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©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Count Objects to Five
Activity 1: Creating a Five Frame
Materials:
0-5 Spinner
Painter’s tape or masking tape
Pencil
Paper clip
1. Create a five frame on the floor using painter’s tape. Each box should measure large enough for a child
to stand in the box (approximately 1 square foot for each box).
2. Ask, “How many spaces do you see?”
3. Use a paper clip to spin the 0-5 Spinner. Ask, "What number did I spin?”
4. Prompt students to represent this number from the spinner on the five frame.
How many students are standing in the five frame?
How many more students are needed to make five? How do you know?
5. Display the following sentence stem for the students to complete orally.
We have ________. We need _______ more to get to five.
6. Prompt students to fill in the five frame to make five.
7. Repeat steps 2-6 to represent a different number on the five frame.
Extension:
The combinations of composing to five may be recorded as “______ and ______ is 5” to bridge to
addition concepts.
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
0-5 Spinner
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Count Objects to Five
Activity 2: Representing a Number on a Five Frame
Materials:
Five Frame
Counters
1. Ask, “How many spaces do you see on the frame?”
2. Prompt students to use counters to represent a given number by saying, “Show me _____.”
How many counters are in the five frame?
How many more counters are needed to make five? How do you know?
3. Display the following sentence stem for the students to complete orally.
I have ________. I need _______ more to get to five.
4. Prompt students to fill in the five frame to make five.
5. Repeat steps 1-4 to represent a different number on the five frame.
Look/listen for:
Students being able to adjust counters without having to remove all of the counters previously
used
Extension:
Ask questions such as, “What is one more than the number on the five frame?” and “What is one
less?”
Activity 3: Making Five on a Five Frame
1. Represent a number on the five frame for the students to see. Students may respond orally or in
written form.
How many counters are in the five frame?
How many more counters are needed to make five? How do you know?
2. Display the following sentence stem for the students to complete orally or in written form.
I have ________. I need _______ more to get to five.
3. Repeat steps 1-2 to represent a different number on the five frame.
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Five Frame
Five Frame
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Count Objects to Ten
Activity 1: Different Representations of Numbers on a Ten Frame
Materials:
Ten Frame
Counters
1. Arrange students in pairs.
2. Ask, “How many spaces do you see on the frame?” and “How is it like the five frame?”
Look/listen for:
Understanding that a ten frame is composed of two five frames.
3. Display a written number, such as eight, for the class.
What is this number?
4. Prompt students to build the number on the ten frame with their counters.
Did your partner place the counters in the same boxes as you?
If not, did you both represent the same number? How do you know?
5. Show students a different representation of eight than that created by the
students.
Does this represent the number eight? Why or why not?
What is another way to represent eight?
Look/listen for:
Correct representations of the number on the ten frame
Understanding that one may have more than one representation of a number on a ten frame
6. Repeat steps 3-5 to represent a different number.
Activity 2: Representing a Number on a Ten Frame
1. Display a written number, such as seven, for the class.
2. Prompt students to represent the number seven on the ten frame by filling in the top row with five
counters and by placing two counters on the bottom row.
How many counters are on your ten frame? How do you know?
How can we use what we know about the top row or five frame to help us
count on to determine the total number of counters placed on the ten
frame?
How many more counters are needed to make 10? Why?
Look/listen for:
Students counting on from five
Students counting one by one
Students subitizing the quantity
Extension:
Ask, “What is one more than the number on the ten frame?” and “What is one less than the
number on the ten frame?”
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Ten Frame
Ten Frame
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Double Ten Frame
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Counting with a Rekenrek
Materials:
Rekenrek
1. Ask students the following questions:
How many beads do you see?
How many are on the top row? How many are on the bottom row?
2. Say, “Put your beads in the starting position. Show me _____.”
How do you know you represented ______?
How many pushes did you use to create your number?
Show me a different way to represent _____.
3. Repeat step 2 using a different number.
4. Say, “Put your beads in the starting position. Without touching any beads, put the number ______ in
your mind. When I say, ‘Go,’ represent the number ______ using one push.”
How do you know you represented ______?
How did you decide how to make the number ______ with only one push?
5. Say, “Put your beads in the starting position. Without touching any beads, put the number 12 in your
mind, and when I say, ’Go,’ represent the number 12 using two pushes.”
How do you know you represented ______?
How did you decide how to make the number ______ with two pushes?
Look/listen for:
Correct representations of the number on the rekenrek
Understanding of a different representation of the same number on the rekenrek
Students counting on from five or 10
Students subitizing the quantity
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Recite Numbers
Activity 1: Counting Around the Circle
Prompt students to form a circle(s) facing in toward each other.
