unit
introduction, p. L-3)
Variation: Instead of spheres, students sort cubes and non-cubes. Examples of cubes include
connecting cubes, dice, base ten cubes, and blocks that are cubes. Examples of non-cubes
include rectangular prisms such as wood blocks, gift boxes, and juice boxes.
Bonus: Students count and say how many cubes there are in the labeled bin, then count and
say how many other objects there are in the unlabeled bin.
(MP.6) 4. Counting Spheres and Cubes while Jumping
Type: Pairs, active
Objective: To identify and count out spheres or cubes while jumping
Preparation: In advance, place a collection of about 18 small objects in a box. The collections
should be composed of 6 spheres (e.g., tennis ball, table tennis ball, toy globe), 6 cubes (e.g.,
connecting cube, die, base ten cube, blocks that are cubes), and 6 objects that are neither
spheres nor cubes.
Instructions: Partner 1 chooses either a sphere or a cube. Partner 2 takes out three or more of
that kind of shape from the box. Partner 1 counts the objects and jumps that many times.
Partners switch roles and repeat.
5. Making a Sphere from Modeling Clay
Type: Individual
Objective: To make a sphere using modeling clay
Preparation: Provide each student with a piece of modeling clay.
Instructions: Have students make a sphere using modeling clay by, first, rolling a piece of clay
between their hands, then placing the lump on a table, holding one hand flat on top of the lump,
and carefully rolling the lump around with a circular motion of the hand. Demonstrate first.
Extensions
(MP.1) 1. After students have crossed out the non-spheres for Question 3 on AP Book K.2,
Unit 9, p. 71, have them count the spheres (the shapes that are not crossed out). You might ask
students to mark each sphere as they count it, and then write the total count somewhere inside
the bubble. Repeat for cubes in Question 8 on p. 74.
Teacher’s Guide for Kindergarten — Unit 9 Geometry
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2. Provide students with a blank sheet of paper, glue, and a pile of pictures of spheres and
cubes from BLM Solid Objects. Tell them to choose one sphere and one cube from the pile,
glue them onto their page, and then draw a picture that incorporates the shapes.
(MP.1) 3. Affix to the board a variety of up to 10 pictures of spheres and several non-spheres
using BLM Solid Shapes and BLM Solid Objects. Write the numerals from 0 to 10 below the
picture. Pointing to each shape, have students signal thumbs up for a sphere or thumbs down
for not a sphere. Remove each non-sphere from the board as it is identified, and then count the
number of spheres as a class before circling the correct numeral. Use examples where there
are no spheres (the numeral 0 must be circled). To help students review the idea of having zero
spheres, start with an example of three spheres for students to count. Remove one sphere at a
time until there are no spheres, and each time have students say how many spheres there are.
When there are no spheres, ASK: Which number means there are no spheres on the board? (0)
(MP.1) 4. Repeat Extension 3 for cubes instead of spheres. You can also use BLM Solid
Shapes (2) for cubes shown in different orientations.
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Teacher’s Guide for Kindergarten — Unit 9 Geometry GK-17
Cylinders and Cones
Pages 75–78
Standards: K.G.A.1, K.G.A.2, K.G.A.3, K.CC.B.5
Goals:
Students describe real-world cylindrical and conical objects using the words “cylinder” and “cone.”
Students name cylinders and cones regardless of their color, size, or orientation.
Students distinguish solid shapes (such as cylinders and cones) from flat shapes (such circles,
squares, rectangles, and triangles).
Prior Knowledge Required:
Can identify flat shapes, such as circles, squares, triangles, and rectangles
Can count up to 10 objects in various arrangements
Can identify spheres and cubes
Vocabulary: circle, cone, cube, cylinder, flat, rectangle, shape, solid, sphere, square, triangle
Materials:
several objects that are spheres and cubes
cylinder block or BLM Net for a Cylinder (p. L-45)
can of soup and other objects that are cylinders
non-cylindrical can
paper circles the same sizes as the bases of a cylinder and a cone
cone block or BLM Nets for Cones (p. L-46) and other objects that are cones
BLM Solid Objects (pp. L-41–44)
BLM Triangles of Different Sizes and Types (p. R-30)
BLM Circles of Different Sizes (p. R-27)
BLM Squares of Different Sizes (p. R-28)
BLM Rectangles of Different Sizes (p. R-29)
pictures of cylinders and cones and BLM Solid Shapes (pp. L-37–40)
collection of small spheres, cubes, cylinders, and cones
opaque bag per student pair
box and 2 bins (see Activity Centers 2, 3)
modeling clay and plastic knives (see Activity Center 5)
paper and glue (see Extension 2)
Counting practice. Practice counting to 90 as a class, having students jump as they count.
Play “Let’s Compare,” using numbers between 1 and 10.
Review spheres and cubes. Hold up a sphere and ASK: What is this shape called? (a sphere)
Repeat with a cube, then with a few more spheres and cubes.
Teacher’s Guide for Kindergarten — Unit 9 Geometry
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(MP.2) Introduce cylinders. Hold up a perfect cylinder. If you don’t have a cylinder block, you
can make a paper cylinder using BLM Net for a Cylinder. SAY: This is called a cylinder. Hold
up a can of soup and ASK: What is this? (a can of soup) SAY: The shape of this can is also
called a cylinder. Repeat with more cans, including short and wide cans such as a can of tuna.
Emphasize that the shape of each can is called a cylinder, even though some are larger and
some are smaller, and even though they are different colors. Repeat with cylinders that are not
cans, such as a toy drum, a roll of toilet paper, paper towel, or wrapping paper (with or without
the paper), the handle of a broom, a marker with its lid on, a hockey puck, or a drinking straw.
For now, hold the cylinders vertically like the can. Each time, ASK: Is it the same shape as a
can? (yes) Explain that anything that has this shape is called a cylinder. Have students say the
word “cylinder” several times together as a class.
Cylinders are cylinders, no matter how you turn them. Hold up the can of soup vertically
and ASK: What is the name of this shape? (a cylinder) Hold the can sideways and ASK: Is it still
a cylinder, even if I turn it? (yes) Turn the can so that one of its circular bases faces the
students, and repeat the question. Hold the can in several orientations, and repeat the question.
SAY: It doesn’t matter which way you turn a cylinder, it’s still a cylinder. Repeat the process with
another cylinder that isn’t a can.
(MP.3) Distinguishing cylinders from other shapes. Hold up objects one at a time, some that
are cylinders and some that are not cylinders, such as spheres, cubes, or other objects in the
classroom that are clearly not cylinders (avoid cones for now). Each time you hold up an object,
ASK: Is this a cylinder? Students signal thumbs up for yes or thumbs down for no. You can
prompt students by asking whether the object looks like a can. Eventually, have students call
out the answer (“cylinder” or “not a cylinder”) so that they can practice using the word “cylinder.”
Hold the cylinders in different orientations.
You might also wish to show students an example of a non-cylindrical can, for example, a can of
sardines. Tell them that it, too, might be called a can, but it is not round and it is not a cylinder.
Cylinders and circles. Hold up a paper circle that is the same size as the base of the can of
soup. ASK: What shape is this? (a circle) Hold up the can vertically, and SAY: The top and
bottom of this can are circles. Turn the can so that the top faces the students, and show how the
paper circle exactly matches the top of the can. Repeat with the bottom of the can.
(MP.2) Introduce cones. Hold up a perfect cone. If you don’t have a cone block, you can
make paper cones using BLM Nets for Cones (add lids as described in the unit introduction).
SAY: This is called a cone. Turn the cone slowly, so that students see all parts of the cone.