Select a counting sequence to be practiced, such as counting to 10 by ones.
Prompt a student to start counting around the circle one by one until the last number is reached.
When the last number is reached, all students in the circle clap and the student who recited
the last number sits down.
The next student starts the counting sequence over again, starting at one, until another student
reaches the number at the end of the sequence. Everyone claps and that student also sits down.
Continue repeating the sequence until only one student is left standing and the rest are seated.
Repeat the process by skip counting to 100 using multiples of 10.
Activity 2: Dance It Out
Prompt students to find a space away from their desk, tables, and/or other furniture and face the
front of the classroom.
Inform students they are going to dance it out to 10.
Model and practice the moves with students.
1 – right hand on top of head
2 – left hand on top of head
3 – right hand on right shoulder
4 – left hand on left shoulder
5 – right hand on right hip
6 – left hand on left hip
7 – right hand on right knee
8 – left hand on left knee
9 – right hand touching right foot
10 – left hand touching left foot
Stand up and turn 90 degrees to your left.
Begin the dance sequence and repeat until students are facing the front of the room.
Repeat the dance by starting at 28 and counting to 67. Each number will have a corresponding
body movement. Keep counting forward until students are facing the front of the room, with the
dance ending at 67.
Activity 3: Blast Off
Prompt students to find a space away from their desk, tables, and/or other furniture.
Select a counting sequence, such as reciting numbers backward by ones starting at 10.
Inform students they are going to recite numbers backward from 10 to one. Each time they recite a
number, students will squat down until they reach one. Inform students that they are going to
“blast off” (jump up from squatting position) when they reach one.
Prompt students to begin reciting numbers backward starting at 10 and “blast off” when they reach
one.
Prompt students to squat to the ground.
Inform students they are going to count forward starting at one, slowly moving up to a standing
position to “blast off” at 10. When they reach 10 they will “blast off” (jump up).
Prompt students to begin reciting numbers forward starting at one and “blast off” when they reach
10.
Repeat the process by reciting numbers backward and forward from 50 to zero and from zero to 50
by multiples of five.
Look/listen for:
Students making easy transitions between decades (multiples of 10)
Students counting forward or backward without long pauses
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Count Objects Using Skip Counting and Counting On
Materials:
Wikki Stix® – 11 per pair of students
Laminated folder (optional)
Counters
Grouping:
Partners
1. Prompt each pair of students to use their Wikki Stix® to create 10 circles and one rectangle on a
laminated folder or table.
2. Prompt students to grab a large number of counters.
3. Prompt students to work together to place 10 counters inside each circle. Leftover counters that do not
make a group of 10 should be placed inside the rectangle.
4. Prompt students to determine the total number of counters by skip counting by tens and pointing to
each circle containing 10 counters and then counting on by ones to count the counters in the
rectangle.
Questions:
How many groups of tens (fives or twos) do you have? How many singles in the rectangle do you
have?
What number will you say when pointing to the first circle? Why? Second circle? Why?
Why can’t you skip count by another 10 for the counters in the rectangle?
If we counted the counters by ones, what would be the total number of counters in the set?
Look/listen for:
Students correctly skip counting and counting on to determine the total number of counters
5. Prompt students to repeat the process with groups of five to practice skip counting by fives and
counting on to determine the total number of counters.
6. Prompt students to repeat the process with groups of two to practice skip counting by twos and
counting on to determine the total number of counters.
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Conserve Numbers
Activity 1: Treat Time
Materials:
Counters
1. Create two rows of counters as shown below. There should be the same amount of counters in each
row, but one row is spread out.
2. Say, “There once was a teacher who told a student she could have the row of cookies that had the
most to take home as a treat.”
Which row of cookies should the student take?
Why?
3. Prompt students to answer the question below.
What advice could you give another student who said the rows of cookies had different numbers of
cookies?
Look/listen for:
Counting the number of counters to determine the total number in each row
Understanding the number is the same regardless of the arrangement or space
4. Repeat the process by creating two groups of counters as shown. There should be the same amount of
counters in each group, but one group is spread out.
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Conserve Numbers
Activity 2: Shake, Rattle, and Roll
Materials:
Counters
1. Prompt students to count out a given number of counters. The number can be counted orally or
written as a numeral.
2. Prompt students to pick up the counters and place them in their hands.
3. Prompt students to shake and rattle the counters in their hands and roll (place) the counters back on
the table, making certain they all stay on the table.
How many counters are on the table? How do you know?