SAY: Some ice-cream cones have the shape of a cone. That is why we call it an ice-cream
cone. Hold up an ice-cream cone that is a perfect cone or a picture of one. (You can show the
ice-cream cone from BLM Solid Objects (4).) Hold a cone block or the paper cone the same
way as the ice cream cone, with the corner pointing down to the ground. ASK: Do these two
things have the same shape? (yes) SAY: They are both cones. Hold up more objects that are
perfect or almost perfect cones, such as a paper cup, funnel, traffic cone, or party hat.
Emphasize that they all have the same shape as the ice-cream cone and that they are all
L-14
Teacher’s Guide for Kindergarten — Unit 9 Geometry called cones, even though some are larger and some are smaller, and even though they are
different colors.
Review triangles. Show several paper triangles (use triangles with two equal sides from BLM
Triangles of Different Sizes and Types) and remind students that they are all triangles, even
though some are thin and tall and others are short and wide. Explain that cones are the same
way. Some are short and wide and some are thin and tall. All cones look a bit like a triangle
from the side and they all have a circle at the bottom. You might use a paper circle the same
size as the base of one of the cones to show this.
Hold the paper triangles at different angles and, for each one, ASK: Is the shape a triangle?
(yes) SAY: It does not matter which way I turn a triangle. It is still a triangle.
Cones are cones no matter how you turn them. Hold up a cone with the corner pointing
down to the floor, and ASK: What is the name of this shape? (a cone) Hold the cone sideways
and ASK: Is it still a cone even if I turn it like this? (yes) Turn the cone so that the circular base
faces the students, and repeat the question. Hold the cone in several different orientations, and
repeat the question. SAY: It does not matter which way I turn a cone. It is still a cone. Repeat
with another cone.
(MP.3) Distinguishing cones from other shapes. Collect some objects that are cones and
some others that are not cones, such as spheres, cubes, cylinders, or objects in the classroom
that clearly are not cones. Hold up the objects one at a time. Each time you hold up an object,
ASK: Is this a cone? Students signal thumbs up for yes or thumbs down for no. You can prompt
students by asking whether the object looks like an ice-cream cone. Eventually, have students
call out the answer (“cone” or “not a cone”), so that they can practice using the word “cone.”
Hold the cones in different orientations.
Cones and circles. Hold up a paper circle that is the same size as the base of one of the paper
cones (or another cone you used). ASK: What shape is this? (a circle) Hold up the cone and
turn it so that the circular base faces the students. Show how the paper circle exactly matches
the base of the cone.
Review flat and solid shapes. Place a cylinder and a cone on a table with the circular faces
down so that the shapes do not roll. Place a paper circle, a square, a rectangle, and a triangle
flat on the table, near the cone and cylinder. Have all students come to the table in groups of
five and crouch down so that they can just barely see over the table. ASK: Can you see the
cylinder? (yes) Can you see the cone? (yes) Can you see the circle? (no) Repeat with the other
flat shapes. SAY: The circle, square, rectangle, and triangle are flat. When you put a flat shape
on a table, it doesn’t stick up. The cylinder and cone are solid. When you place a solid shape on
a table, it sticks up. Hold up some other examples of solid shapes (such as spheres, cubes, and
other objects around the classroom) and flat shapes (such as paper circles, squares,
rectangles, and triangles from BLM Circles of Different Sizes, BLM Squares of Different
Sizes, BLM Rectangles of Different Sizes, and BLM Triangles of Different Sizes and Types).
Each time, ASK: Is this shape solid or flat?
Teacher’s Guide for Kindergarten — Unit 9 Geometry
L-15
Pictures of cylinders and cones. Show students several pictures of cylinders and cones, such
as may be found in children’s books (see unit introduction for a recommendation). Students
should be able to recognize actual cylinders and cones (solid, three-dimensional objects) as
well as pictures of cylinders and cones (solid objects represented on a flat surface). Be sure to
include all the cones and cylinders from BLM Solid Shapes (3) and (4), which show cones and
cylinders with different proportions and orientations.
(MP.3) Distinguishing pictures of cylinders from other shapes and objects. One at a time,
post pictures of cylinders and other shapes on the board. Use pictures from BLM Solid Shapes
and BLM Solid Objects. Include all the cylinders from BLM Solid Shapes (3), which shows
cylinders in different proportions and orientations. Each time, ASK: Is this a cylinder? Students
signal thumbs up for yes or thumbs down for no.
(MP.3) Distinguishing pictures of cones from other shapes and objects. Repeat the above
exercise for cones. Include all the cones from BLM Solid Shapes (4).
Counting cylinders. On the board, post pictures of several cylinders from BLM Solid Shapes
and BLM Solid Objects. Write the numerals 1 to 10 below the cylinders, as shown below:
1
2
3
4
5
6
7
8
9
10
SAY: Let’s count the cylinders together. Set the pace by pointing to the cylinders one at a time
as students count together. ASK: How many cylinders are there? (6) SAY: Let’s decide what
number we write for 6. As I point to each number, signal thumbs up if it is 6. Signal thumbs
down if it is not 6. After the class identifies the correct numeral, circle the “6,” and SAY: There
are six cylinders. Repeat for various examples of one to 10 cylinders, in different arrangements.
Then, include examples of shapes that are not cylinders (for example, four cylinders, two
spheres, and one cube). Point to each shape and have students signal thumbs up for a cylinder
or thumbs down for not a cylinder. Remove the shapes that are not cylinders. As a class, count
the cylinders, as before.
Counting cones. Repeat the above exercise for cones.
NOTE: In advance, collect small cylinders, cones, spheres, and cubes for students to explore
during the activities and activity centers.
Activities 1–2
1. Comparing cylinders and cones by touch. Have students hold cones and cylinders in their
hands, and discuss how the cones and cylinders feel different from each other. Students might
say that the cones have a pointy corner, while the cylinders do not.
L-16
Teacher’s Guide for Kindergarten — Unit 9 Geometry 2. Identifying cylinders and cones by touch. Provide each pair of students with an opaque
bag that contains two cones and two cylinders. Partner 1 holds the bag while Partner 2 reaches
into the bag and feels the shapes with his eyes closed. When Partner 2 thinks he knows which
shape he is holding, he pulls out the shape and says “cylinder” or “cone.” He then opens his
eyes to see if he was correct. Partner 2 continues until he has identified all of the shapes in the
bag. Then, players switch roles and play again. For an extra challenge, increase the number of
cylinders and cones in the bag.
(end of activities)
Preparing for the AP pages. For Questions 1–3 on AP Book K.2, Unit 9, pp. 75–76, make
sure students understand that they are supposed to count or color all the cylinders in each
question, including colored cylinders and objects shaped like cylinders, such as a can of soup.
Similarly, for Questions 4–6 on pp. 77–78, students must count or color all cones and objects
shaped like cones, such as an ice-cream cone.
Activity Centers
(MP.2) 1. Finding Cylinders and Cones in the Classroom
Type: Pairs, active
Objective: To find cylinders and cones in the classroom
Preparation: Place objects around the classroom that are cylinders and cones.
Instructions: Tell students to walk around and find cylinders and cones. Students then tell their
partners about what they found.
(MP.6) 2. Sorting Examples of a Specified 3-D Shape from Non-Examples (see unit
introduction, p. L-3)
Variation: Instead of spheres, students sort cylinders and non-cylinders. Examples of cylinders
include rolls of toilet paper, paper towel, or wrapping paper (with or without the paper), markers
with their lids on, hockey pucks, and unsharpened pencils. Examples of non-cylinders include
balls, cubes, and cones of various kinds. Provide a bin with a picture of a cylinder and an
unlabeled bin.
Bonus: Students count and say how many cylinders there are in the labeled bin, then how count
and say how many other objects there are in the unlabeled bin.