Did you need to count the counters after you rolled them on the table? Why?
Look/listen for:
Describing the number of the rolled set as the number of counters originally counted out
Understanding that the counters did not need to be recounted
Understanding the number is the same regardless of the arrangement or space
4. Repeat the process using a different number of counters.
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Conserve Numbers
Activity 3: Hidden Counters
Materials:
Counters
Blank piece of paper
1. Display six counters.
How many counters are there? Students may respond orally or in written form.
2. Cover the counters.
How many counters are hidden? How do you know?
Look/listen for:
Understanding that the total number of counters remains the same
Use of counting on from the number of counters that are visible to determine the number of
counters hidden
3. Repeat steps 1-2 using different numbers.
Extension:
1. Display nine counters.
How many counters are in the set? Students may respond orally or in written form.
2. Cover some of the counters.
How many counters are hidden? How do you know?
How many counters are there in all? How do you know?
Look/listen for:
Understanding that the total number of counters remains the same
Use of counting on from the number of counters that are visible to determine the number of
counters hidden
3. Repeat steps 1-2 using different numbers.
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Using Counting to Compare Numbers
Activity 1: Comparing Numbers Using Frames Materials:
Five Frame Cards
Ten Frame and Double Ten Frame Cards
1. Arrange students in pairs.
2. Prompt each student to turn over a Five Frame Card from his or her set.
3. Prompt partners to compare the numbers represented on the cards.
What number is represented by your five frame?
4. Prompt students to use words to describe the comparison of the two sets. Display or provide sentence
stems.
__________ is more than __________.
__________ is the same number as __________.
__________ is less than __________.
Questions:
How did you determine your comparison statement?
How are the quantities ___ and ___ alike? How do you know?
How are the quantities ___ and ___ different? How do you know?
o How many more is ___ than ___?
o How many less is ___ than ___?
5. Repeat, as appropriate, using Ten Frame and Double Ten Frame Cards.
Activity 2: Find a Frame
Materials:
Five Frame Cards
Ten Frame and Double Ten Frame Cards
1. Prompt each student to turn over one Five Frame Card.
What number is represented by your five frame?
2. Prompt each student to find a Five Frame Card that is more than the number represented on the
card he or she turned over.
3. Prompt students to use words to describe the comparison of the two sets shown on the cards in front
of him or her. Sentence stems can be provided.
__________ is more than __________.
__________ is less than __________.
Questions:
How did you determine your comparison statement?
How are the quantities ___ and ___ alike? How do you know?
How are the quantities ___ and ___ different? How do you know?
How many more is ___ than ___?
How many less is ___ than ___?
4. Repeat, as appropriate, using Ten Frame and Double Ten Frame Cards.
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Five Frame Cards
Two sets of cards are provided.
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Ten Frame and Double Ten Frame Cards
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Activity 3: Comparing Numbers Using a Rekenrek – Part A
Materials:
Rekenrek Comparisons (optional)
Individual rekenrek
1. Arrange students in pairs.
2. Prompt each student to represent a number of his or her choice on the rekenrek.
3. Prompt each student to show his or her partner the rekenrek and say the name of the represented
number.
What number is represented on your rekenrek?
4. Prompt students to use words to describe the comparison of the two numbers. Display or provide
sentence stems.
__________ is more than __________.
__________ is the same number as __________.
__________ is less than __________.
Questions:
How did you determine your comparison statement?
How are the quantities ___ and ___ alike? How do you know?
How are the quantities ___ and ___ different? How do you know?
o How many more is ___ than ___?
o How many less is ___ than ___?
Extension:
Prompt students to circle the beads on the Rekenrek Comparisons page to show the numbers
they represented and the comparisons they made.
For example:
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Rekenrek Comparisons
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Activity 4: Comparing Numbers Using a Rekenrek – Part B
Materials:
Comparing Numbers Cards
Rekenrek
1. Arrange students in pairs.
2. Prompt each pair to choose one Comparing Numbers Card.
For the blank card, prompt each partner to choose his or her own number up to 20.
3. Prompt students to complete the comparison statement by circling the appropriate statement that
makes the comparison statement true.
For example:
Question:
How did you determine your comparison statement?
4. Prompt one partner to build the first number (the number on the left-hand side) and the other partner
to build the second number (the number on the right-hand side) on the rekenrek.
What number is represented by your rekenrek?
5. Prompt students to justify their comparison statement by comparing the numbers represented on the
rekenreks.
For example:
Questions:
How did you use the rekenrek to justify your comparison statement?