(MP.6) 3. Sorting Examples of a Specified 3-D Shape from Non-Examples (see unit
introduction, p. L-3)
Variation: Instead of spheres, students sort cones and non-cones. Examples of cones include
certain paper cups, ice-cream cones, funnels, and party hats. Examples of non-cones include
balls, cubes, and cylinders of various kinds. Provide a bin with a picture of a cone and an
unlabeled bin.
Bonus: Students count and say how many cones there are in the labeled bin, then how many
other objects there are in the unlabeled bin.
Teacher’s Guide for Kindergarten — Unit 9 Geometry
L-17
(MP.6) 4. Counting Cylinders and Cones while Jumping
Type: Pairs, active
Objective: To identify and count out cylinders or cones while jumping
Preparation: In advance, place a collection of about 18 objects in a box, 6 that are cylinders
(e.g., a toy drum, a marker with the lid on, an unsharpened pencil, a drinking straw), 6 that are
cones (e.g., a paper cup, an ice-cream cone, a funnel, a party hat), and 6 that are neither
cylinders nor cones.
Instructions: Partner 1 chooses either a cylinder or a cone. Partner 2 takes out three or more of
that kind of shape from the box. Partner 1 counts the objects and jumps that many times.
Partners switch roles and repeat.
5. Making a Cylinder and a Cone from Modeling Clay
Type: Individual
Objective: To make a cylinder and then a cone using modeling clay
Preparation: Provide each student with a piece of modeling clay.
Instructions: Demonstrate how to make a cylinder by rolling a piece of modeling clay on a table,
using a back-and-forth movement with a flat, horizontal hand. Cut off the ends of the rolled clay
with a plastic knife to make the flat faces. Alternatively, put the rolled piece of clay upright on the
table, press gently on top to flatten the bottom end, turn the cylinder over, repeat to flatten the
other end, and then roll the clay a little more to improve the curved face. Have students make a
cylinder in the same way you did. To make a cone, first roll a piece of clay back and forth as for
a cylinder; then, continue to roll with your hand but, instead of horizontal, hold it at a slight
upward angle against one end of the clay to create a pointed end. Put the cone upright on the
table with the pointed end facing up, and press gently to flatten the base. Have students make a
cone in the same way.
Extensions
(MP.1) 1. After students have crossed out the non-cylinders for Question 3 on AP Book K.2,
Unit 9, p. 76, have them count the cylinders (the shapes that are not crossed out). You might
ask students to mark each cylinder as they count it, and then write the total count somewhere
inside the bubble. Repeat for cones in Question 6 on p. 78.
2. Provide students with a blank sheet of paper, glue, and a pile of pictures of cylinders and
cones from BLM Solid Objects. Tell them to choose one cylinder and one cone from the pile,
glue them onto their page, and draw a picture that incorporates the shapes.
(MP.1) 3. Repeat Extension 3 in Lesson GK-16 using pictures of up to 10 cylinders instead of
spheres. Make use of BLM Solid Shapes and BLM Solid Objects.
(MP.1) 4. Repeat Extension 3 in Lesson GK-16 using pictures of up to 10 cones instead.
Make use of BLM Solid Shapes and BLM Solid Objects.
L-18
Teacher’s Guide for Kindergarten — Unit 9 Geometry GK-18
Faces and Corners
Pages 79–82
Standards: K.G.A.1, K.G.A.2, K.G.A.3, K.G.B.4
Goals:
Students identify the faces of solid shapes as flat geometrical shapes.
Students identify the corners on solid shapes.
Students compare solid shapes using the concepts of rolling and sliding.
Students compare solid shapes by their faces and corners.
Prior Knowledge Required:
Can identify circles, squares, rectangles, and triangles regardless of size, color, and orientation
Can count up to 10 objects in various arrangements
Can identify spheres, cubes, cylinders, and cones regardless of size, color, and orientation
Vocabulary: circle, cone, corner, cube, curved face, cylinder, face, flat, flat face, rectangle,
shape, solid, sphere, square, triangle
Materials:
objects that are cubes, spheres, cylinders, and cones
6 paper squares the same size as the faces of a cube
tape
paper circles the same sizes as the bases of a cylinder and a cone
BLM Nets for Cones (p. L-46)
BLM Net for a Cylinder (p. L-45)
collection of small spheres, cubes, cylinders, and cones
opaque bag per student pair
BLM Solid Shapes (pp. L-37–40)
BLM Solid Objects (pp. L-41–44)
BLM Squares of Different Sizes (p. R-28)
BLM Rectangles of Different Sizes (p. R-29)
BLM Triangles of Different Sizes and Types (p. R-30)
BLM Circles of Different Sizes (p. R-27, see Activity Centers 1, 2)
box (see Activity Centers 1, 3, 4)
bins (see Activity Centers 1–3)
stickers (see Extensions 2, 3)
BLM Net for a Cube (p. L-36, see Extension 4)
craft sticks and modeling clay (see Extension 5)
BLM Matching Solid Shapes with Objects (p. L-47, see Extension 6)
BLM Curved Faces and Flat Faces (p. L-48, see Extension 7)
Teacher’s Guide for Kindergarten — Unit 9 Geometry
L-19
Counting practice. Practice counting to 90 as a class by playing I Start, You Finish (see
introduction to Unit 1, p. C-1) for the numbers from 80 to 90, and then from 60 to 90. Play “Let’s
Compare” using numbers between 1 and 10.
(MP.7) The faces of a cube are flat and square. Hold up a cube, such as a cube-shaped
tissue box, and ASK: What do we call this shape? (a cube) In your other hand, hold up a paper
square the same size as the faces of the cube, and ASK: What is the name of this shape? (a
square) Is a cube a flat shape or a solid shape? (a solid shape) Is a square a flat shape or a
solid shape? (a flat shape)
Put down the paper square but keep holding up the cube. SAY: Look at the cube. ASK: Does
any part of the cube look like a square? SAY: When you see a square on the cube, raise your
hand. After giving students some time to look at the cube, trace a square by running your finger
along the edges of one face of the cube. SAY: This part of the cube is a square. Pointing to that
square face, SAY: This is called a face of the cube. Each side of a solid shape is called a face.
You might say that a face is any part of a shape where you can draw a smiley face. (If students
need further explanation, you might explain that to draw a smiley face, you need room to draw
eyes and a mouth, so any part of the shape that provides even a small amount of room for you
to do so is a face.) Holding the paper square beside the square face of the cube, ASK: Are the
paper square and the face of the cube the same shape? (yes) Hold the paper square against
the face of the cube so that the face is fully covered, demonstrating they are the same shape.
Tape the paper square on top of the face. SAY: This face is a square, and a square is a flat
shape. So, we call this face of the cube a flat face. Repeat with the remaining faces of the cube
until all of the faces are covered with paper squares.
ASK: Did we cover all the faces of the cube with paper squares? (yes) Are all of the faces the
same shape? (yes) SAY: All of the faces of the cube are flat. All of the faces are squares of the
same size.
A sphere has a curved face and can roll. Holding up a tennis ball, ASK: What is this? (a
tennis ball) What is the name of the shape of a tennis ball? (a sphere) Place the ball on the floor
(or on a table) so that all students can see it. SAY: When you push a sphere, it rolls.
Demonstrate by giving the ball a push and letting it roll. Repeat with more spheres, such as a
basketball, a marble, and a baseball. SAY: Spheres have no flat faces. A sphere has a curved
face. Run your fingers along the curved face of the sphere. SAY: This is a curved face. A shape
with a curved face can roll.
A cube has all flat faces and cannot roll. Hold up a cube, such as a connecting cube.
ASK: What is the name of this shape? (a cube) Place the cube on the floor (or on a table) so
that all students can see it. SAY: When you push a cube, it slides. Demonstrate by pushing the
cube steadily along the floor; however, don’t let the cube turn over. SAY: Cubes have flat faces.