How are the quantities ___ and ___ alike? How do you know?
How are the quantities ___ and ___ different? How do you know?
o How many more is ___ than ___?
o How many less is ___ than ___?
4
is more than
8 is the same number as
is less than
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Comparing Numbers Cards
Cut along dotted lines.
4
is more than
8 15
is more than
18 is the same number as is the same number as
is less than is less than
6
is more than
6 13
is more than
12 is the same number as is the same number as
is less than is less than
10
is more than
10 13
is more than
16 is the same number as is the same number as
is less than is less than
11
is more than
1 9
is more than
10 is the same number as is the same number as
is less than is less than
19
is more than
19 18
is more than
8 is the same number as is the same number as
is less than is less than
_____
is more than
_____ _____
is more than
_____ is the same number as is the same number as
is less than is less than
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Activity 5: Handful of Cubes Materials:
Linking cubes – 20 per student
Blank paper
Blank Hand (optional)
1. Arrange students in pairs.
2. Prompt each student to trace one of his or her hands on blank paper.
3. Prompt each student to grab a handful of linking cubes.
4. Prompt students to count the number of cubes grabbed and record the number on their traced thumb.
5. Prompt each student to link the cubes to make a linking cube train.
6. Prompt partners to compare their linking cube trains. Display or provide sentence stems.
__________ is more than __________.
__________ is the same number as __________.
__________ is less than __________.
7. Prompt partners to determine who has more linking cubes.
8. Prompt the partner with the greater or larger number of linking cubes to circle the number written on
his or her traced thumb.
If both partners have the same number, allow students to determine how to note that on their
traced thumbs. Some students may circle the numbers on both thumbs. Others may circle neither
of the two numbers. Other students may choose to create a symbol to represent that the same
number was written on both traced thumbs.
Questions:
How did you determine your comparison statement?
How are the quantities ___ and ___ alike? How do you know?
How are the quantities ___ and ___ different? How do you know?
o How many more is ___ than ___?
o How many less is ___ than ___?
9. Repeat steps 3-8 four times, recording the number in each handful on a different finger.
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Blank Hand
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Whole Number Concepts: Generating Numbers
Activity 1: Generate a Set Using Objects – Kindergarten
Materials:
Number Cards: Set A – Kindergarten
More Than and Less Than Mat
Counters
1. Prompt students to select one Number Card and place the card in the number column of the More
Than and Less Than Mat.
2. Prompt students to use counters to represent the number shown on the card and place the counters in
the number column.
What number is represented by your counters?
3. Prompt students to use counters to generate a set that is less than the number and a set that is more
than the number. Place the counters in the appropriate column.
Questions:
How did you generate a set that was less than your number?
How did you generate a set that was more than your number?
Look/listen for:
Using objects to count out a number that is more or less than another number, excluding building
onto an existing set for a given number
Appropriate methods to use objects as tools, including building a number, counting on, or taking
one away, that provide indications that a student is transitioning away from solely counting to
comparing two numbers
4. Prompt students to use words to describe the comparison of the two sets. Display or provide sentence
stems.
__________ is less than __________.
__________ is more than __________.
Extension:
Pictorial models such as Five Frame, Ten Frame, or Double Ten Frame cards may be used
instead of counters.
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Number Cards: Set A – Kindergarten
Two sets of cards are provided.
3 5 6 8
9 10 12 14
15 16 17 18
3 5 6 8
9 10 12 14
15 16 17 18
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
More Than and Less Than
Less Than Number More Than
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Activity 2: More or Less Problems – Kindergarten
Materials:
20 Counters
1. Share the following situation with students.
Ethan has six gumballs. Make a set of gumballs that is more than Ethan’s set of
gumballs.
2. Prompt students to use counters to generate a set that is more than Ethan’s set of gumballs.
Questions:
What number did you make or represent?
How did you determine that your set is more than six?
Look/listen for:
Numbers greater than six
Models to justify thinking
Understanding of relative magnitude of numbers
3. Prompt students to use words to describe the comparison of their set to Ethan’s set. Display or
provide sentence stems.
6 is less than __________.
__________ is more than 6.
4. Share the following situation with students.
Kaylee has 15 stickers. Create a set of stickers that is less than Kaylee’s set of stickers.
5. Prompt students to use counters to generate a set that is less than Kaylee’s set of stickers.
Questions:
What number did you represent?
How did you determine that your set is less than 15?
Look/listen for:
Numbers less than 15
Models to justify thinking
Understanding of relative magnitude of numbers
6. Prompt students to use words to describe the comparison of their set to Kaylee’s set. Display or
provide sentence stems.
__________ is less than 15.
15 is more than __________.
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Activity 3: Generate One More or One Less – Kindergarten
Materials:
Number Cards: Set B – Kindergarten
Sticky notes
1. Arrange students in pairs.
2. Prompt students to select one Number Card.
3. Prompt each student to trade numbers with his or her partner.
4. Prompt students to determine a number that is one less than the number on their card.
5. Prompt students to record the number on a sticky note.
6. Prompt students to verify their answer with their partner.
7. Prompt students to determine a number that is one more than the number on their card.
8. Prompt students to record the number on a different sticky note.
9. Prompt students to use words to describe their numbers. Display or provide sentence stems.
__________ is one less than __________.
__________ is one more than __________.
Questions:
How did you determine the number that is one less than your number?
How did you determine the number that is one more than your number?
Look/listen for:
Appropriate methods to generate a number that is one more or one less
Understanding of relative magnitude of numbers
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Number Cards: Set B – Kindergarten
Two sets of cards are provided.
2 4 6 7
8 10 11 12
13 15 17 19
2 4 6 7
8 10 11 12
13 15 17 19
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Activity 4: Generate One More or One Less Problems
Materials:
Paper or sticky notes
1. Share the following situation with students.
It took Ruben 14 minutes to walk around the track. What is one minute less than 14
minutes?
2. Prompt students to determine and record the number that is one less than 14.
Questions:
What number did you represent?
How did you determine the number that is one less than 14?
Look/listen for:
Appropriate methods to generate a number that is one less than the given number
Understanding of relative magnitude of number
3. Prompt students to use words to describe the relationship between the two numbers. Display or
provide sentence stems.
__________ is one less than 14.
4. Share the following situation with students:
Landon has nine cookies. What is one more than nine cookies?
5. Prompt students to determine and record the number that is one more than nine.
Questions:
What number did you represent?
How did you determine a number that is one more than nine cookies?
Look/listen for:
Appropriate methods to generate a number that is one more than the given number
Understanding of relative magnitude of numbers
6. Prompt students to use words to describe the relationship between the two numbers. Display or
provide sentence stems.
__________ is one more than 9.
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Whole Number Concepts:
Using Magnitude to Compare Numbers Activity 2: Comparing Numbers Using the Number Path
Materials:
Number Path 1−10
Number Path 1−20 – 2 per person
Counters
1. Prompt students to place a counter on two different numbers on the Number Path 1−10.
For example:
1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 10
Questions:
How can we describe the relationship between the two numbers?
______ is more than ______.
______ is less than ______.
Which number is more than the other number?
o How can you use the number paths to prove your answer?
Which number is less than the other number?
o How can you use the number paths to prove your answer?
2. Compare the numbers ______ and ______ using the Number Path 1−10.
Questions:
How can we describe the relationship between the two numbers?
______ is more than ______.
______ is less than ______.
Which number is more than the other number?
o How can you use the number path to prove your answer?
Which number is less than the other number?
o How can you use the number path to prove your answer?
3. Prompt students to place a counter on one number on the Number Path 1−10.
Questions:
What number is less than your number?
What number is more than your number?
What number is one less than your number? One more?
The activity may be repeated using the Number Path 1−20.
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Number Path 1−10
1 2 3 4 5 6 7 8 9 10
Number Path 1−10
1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 10
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Number Path 1−20
Cut out the number paths (1-10 and 11-20). Tape or glue in the space indicated to make a number path from 1 to 20.
1 2 3 4 5 6 7 8 9 10
Tape o
r glu
e
1 2 3 4 5 6 7 8 9 10
Tape o
r glu
e
11 12 13 14 15 16 17 18 19 20
11 12 13 14 15 16 17 18 19 20
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Subitizing
Activity 1: Quick Images
Materials:
Dot Cards, Five Frame Cards, or Ten Frame Cards
1. Display a quick image for approximately 3-5 seconds.
Questions:
How many dots did you see? How did you know? Note: Students may respond orally or with a
written numeral.
Did anyone see it a different way? How did you see it?
Activity 2: Quick Images Strings
Materials:
Dot Cards, Five Frame Cards, or Ten Frame Cards
1. Display a quick image for approximately 3-5 seconds that has the same value as others in the given
string of quick images.
For example:
Questions:
How many dots did you see? How did you know?
Did anyone see it a different way? How did you see it?
Activity 3: I Wish I Had . . .
Materials:
Dot Cards, Five Frame Cards, or Ten Frame Cards
1. Display a quick image for approximately 3-5 seconds.
2. Say, “I have this number. I wish I had ______.”
For example, “I wish I had eight.”