A shape with a flat face can slide. Repeat with more cubes (e.g., a cube-shaped tissue box).
ASK: Does a cube have any curved faces? (no) Can a cube roll like the sphere? (no)
A cylinder has a curved face and flat faces; it can roll and slide. Hold up a cylinder, such as
a can of soup. ASK: What is the name of this shape? (a cylinder) SAY: Look at the cylinder.
L-20
Teacher’s Guide for Kindergarten — Unit 9 Geometry When you see a curved face, raise your hand. As you run your fingers along the curved face of
the cylinder, ASK: Is this a curved face? (yes) Hold up a paper circle the same size as the
bases of the cylinder, and ASK: What is this shape called? (a circle) Is a circle a flat shape or a
solid shape? (a flat shape) On the cylinder, can you see a flat face that is the shape of a circle?
Hold the cylinder so that one of the circular bases faces the students. Trace your finger along
the circular edge, and SAY: This part of the cylinder is a circle. While holding up the paper circle
beside the circular base on the cylinder, ASK: Does this paper circle have the same shape as
this face of the cylinder? (yes) Hold the paper circle against the face of the cylinder so that the
face is fully covered to demonstrate they are the same shape. Tape the paper circle on top of
the face. SAY: This face is a circle, and a circle is a flat shape. So, this face of the cylinder is a
flat face. Repeat with the other circular face of the cylinder. SAY: A cylinder has a curved face
(point to the curved face) and two flat faces that are circles (point to the circular faces).
Place the cylinder on the floor with the curved face touching the ground. SAY: I put the curved
face of the cylinder on the floor. ASK: If I push the cylinder, will it slide or roll? (roll) Demonstrate
by pushing the cylinder. SAY: A cylinder has a curved face and so it can roll.
Place the cylinder on the floor with a circular face touching the ground. SAY: Now, I put one of
the flat faces of the cylinder on the floor. ASK: If I push the cylinder now, will it slide or roll?
(slide) Demonstrate by pushing the cylinder steadily along the floor. Repeat with the other
circular face on the ground. SAY: A cylinder has flat faces and so it can slide. Repeat with more
cylinders. Include a hockey puck, and SAY: When playing hockey, the puck slides along the ice
on its flat faces. Sometimes, a puck rolls on its curved face. Demonstrate a puck rolling on its
curved face. SAY: So, a puck can roll and slide!
A cone has a curved face and a flat face; it can roll and slide. Repeat the exercise above
using a wood or foam cone, and show students that a cone has one curved face that rolls and
one flat face that slides. SAY: So, a cone can roll and slide too!
(MP.7) Corners on solid shapes. Hold up a cone, such as a wood or foam cone or a paper
cone that includes a circular base (made from BLM Nets for Cones), and SAY: Raise your
hand if you see a corner on this cone. Give students time to look at the cone. Then, point to an
incorrect place on the cone and ask if you are touching a corner. Have students signal thumbs
up for yes or thumbs down for no. Repeat with several more incorrect places before finally
touching the actual corner. ASK: How many corners does this cone have? (1) Repeat with more
cones. SAY: A cone has one corner.
Hold up a sphere. ASK: Does this sphere have any corners? (no) Repeat with more spheres.
SAY: Spheres have no corners. Hold up a cylinder, such as a cylinder block or a paper cylinder
(made from BLM Net for a Cylinder). ASK: Does this cylinder have any corners? (no) Repeat
with more cylinders. SAY: Cylinders have no corners.
Hold up a cube. SAY: Raise your hand if you see any corners on this cube. Point to a corner,
and ASK: Is this a corner? (yes) Keep touching that corner and SAY: Raise your hand if you see
any more corners. Touch a different corner, and ASK: Is this a corner? (yes) Repeat with
several more corners on the cube. SAY: A cube has many corners.
Teacher’s Guide for Kindergarten — Unit 9 Geometry
L-21
Activity
Identifying solid shapes by touch. Provide each pair of students with an opaque bag that
contains several solid shapes (i.e., spheres, cubes, cylinders, cones). Partner 1 holds the bag
while Partner 2 reaches into the bag and feels the shapes with her eyes closed. When Partner 2
thinks she knows which shape she is holding, she pulls out the shape and says the name of the
shape. She then opens her eyes to see if she is correct. Partner 2 continues until she has
identified all of the shapes in the bag. Then, players switch roles and play again.
(end of activity)
(MP.6) Preparing for the AP pages. To prepare students for Question 1 on AP Book K.2,
Unit 9, p. 79, post on the board pictures of solid shapes and objects from BLM Solid Shapes
and BLM Solid Objects as well as pictures of squares, rectangles, and triangles from
BLM Squares of Different Sizes, BLM Rectangles of Different Sizes, and BLM Triangles
of Different Sizes and Types. As you point to each shape, have students signal thumbs up if
the shape is a solid (three-dimensional) shape and thumbs down if it is a flat (two-dimensional)
shape. Remove each flat shape from the board as it is identified. To prepare students for
Questions 2–7 on p. 80, post on the board pictures of solid shapes (from BLM Solid Shapes),
two at a time. Either post two copies of the same shape (but have one shape tilted), two
examples of the same shape (from BLM Solid Shapes (2) to (4)) that differ in their proportions or
orientation, or two different shapes. Have students signal thumbs up if the shapes are the same
or thumbs down if the shapes are different.
Activity Centers
(MP.6) 1. Distinguishing Between Solid Shapes and Flat Shapes
Type: Small groups
Objective: To identify shapes as solid or flat
Preparation: In advance, collect actual spheres, cubes, cylinders, and cones (at least three of
each shape) and paper circles, squares, rectangles, and triangles (at least three of each shape)
from BLM Circles of Different Sizes, BLM Squares of Different Sizes, BLM Rectangles of
Different Sizes, and BLM Triangles of Different Sizes and Types. Place the collection of solid
shapes and flat shapes in the same box. Provide each group with two bins, one labeled with
pictures of solid shapes (i.e., cube, cone, sphere, cylinder) and one labeled with pictures of flat
shapes (i.e., square, triangle, circle, rectangle).
Instructions: In turn, each student takes a shape from the box, says whether it is a flat shape or
a solid shape, and puts it into the correct bin.
Bonus: Repeat, but replace the actual solid shapes with pictures of solid shapes cut from BLM
Solid Shapes and BLM Solid Objects. Students place the pictures of solid objects into the bin for
solid objects and the pictures of flat shapes into the bin for flat shapes.
(MP.7) 2. Identifying Flat Faces
Type: Pairs
Objective: To point out a flat face on a solid shape and identify the specific flat shape
Preparation: In advance, collect actual cubes, cylinders, and cones (at least three of each
shape) and paper circles, squares, rectangles, and triangles (at least three of each shape) from
BLM Circles of Different Sizes, BLM Squares of Different Sizes, BLM Rectangles of Different
L-22
Teacher’s Guide for Kindergarten — Unit 9 Geometry Sizes, and BLM Triangles of Different Sizes and Types. Put the solid shapes in a bin labeled
with pictures of a cube, a cylinder, and a cone, and put the paper shapes in another bin labeled
with pictures of a circle, a square, a rectangle, and a triangle.
Instructions: Partner 1 chooses a solid shape from the bin of solid shapes and points to a flat
face on the shape. Partner 2 looks in the bin of flat shapes to find a paper shape that matches
that face. The paper shape may be smaller or larger than the face of the solid, but the shapes
must match. For example, if the solid shape is a cube, Partner 1 can point to any face, and any
paper square will be a match. If the solid shape is a cylinder or a cone, Partner 1 must point to a
flat circular face, and any paper circle will be a match. Students return the shapes to the correct
bins, switch roles, and continue playing.