Questions:
How many dots did you see? How did you know?
How many more dots are needed to equal _____? How did you know?
How many fewer dots are need to equal _____? How did you know?
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Five Frame Cards
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Ten Frame Cards
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Activity 4: Subitizing with a Rekenrek
Materials:
Rekenrek
Subitizing with a Rekenrek
1. Display a rekenrek for approximately 3-5 seconds that shows three beads pushed to the left on the
top row and four beads pushed to the left on the bottom row.
2. Complete the string by displaying the following arrangements:
5 beads on top
0 beads on bottom
5 beads on top
5 beads on bottom
6 beads on top
0 beads on bottom
8 beads on top
0 beads on bottom
7 beads on top
0 beads on bottom
2 beads on top
5 beads on bottom
0 beads on top
10 beads on bottom
Questions:
How many beads did you see? How did you know?
Did anyone see it a different way? How did you see it?
3. Repeat using additional strings such as the strings listed on Subitizing with a Rekenrek.
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Subitizing with a Rekenrek
2 beads on top 2 beads on top 5 beads on top
2 beads on bottom 4 beads on bottom 5 beads on bottom
4 beads on top 2 beads on top 4 beads on top
0 beads on bottom 6 beads on bottom 5 beads on bottom
3 beads on top 4 beads on top 5 beads on top
1 bead on bottom 4 beads on bottom 4 beads on bottom
1 bead on top 6 beads on top 4 beads on top
3 beads on bottom 2 beads on bottom 4 beads on bottom
8 beads on top 2 beads on top 6 beads on top
0 beads on bottom 1 bead on bottom 4 beads on bottom
7 beads on top 3 beads on top 6 beads on top
1 bead on bottom 2 beads on bottom 6 beads on bottom
6 beads on top 3 beads on top 7 beads on top
2 beads on bottom 1 bead on bottom 7 beads on bottom
5 beads on top 4 beads on top 6 beads on top
3 beads on bottom 2 beads on bottom 8 beads on bottom
10 beads on top 6 beads on top 8 beads on top
2 beads on bottom 6 beads on bottom 2 beads on bottom
9 beads on top 5 beads on top 8 beads on top
2 beads on bottom 5 beads on bottom 3 beads on bottom
9 beads on top 5 beads on top 8 beads on top
3 beads on bottom 6 beads on bottom 4 beads on bottom
8 beads on top 4 beads on top 9 beads on top
4 beads on bottom 8 beads on bottom 5 beads on bottom
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Representing Numbers and Comparing Numbers: Workstation 1
Use counters to show 16.
Use counters to show 12.
Compare the sets.
________ is more than ________.
________ is less than ________.
Representing Numbers and Comparing Numbers: Workstation 1
Use counters to show 16.
Use counters to show 12.
Compare the sets.
________ is more than ________.
________ is less than ________.
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Representing Numbers and Comparing Numbers: Workstation 2
What number is shown on the rekenrek? ______________
What number is shown on the rekenrek? ______________
Compare the sets.
________ is more than ________.
________ is less than ________.
Representing Numbers and Comparing Numbers: Workstation 2
What number is shown on the rekenrek? ______________
What number is shown on the rekenrek? ______________
Compare the sets.
________ is more than ________.
_________ is less than ________.
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Representing Numbers and Comparing Numbers: Workstation 3
15 is more than 13. How do you know?
9 is less than 11. How do you know?
12 is equal to 12. How do you know?
Representing Numbers and Comparing Numbers: Workstation 3 15 is more than 13. How do you know?
9 is less than 11. How do you know?
12 is equal to 12. How do you know?
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Find the Same Value
Materials:
Dot, Ten Frame, Rekenrek, and Number Cards
1. Distribute one card to each student.
2. Prompt students to move around the room to find three other students with a card that represents the
same value.
Question:
How do your cards represent the same value?
Look/listen for:
Use of counting or subitizing to determine the value represented on each card
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Dot, Ten Frame, Rekenrek, and Number Cards
Cut along dotted lines.
5
15
Cut along dotted lines.
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
9
13
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Cut along dotted lines.
20
17
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Composing and Decomposing Numbers to Ten Activity 1: Rocks and Containers
Materials:
Rocks and Containers
1. Display and read the following situation to the students.
Cameron has eight rocks. He has two containers to hold these rocks.
How many rocks can he place in each container?
2. Prompt students to record their ideas using counters, pictures, and/or number sentences to
answer the question.