(MP.6) 3. Corners or No Corners
Type: Small groups
Objective: To explore spheres, cubes, cylinders, and cones, and decide which shapes have
corners and which do not
Preparation: Provide students with an empty bin and a box filled with at least three of each solid
shape (i.e., spheres, cubes, cones, and cylinders).
Instructions: Each student in turn takes a shape from the box. The student says the name of the
shape. If the shape has corners, he points out at least one corner, and then puts the shape
directly on the table. If the shape has no corners, he says “no corners,” and then puts the shape
into the bin. When all the shapes in the box have been placed either on the table or in the bin,
students look at the shapes in both groups and then say which shapes have corners and which
do not. (cubes and cones have corners; spheres and cylinders do not have corners)
(MP.6) 4. Rolling and Sliding Shapes
Type: Pairs, active
Objective: To explore spheres, cubes, cylinders, and cones, and decide which shapes can roll
and which can slide
Preparation: Provide students with a box filled with two of each solid shape (i.e., spheres,
cubes, cylinders, and cones).
Instructions: First, students attempt to roll each of the eight objects on the floor. Remind them
that objects will roll on a curved face. Students determine which objects can roll (spheres,
cylinders, and cones) and which cannot roll (cubes). Then, students try to slide each of the eight
objects. Remind students that objects will slide on a flat face. Students determine which objects
can slide (cubes, cylinders, and cones) and which cannot slide (spheres).
Extensions
(MP.1) 1. After students have crossed out the flat shapes for Question 1 on AP Book K.2,
Unit 9, p. 79, have them count the solid shapes (the shapes that are not crossed out). You
might ask students to mark each solid shape as they count it, and then write the total count
somewhere inside the bubble.
(MP.6) 2. Provide each student with a cube, and have them count the faces on the cube. To
help students be sure they count each face only once, provide stickers for them to stick on each
face as they count it.
Teacher’s Guide for Kindergarten — Unit 9 Geometry
L-23
Bonus: Provide each student with two or three more cubes, and have them count the faces of
each cube. ASK: Do you think all cubes will have the same number of faces? (yes) How many
faces? (6)
(MP.6) 3. Repeat Extension 2, except this time have students count the corners of a cube
instead of the faces. To help with counting, provide stickers and demonstrate how to put a
sticker on top of a corner by flattening the sticker around the corner with your fingers.
Bonus: Provide each student with two or three more cubes, and have them count the corners of
each cube. ASK: Do you think all cubes will have the same number of corners? (yes) How many
corners? (8)
4. Demonstrate how to create a cube from a net for a cube, using BLM Net for a Cube. (See
unit introduction for some tips.) Repeat for a cylinder, using BLM Net for a Cylinder. Have very
advanced students with strong motor skills create these shapes using the nets.
5. Demonstrate how to create a cube using 12 craft sticks of the same length and modeling
clay. First, create two squares using craft sticks for the edges and modeling clay for the corners.
Then, join opposite corners of the two squares using four more craft sticks. Have very advanced
students with strong motor skills create a cube in the same way.
(MP.4) 6. Have students complete BLM Matching Solid Shapes with Objects.
(MP.6) 7. Have students complete BLM Curved Faces and Flat Faces.
(MP.7) 8. Have student pairs repeat the Activity, except this time, the student who feels the
shapes in the bag must count how many cylinders (or another specified shape) are in the bag
without removing any shapes or peeking into the bag. To begin, use at most two of a single kind
of shape and no more than four objects in total.
(MP.1) 9. Post three pictures of shapes on the board (from BLM Solid Shapes, BLM Squares of
Different Sizes, BLM Rectangles of Different Sizes, and BLM Triangles of Different Sizes). For
example, post a picture of a cylinder, a square, and a triangle. SAY: I’m thinking of one of these
shapes. The mystery shape is a flat shape. ASK: Could the mystery shape be the cylinder? (no)
Prompt students by asking if a cylinder is flat or solid. (solid) SAY: We know that the mystery
shape is not the cylinder. So, let’s remove the cylinder from the board. After removing the
cylinder, give a second clue for the mystery shape. For example, SAY: The mystery shape
has four corners. ASK: Does the triangle have four corners? (no) How many corners does it
have? (3) Remove the triangle from the board. ASK: Does the square have four corners? (yes)
SAY: You found the mystery shape. It is the square! Repeat with different sets of three shapes
on the board and different sets of clues. Examples:
a) cube, cylinder, triangle (first clue: the shape is solid; second clue: the shape rolls)
b) sphere, cube, cone (first clue: the shape rolls; second clue: the shape has a corner)
c) sphere, cube, cylinder (first clue: the shape slides; second clue: the shape has all flat faces)
Answers: a) cylinder, b) cone, c) cube
L-24
Teacher’s Guide for Kindergarten — Unit 9 Geometry GK-19
In Front and Behind
Pages 83–84
Standards: K.G.A.1, K.CC.B.5
Goals:
Students learn the terms “in front of” and “behind,” and use them to describe the relative
position of objects and solid shapes.
Students create configurations of two solid shapes, where one is in front of or behind the other.
Prior Knowledge Required:
Can count up to 10 objects in various arrangements
Can identify spheres, cubes, cylinders, and cones
Vocabulary: behind, cone, cube, cylinder, in front of, shape, sphere
Materials:
3 small objects, such as a pencil, a ball, and a book
objects that are spheres, cubes, cylinders, or cones
BLM Train (p. L-49)
BLM Solid Objects (pp. L-41–44)
BLM Solid Shapes (pp. L-37–40)
orange and blue colored pencils or crayons
bins (see Activity Center 1)
BLM Net for a Cube (p. L-36, see Activity Center 1)
BLM Net for a Cylinder (p. L-45, see Activity Center 1)
BLM Nets for Cones (p. L-46, see Activity Center 1)
BLM Solid Shape and Object Cards (p. L-50, see Activity Center 2, Extension 3)
Counting practice. Practice counting to 90 as a class; have a volunteer lead the count. Play
“Let’s Compare” using numbers between 1 and 10.
(MP.4) Introduce the words “in front of” and “behind.” Have four students stand in a line
facing the door, for example, Abdul, Beth, Cathy, and Don, in that order. SAY: Let’s pretend that
these students are lined up for recess. ASK: Who is at the start of the line? (Abdul) Rest your
hand above the student at the front of the line to prompt students. ASK: Who is at the end of
the line? (Don) Rest your hand above the student at the back of the line to prompt students.
ASK: Who is closer to the start of the line, Beth or Cathy? (Beth) SAY: We say Beth is in front of
Cathy because Beth is closer to the start of the line. Who is closer to the end of the line, Beth or
Cathy? (Cathy) SAY: We say Cathy is behind Beth because Cathy is closer to the end of the
line. Repeat with other pairs of volunteers standing in the line, and each time, ask who is in front
and who is behind. Then repeat with four or five different volunteers lined up facing the door.
Teacher’s Guide for Kindergarten — Unit 9 Geometry
L-25
(MP.4) Using the words “in front of” and “behind” with objects and solid shapes. Hold up
a pencil and a small ball so that, from the students’ perspective, the pencil is in front of the ball.
ASK: Which is closer to you, the pencil or the ball? (the pencil) SAY: The pencil is closer to you.
So, we say, “The pencil is in front of the ball.” Have students repeat the sentence as a class.
Then, SAY: The ball is farther away from you. So, we say, “The ball is behind the pencil.” Have
students repeat the sentence as a class. Repeat with several pairs of objects. Then, repeat
with a pencil and a book, so that when the pencil is behind the book, the pencil is out of sight.
SAY: Now, the pencil is behind the book. ASK: Can we see the pencil? (no) SAY: Sometimes,
you cannot see the thing that is behind. Repeat with more examples of objects in front of and
behind each other, such that the object behind is hidden.
Place an object, such as a book, on the table or floor. Then, tell students that you will put an
object either in front of or behind the book (and say that it is in front of or behind the book) and
that they need to signal thumbs up if you put it in the correct position or thumbs down if you did
not. Repeat with objects that are spheres, cubes, cylinders, and cones.
(MP.2) Solid shapes in front of and behind on a train. On the board, draw a larger version of
the train from BLM Train or post an enlarged photocopy of the BLM. Tape pictures of objects
onto the car of the train; for example, in order from front to back, a ball, a can, a die, and an
ice-cream cone from BLM Solid Objects. Point to the very front of the train, and SAY: This is
the front of the train. Then, choose two of the pictures, for example, the can and the ice-cream
cone, and ASK: Which one is closer to the front of the train, the can (point to the can) or the
ice-cream cone (point to the cone)? (the can) SAY: The thing closer to the front of the train is in
front. ASK: Which one is closer to the end of the train, the can or the ice-cream cone? (the icecream cone) SAY: The thing closer to the end of the train is behind. Repeat with various pairs of
objects, and each time, ask which one is in front and which one is behind. Then, choose one
object, for example, the die, and ASK: Which things are in front of the die? (the ball and the can)
Which thing is behind the die? (the ice-cream cone) Then, ASK: How many things are in front of
the die? (2) Lead students in counting. ASK: How many things are behind the die? (1) Repeat
as needed, using more objects and shapes from BLM Solid Objects and BLM Solid Shapes.
Preparing for the AP pages. For Questions 1–3 on AP Book K.2, Unit 9, p. 83, tell students
that the animals are lined up to go outside. Remind them that “in front” means closer to the front
of the line or closer to the door, and “behind” means closer to the end of the line or farther away
from the door. For Questions 4–6 on p. 84, explain that the shapes are lined up on the cart of a
train. Again, remind them that “in front” means closer to the front of the line or closer to the front
of the train, and “behind” means closer to the end of the line or farther away from the front of the
train. Students will need orange and blue pencils or crayons.
Activity Centers
(MP.6) 1. Solid Shapes and Objects In Front of and Behind
Type: Pairs
Objective: To describe the relative positions of solid shapes and objects using the phrases “in
front of” and “behind”
L-26
Teacher’s Guide for Kindergarten — Unit 9 Geometry Preparation: Provide students with a bin containing wood or foam cones, cylinders, and cubes
or shapes that are made using nets from BLM Net for a Cube, BLM Net for a Cylinder, and
BLM Nets for Cones. You might also include solid objects that are cubes, cylinders, and cones.
Instructions: Partner 1 positions three or four solid shapes and/or objects on the floor (or a
table). Both students should face the objects in the same direction, so that from the perspective
of the students, the objects form a line one behind the other. (Each object should be placed on
one of its flat faces so it does not roll.) Students take turns choosing two of the objects and
asking their partner which one is in front and which one is behind. After several rounds, students
remove the shapes, Partner 2 chooses a new set of three or four shapes, and they play again.
Bonus:
a) Partner 1 places one object on the floor and asks Partner 2 to place an object in front of or
behind that object. After doing so, Partner 2 asks Partner 1 to place another object in front of or
behind one of the objects. After there are five or six objects in a line, students remove the
objects and start again.
b) Students place five or six objects in a line, one behind the other. Then, they take turns
pointing to one of the objects while their partner counts how many objects are in front of that
object and how many are behind it.
(MP.6) 2. In Front of and Behind on a Train
Type: Pairs
Objective: To describe the relative positions of pictures of solid shapes and objects on a train
using the phrases “in front of” and “behind”
Preparation: Provide each pair with one train from BLM Train and a set of cards from BLM
Solid Shape and Object Cards.
Instructions: Partner 1 positions four pictures of solid shapes and/or objects on the car of the
train. Students take turns choosing two of the objects and asking their partner which one is in
front and which one is behind. After several rounds, students remove the shapes, Partner 2
chooses a new set of four pictures, and they play again.
Bonus: Students place five objects on the train. Then, they take turns pointing to one of the
objects on the train while their partner counts how many objects are in front of that object and
how many are behind it.
(MP.6) 3. In Front of and Behind While Standing in a Line
Type: Groups of five
Objective: To describe the relative positions of students standing in a line using the phrases “in
front of” and “behind”
Instructions: The leader helps the other students in the group stand in a line, facing a door or an
imaginary door. The leader chooses two people in the line and asks the other students which
one of the two is in front and which one is behind. Students in the line can look back to see their
classmates, but they should not step out of line. After a few rounds, students start again, with
another student taking the role of leader.
Bonus: The leader chooses one student in the line and asks the other students how many
students are in front of that student and how many are behind that student.
Teacher’s Guide for Kindergarten — Unit 9 Geometry
L-27
Extensions
(MP.6) 1. After students have colored the animals for Questions 1–3 on AP Book K.2, Unit 9,
p. 83, ask them to count how many animals are in front of the dog (for each question). All of
those animals should be colored orange. They can write the number somewhere inside the
bubble using the same orange pencil used to color those animals. For Questions 4–6 on p. 84,
have students count how many shapes are in front of the sphere (for each question). All of
those shapes should be colored orange. They can write the number somewhere inside the
bubble using the same orange pencil.
(MP.6) 2. For Questions 1–3 on AP Book K.2, Unit 9, p. 83, have students count how many
animals are behind the dog. All of those animals should be colored blue. They can write the
number somewhere inside the bubble using the same blue pencil used to color those animals.
For Questions 4–6 on p. 84, have students count how many shapes are behind the sphere. All
of those shapes should be colored blue. They can write the number somewhere inside the
bubble using the same blue pencil.
(MP.1) 3. Provide each pair of students with a copy of BLM Train (one train for each student in
the pair) and two matching sets of three pictures of solid shapes and/or objects from BLM Solid
Shape and Object Cards. A matching set could be, for example, a cube, a sphere, and a cone
for each partner. Partners face away from each other so they cannot see each other’s train.
Partner 1 positions three shapes on the train (for example, the cube at the front, followed by the
sphere, and then the cone). Partner 2 then asks questions about the relative positions of
Partner 1’s shapes and tries to make a copy of Partner 1’s train. For example, Partner 2 might
ask, “Is the cube in front of the cone?” When Partner 2 has figured out Partner 1’s train, the
players reveal their trains to each other. Partners then switch roles and play again.
Bonus: Partners use four shapes instead of three.
L-28
Teacher’s Guide for Kindergarten — Unit 9 Geometry GK-20
Next To
Pages 85–86
Standards: K.G.A.1
Goals:
Students learn the term “next to” and use it to describe the relative position of objects and
solid shapes.
Students create configurations of two solids where one is next to the other.
Prior Knowledge Required:
Can count up to 10 objects in various arrangements
Can identify spheres, cubes, cylinders, and cones
Can use the phrases “in front of” and “behind”
Vocabulary: behind, beside, cone, cube, cylinder, in front of, next to, shape, sphere
Materials:
2 shapes
2 small objects, such as a pencil and a toy car
objects that are spheres, cubes, cylinders, or cones
BLM Solid Shapes (pp. L-37–40)
bins (see Activity Centers 1, 2)
wood or foam blocks (spheres, cubes, cylinders, and cones) or shapes from BLM Net for a
Cube (p. L-36), BLM Net for a Cylinder (p. L-45), and BLM Nets for Cones (p. L-46; see
Activity Center 1, Extension 3)
tennis ball and plastic water bottle cap (optional, see Activity Center 1)
blank sheets of paper (see Activity Center 2, Extensions 2, 4)
glue (see Activity Center 2, Extension 2)
BLM Solid Shape and Object Cards (p. L-50, see Activity Center 2)
lid of a shoe box (optional, see Extension 3)
small objects (e.g., spherical beads, see Extension 4)
Counting practice. Practice counting to 90 as a class; have students jump as they count. Play
“Let’s Compare” using numbers between 1 and 10.