Question:
Is there another way to place the rocks in the two containers?
Look/listen for:
Appropriate methods for composing and decomposing the number eight
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Rocks and Containers
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Activity 2: Ten Tower
Materials:
Linking cubes
1. Arrange students in pairs.
2. Prompt each pair to decide who will be Partner A and who will be Partner B.
3. Use the following directions to help students complete the activity.
Partner A:
Make a train of 10 linking cubes using two different colors (five of each color).
Break the tower into two parts.
Hide one of the parts behind your back.
Show Partner B the set of linking cubes that is not hidden.
Partner B:
How many linking cubes do you see?
How many linking cubes are behind your partner’s back? How do you know?
Partner B:
Put the train of linking cubes back together to create a train of 10.
Break the tower into two parts.
Hide one of the parts behind your back.
Show Partner A the set of linking cubes that is not hidden.
Partner A:
How many linking cubes do you see?
How many linking cubes are behind your partner’s back? How do you know?
Question:
How did you determine the number of linking cubes that were behind your partner’s back?
Activity 3: Beans in a Bag
Materials:
Dried beans
Resealable bag
Permanent marker
Advanced Preparation:
Place 10 or fewer dried beans in a resealable bag. Draw a line with a marker down the middle of
one side of the bag
1. Provide each student or pair of students with a bag of beans.
2. Ask, “How many ways can you arrange the beans in the bag?”
3. Prompt students to record their ideas using pictures, words such as “four on one side and four on the
other side,” or number sentences.
Question:
How did you determine the number of ways you could arrange the beans in the bag?
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Pre-Assessment: Kindergarten: Joining and Separating
Materials:
Counters
1. Display and read the following situation aloud:
Camille had five pencils. D’Shaun gave her three more. How many pencils does Camille have now?
2. Prompt students to use counters to solve the problem.
Question:
How did you use your counters to solve the problem?
Look/listen for:
Modeling the action of joining three counters with five counters
Using a counting strategy, such as counting all, counting on from the first number, and counting on
from the largest number
3. Display and read the following situation aloud:
Norma had six pennies. She gave two pennies to her sister. How many pennies does Norma have now?
4. Prompt students to use the counters to solve the problem.
Question:
How did you use your counters to solve the problem?
Look/listen for:
Modeling the action of separating two counters from six counters
Using a counting strategy, such as counting back or counting remaining
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Joining and Separating Problems: Result Unknown
Activity 1: Joining Result Unknown
Materials:
Story Mat
Joining Result Unknown Cards
Counters
1. Display and read one problem aloud from the Joining Result Unknown Cards.
Questions:
What do you know?
What do you need to know?
2. Prompt students to use the Story Mat and counters to model the situation.
Questions:
How did you use your counters to determine the result?
How many ____ were there at the start? What happened next?
Are the objects in the problem being joined together or separated? How do you know? Prompt
students to respond with the joining or separating gesture.
What do we need to determine?
3. Ask, “How many counters are being joined together to determine the result?”
4. Display the following sentence stems for students to use when creating a number sentence for the
context of the problem. Choose the most appropriate number sentence based on previous instruction
with symbolic representations.
_____ and _____ is _____. _____ is _____ and _____.
+ = = +
_____ and _____ is _____. _____ is _____ and _____.
+ = = +
_____ plus _____ equals _____ _____ equals _____ plus _____
_____ + _____ = _____ _____ = _____ + _____
5. Repeat steps 1-4 using the remaining word problems.
Look/listen for:
Modeling the action of joining sets of objects
Using direct modeling or counting strategies to solve the word problem
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Story Mat
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Joining Result Unknown Cards Cut along dotted lines.
Problem A
Gabby had 3 flowers. Jillian gave her 2 more flowers. How many
flowers does Gabby have now?
Problem B
There were 5 birds sitting in a tree. Then 4 more birds flew up to
sit in the tree. How many birds are in the tree now?
Problem C
Angel had 8 buckets in the sandbox. Jocelyn gave her
2 more buckets. How many buckets does Angel have now?
Problem D
There were 4 children playing in the playhouse. Then 6 more
children came to play in the playhouse. How many children are
playing in the playhouse now?
Problem E
There were 7 dogs at the park. Then 1 more dog came to the
park. How many dogs are at the park now?
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Activity 2: Separating Result Unknown
Materials:
Story Mat
Separating Result Unknown Cards
Counters
1. Display and read one problem aloud from the Separating Result Unknown Cards.
Questions:
What do you know?
What do you need to know?
2. Prompt students to use the Story Mat and counters to model the situation.
Questions:
How did you use your counters to determine the result?