Review “in front of” and “behind.” Have four students stand in a line facing the door.
SAY: Let’s pretend these students are lined up to go to the library. Choose two students from
the line and ask who is in front and who is behind. Remind students that “in front” means closer
to the front of the line, and “behind” means closer to the back of the line. Repeat as needed.
Then, hold up two shapes, one behind the other, and ask students which one is in front and
which one is behind. Remind students that the shape closer to them is in front, and the shape
farther away is behind.
Teacher’s Guide for Kindergarten — Unit 9 Geometry
L-29
(MP.4) Introduce the term “next to.” Have two volunteers stand side by side at the front of the
class, for example, Jayden and Marta. SAY: Jayden is beside Marta. We also say Jayden is
next to Marta. Also, Marta is next to Jayden. Marta and Jayden are next to each other. Repeat
the sentences together as a class. Then, ask Jayden and Marta to switch places, and repeat.
SAY: It does not matter if Jayden and Marta switch places. They are still next to each other.
Hold up a pencil and a toy car side by side, and ASK: Is the pencil next to the car? (yes) Is the
car next to the pencil? (yes) Are the pencil and car next to each other? (yes) Repeat these
sentences together as a class. Switch the positions of the pencil and car, and repeat. Repeat
this exercise several times using pairs of solid shapes (spheres, cubes, cylinders, cones) next to
each other.
(MP.2) Using the term “next to” with shapes. On the board, affix a picture of a cone from
BLM Solid Shapes. ASK: What shape is this? (a cone) Post a picture of a cylinder next to the
cone, as shown below:
While pointing to the cylinder, ASK: What shape is this? (a cylinder) Is the cylinder next to the
cone? (yes) Is the cone next to the cylinder? (yes) Are the cone and cylinder next to each
other? (yes) Repeat the sentences as a class: “the cylinder is next to the cone; the cone is next
to the cylinder; the cone and cylinder are next to each other.” Repeat this exercise with several
different pairs of solid shapes.
(MP.4) People and objects next to and not next to each other. Have three volunteers stand
side by side at the front (for example, Amy, Billy, and Hanna, in that order). ASK: Are Amy and
Billy next to each other? (yes) Rest your hand just above each child’s head as you refer to them.
ASK: Are Billy and Hanna next to each other? (yes) Are Amy and Hanna next to each other?
(no) SAY: Amy and Hanna are not next to each other because Billy is in between. Have a fourth
volunteer join the row (for example, Greg) beside Hanna. Ask several questions of the form:
Which two students are next to Billy? (Amy and Hanna) Which two students are next to Hanna?
(Billy and Greg) Who is next to Greg? (Hanna) Is Billy next to Greg? (no) Repeat with different
arrangements of volunteers. Eventually, include arrangements where some pairs of volunteers
are next to each other but in front of or behind another volunteer. Have students describe the
relative positions of pairs of volunteers using the phrases “in front of,” “behind,” and “next to.”
Then, ask all students to put their own hands side by side. ASK: Are your hands next to each
other? (yes) Ask them to hold one hand on each side of their head (demonstrate). ASK: Are
your hands next to each other now? (no)
Have two volunteers (for example, Rani and Sal) stand far away from each other. SAY: Rani
and Sal are not next to each other. They are far away from each other. Repeat with other pairs
of volunteers and objects that are far away from each other. Each time, ask if the two volunteers
(or objects) are next to each other. Then, mix examples of “next to” and “not next to,” and each
L-30
Teacher’s Guide for Kindergarten — Unit 9 Geometry time, ask whether the volunteers (or objects) are next to each other. Students signal thumbs up
for yes or thumbs down for no.
(MP.2) Shapes next to or not next to each other. Affix pictures of the solid shapes shown
below to the board:
ASK: What shapes do you see? After several volunteers answer, point to each shape one at a
time from left to right, and have the whole class say the names of the shapes. (sphere, cube,
cone, cylinder) Have a volunteer choose two shapes (for example, the cylinder and the cube).
ASK: Are the cylinder and cube next to each other? (no) Repeat, having several volunteers
choose other pairs of shapes on the board. Proceed to questions of the form: Which shapes are
next to the cube? (sphere and cone)
Preparing for the AP pages. For Questions 1–4 on AP Book K.2, Unit 9, p. 85, tell students
that there is one shape next to the cone (in each question). They need to find the shape that is
next to the cone and color it. For Questions 5–8 on p. 86, tell students that there are two
shapes next to the cylinder. They need to color both shapes. No other shapes should be colored.
Activity Centers
(MP.6) 1. Solid Shapes Next To and Not Next To Each Other
Type: Pairs
Objective: To place solid shapes side by side and describe shapes next to and not next to
each other
Preparation: Place a bin containing spheres, cubes, cylinders, and cones on the center of a
table. Use wood or foam blocks and/or solid shapes made using nets from BLM Net for a
Cube, BLM Net for a Cylinder, and BLM Nets for Cones. Students might use a tennis ball for
the sphere and rest it on a plastic bottle cap to prevent it from rolling.
Instructions: Student 1 puts three shapes side by side on the table. Student 2 says which
shapes are next to each other and which shapes are not. Partners switch roles and repeat.
Bonus: Students use four shapes instead of three shapes.
(MP.6) 2. Pictures of Solid Shapes Next To and Not Next To Each Other
Type: Pairs
Objective: To place (or glue) pictures of solid shapes side by side and describe shapes next to
and not next to each other
Preparation: Place a bin containing pictures of solid shapes (i.e., spheres, cubes, cylinders,
cones) from BLM Solid Shape and Object Cards on the center of a table. Give each student a
blank sheet of paper. You might also provide glue.
Instructions: Student 1 puts pictures of three shapes side by side on the paper. Student 2 says
which shapes are next to each other and which shapes are not. Partners switch roles and repeat.
Bonus: Students use pictures of four shapes instead of three shapes.
Teacher’s Guide for Kindergarten — Unit 9 Geometry
L-31
(MP.6) 3. People Next To and Not Next To Each Other
Type: Groups of five or six, active
Objective: To describe the relative position of three students side by side, using the words “next
to” and “not next to”
Instructions: Have three members of the group stand side by side in a row. The remaining group
members should be sitting, and they say who is next to and who is not next to each other
(referring to the standing students). Students take turns standing up and sitting down.
Bonus: Instead of three students, four students stand in a row.
(MP.4) 4. Next To and Not Next To in the Classroom
Type: Pairs, active
Objective: To find objects in the classroom that are next to or not next to each other
Instructions: Students walk around and find objects that are next to each other and objects that
are not next to each other. Students then meet with their partner and take turns telling one
another what objects in the room are next to each other and not next to each other.
Extensions
(MP.3, MP.6) 1. Review the words “above” and “below.” On the board, post an arrangement of
pictures of solid shapes (from BLM Solid Shapes) in such a way that you can use the words
“above,” “below,” and “next to” to describe the relative position of the shapes. Tell students you
will say some correct sentences and some incorrect sentences, and so they need to listen
carefully. Students signal thumbs up if the sentence is correct or thumbs down if the sentence is
incorrect. Choose two of the shapes and describe their positions in a sentence using the words
“above,” “below,” and “next to,” sometimes correctly and sometimes incorrectly. For each
incorrect sentence they identify, ask students how to make a correct sentence about the
two shapes.
(MP.6) 2. Provide paper shapes (from BLM Solid Shape and Object Cards) that students can
glue onto paper. Have students create a picture with the solid shapes above, below, and next to
each other. Students use the words “above,” “below,” and “next to” to describe their picture to
a partner.
(MP.6) 3. Repeat Extension 2, but this time students use actual solid shapes to create
arrangements of shapes. You might provide each student with something to prevent the solid
shapes from rolling away, for example, the lid of a shoe box. Students use the words “above,”
“below,” “in front of,” “behind,” and “next to” to describe the positions of their shapes to
a partner.
(MP.6) 4. Similar to Extensions 2 and 3, students make pictures on paper (they need not glue
the objects) using small objects, such as spherical beads, connecting cubes, dried cylindrical
pasta, and pieces of drinking straws. They show their pictures to a classmate and identify the
solid shapes by name, and then describe the relative positions of the shapes using words, such
as “above,” “below,” and “next to.”
L-32
Teacher’s Guide for Kindergarten — Unit 9 Geometry GK-21
Building Solids
Pages 87–88
Standards: K.G.B.5, K.G.B.6
Goals:
Students compose solid shapes to form larger shapes, make designs, and model real-world
objects.
Prior Knowledge Required:
Can identify spheres, cubes, cylinders, and cones
Can use the terms “in front of,” “behind,” and “next to”
Vocabulary: above, below, cone, cube, curved face, cylinder, flat face, next to, shape, sphere
Materials:
solid cylinders, cubes, spheres, and cones
wood or foam blocks (spheres, cubes, cylinders, and cones) or shapes from BLM Net for a
Cube (p. L-36), BLM Net for a Cylinder (p. L-45), and BLM Nets for Cones (p. L-46)
yellow, green, red, and blue colored pencils, crayons, or markers
rectangular prisms (optional, see Extension 1)
large sheet of paper, toy plate, toy cup, toy spoon, and folded napkin per student (see
Extension 2)
Counting practice. Practice counting to 90 as a class by playing I Start, You Finish (see
introduction to Unit 1, p. C-1) for the numbers from 80 to 90, then from 60 to 90. Play “Let’s
Compare” using numbers between 1 and 10.
NOTE: For the following exercise, begin with cylinders and cubes of about the same size before
using solid shapes of different sizes.
(MP.4) Stacking shapes of the same type. SAY: Today, we will put some solid shapes
together to make larger shapes and designs. Hold up two cylinders of the same size.
ASK: What are these shapes called? (cylinders) SAY: Let’s try to put the cylinders on top of
each other. Place the first cylinder on the floor (or a table) with the curved face down, and
attempt to balance the other cylinder on top. Students should see that the cylinders do not stack
this way; the cylinder on top falls off. Pointing to the curved face of one cylinder, SAY: When we
put the curved face down, the cylinder on top falls off. ASK: What will happen if we put each
cylinder on a flat face? Will the cylinder on top fall off? (no) Demonstrate stacking one cylinder
on top of the other one in this way. Repeat with more pairs of cylinders, and then stack three or
more cylinders.
Hold up two cubes, and ASK: What are these shapes called? (cubes) SAY: Let’s try to put
cubes on top of each other. Place one cube on the floor (or a table), and place the other cube
Teacher’s Guide for Kindergarten — Unit 9 Geometry
L-33
on top of it. ASK: Does it look like the cube on top will fall? (no) Repeat with more pairs of
cubes, and then stack three or more cubes.
Hold up a sphere, and ASK: What is this shape called? (a sphere) Does a sphere have any flat
faces? (no) What will happen if we put a sphere on top of another sphere? Will the sphere on
top fall off? (yes) Demonstrate by attempting to stack pairs of spheres. Point out that the top
sphere will always roll off.
Hold up a cone. ASK: What is this shape called? (a cone) SAY: Let’s try to put a cone on top of
another cone. ASK: Which face should we put down, the curved face or the flat face? (flat face)
Put down the cone, and then try to place another cone on top. Point out that the top cone
always falls off. Pointing to the corner on the bottom cone, SAY: The top of this cone is a pointy
corner. When we try to put a shape on top, it falls off. Repeat with several more pairs of cones.
(MP.4) Stacking shapes of different types. Repeat the stacking demonstrations, but use
several shapes of different kinds. For example, the picture below shows a cube, followed by a
cylinder, followed by a cone. Remind students that no shape can go on top of a cone.
Activities 1–4
NOTE: Provide each student with wood or foam blocks. They will need several of each solid
shape (i.e., spheres, cubes, cones, and cylinders). Do not provide spheres for Activities 2–4. If
you do not have enough blocks, you can make them using the nets from BLM Net for a Cube,
BLM Net for a Cylinder, and BLM Nets for Cones.
(MP.4) 1. Stacking shapes. Students use two of each solid shape (i.e., spheres, cubes,
cylinders, and cones). They work individually, in pairs, or in small groups to explore which of the
four solid shapes stack and which do not. First, have students try to stack two cubes on top of
each other. Next, they try to stack two cylinders on top of each other. Then, students explore
what happens when they try to stack a sphere on top of another sphere and a cone on top of
another cone.
2. Making designs. Students work on their own and make designs or structures by stacking
blocks on top of each other. Then, they pair up and tell their partners about what they made,
including which shapes they used.
(MP.6) 3. Matching designs. Students work in pairs. Partner 1 makes a design using several
blocks, while Partner 2 closes her eyes. When Partner 1 is finished, Partner 2 opens her eyes
and tries to copy the structure that Partner 1 built. Partner 2 begins by selecting the blocks
needed. Partners switch roles and play again.
L-34
Teacher’s Guide for Kindergarten — Unit 9 Geometry 4. Making models. Students work on their own and use blocks to make models of people,
houses, or buildings.
(end of activities)
(MP.6) Preparing for the AP pages. For AP Book K.2, Unit 9, p. 87, provide students with
yellow, green, red, and blue colored pencils, markers, or crayons. Tell students to use the labels
underneath each shape as a guide to color the shapes in the teaching box at the top of the
page. Then have students color each shape in Question 1 the same color as the shape in the
teaching box. For example, they should color each cone yellow and each cube green. For
Questions 2–4 on p. 88, have students circle the shapes used to make the gray building. You
might use blocks to demonstrate an example.
Extensions
(MP.4) 1. Students use cube, cylinder, and cone blocks (several of each shape) to make a
model of the classroom. For example, they might use cylinders and cubes to model desks and
tables, and cylinders, cubes, and even cones to model other objects in the classroom, such as a
computer station or cupboards. If available, provide additional blocks, such as rectangular
prisms (these can be called long boxes or wide boxes to the students, depending on the shape).
(MP.4) 2. Provide each student with a sheet of paper, a toy plate, a toy cup, a toy spoon, and a
folded napkin. Tell students that the sheet of paper will be a placemat. Students use the objects
to set a place setting on the piece of paper (for example, the plate near the bottom center, the
spoon next to the plate on the right, the folded napkin next to the plate on the left, and the cup
above the spoon). Students then trace around each object using a pencil or a marker. Then,
they remove the plate, cup, napkin, and spoon to reveal a “map” of where the objects belong.
You might have students show their placemat to a classmate. Encourage them to describe the
position of the objects relative to each other using words such as “above,” “next to,” and
“below.” You might laminate the map for students to use as a placemat at school or at home.
(MP.3) 3. Have students try to stack shapes to answer the following question: Which shapes
stack the best: cones, cylinders, or cubes? Explain.
Answer: Cubes can be stacked on any one of their faces. Cylinders can be stacked only if they
stand on one of the two flat faces. A cone can only be the top object in a stack. So, cubes stack
the best.
(MP.1) 4. In pairs, students repeat Activity 3, except this time the student who tries to match the
design also tries to make as many copies of the design as possible with the blocks available.
The student then says how many of that design can be made with the blocks available.
Students switch roles and play again several times.
Teacher’s Guide for Kindergarten — Unit 9 Geometry
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