How many ____ were there at the start? What happened next?
Are the objects in the problem being joined together or separated? How do you know? Prompt
students to respond with the joining or separating gesture.
What do you need to determine?
3. Ask, “How many counters were separated from the counters that were there at the start? How does
this help us to determine the result?”
4. Display the following sentence stems for students to use when creating a number sentence for the
context of the problem. Choose the most appropriate number sentence based on previous instruction
with symbolic representations.
_____ take away _____ is _____. _____ is _____ take away _____.
— = = —
_____ take away _____ is _____. _____ is _____ take away _____.
— = = —
_____ minus _____ equals _____ _____ equals _____ minus _____
_____ — _____ = _____ _____ = _____ — _____
5. Repeat steps 1-4 using the remaining word problems.
Look/listen for:
Modeling the action of separating a set of objects from a given set of objects
Using direct modeling and counting strategies to solve the word problem with counters
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Separating Result Unknown Cards
Cut along dotted lines.
Problem A
Jillian had 3 jump ropes. She gave 2 jump ropes to Gabby. How
many jump ropes does Jillian have now?
Problem B
There were 10 boys at the park. Then 6 boys went home. How
many boys are at the park now?
Problem C
Jocelyn had 9 shovels in the sandbox. She gave 3 shovels to
Angel. How many shovels does Jocelyn have now?
Problem D
There were 7 girls playing in the playhouse. Then 4 girls went to
the sandbox. How many girls are playing in the playhouse now?
Problem E
There were 8 dogs at the park. Then 5 dogs went home. How
many dogs are at the park now?
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Activity 3: Joining and Separating: Result Unknown
Materials:
Story Mat
Joining and Separating: Result Unknown Cards (*Kindergarten appropriate)
Counters
1. Display and read one problem aloud from the Joining and Separating: Result Unknown Cards.
Questions:
What do you know?
What do you need to know?
Are the objects being joined together or separated in the problem? How do you know? Prompt
students to respond with the joining or separating gesture.
How many ____ were there at the start? What happened next?
2. Prompt students to use their Story Mat and counters to model the problem.
Questions:
How did you use your counters to determine the result?
How many ____ were there at the start? What happened next?
Are the objects being joined together or separated in the problem? How do you know? Prompt
students to respond with the joining or separating gesture.
What do we need to determine?
3. Ask, “How many counters are being joined together to determine the result?” or “How many counters
were separated from the counters that were there at the start?”
4. Prompt students to explain how they determined the result using words, pictures, or a number
sentence.
5. Repeat steps 1-4 using remaining word problems.
Look/listen for:
Modeling the action of joining sets of objects or separating sets of objects
Using direct modeling and counting strategies to solve the word problem
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Joining and Separating: Result Unknown Cards Cut along dotted lines.
*Problem A
There were 3 boys playing by the slide. Two more boys came to
play by the slide. How many boys are playing by the slide now?
*Problem B
There were 8 squirrels in a tree. Four squirrels climbed out of the
tree. How many squirrels are in the tree now?
*Problem C
There were 6 girls sitting on the bench. Four of the girls went to
play on the slide. How many girls are on the bench now?
Problem D
Isabella had 12 toys at the park. Marcus gave her 3 more toys.
How many toys does Isabella have altogether?
Problem E
Miguel saw 5 ants in the dirt. Then 2 ants left to hide. How many
ants are still there?
*Kindergarten (quantities up to 10)
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Part-Part-Whole Problems
Activity 1: Making a Part-Part-Whole Mat
Materials:
Part-Part-Whole: Whole Unknown Cards (*Kindergarten Appropriate)
Painter’s tape or masking tape
1. Create a part-part-whole mat on the floor using painter’s tape. Each box should measure large enough
for several students to stand in each box. Label each box with a P or a W.
P P
W
2. Display and read one problem aloud.
Questions:
What do you know?
What do you need to know?
Is there an action in this problem? How do you know?
How many ______ are in one part? How many ______ are in the other part?
Do we know the total number of ______? Do we know the parts of the set of ______?
3. Prompt students to stand in the boxes to represent the known parts on the part-part-whole
representation.
How did you know the number of students needed to represent the situation?
4. Ask, “How can we determine the number of ______?”
5. Prompt the students representing the parts to move to the whole box.
What do the students in the whole represent? How do you know?
6. Repeat steps 2-5 for the remaining problems.
Look/listen for:
Understanding the parts and the whole in a word problem
Using strategies to solve the part-part-whole word problem
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Part-Part-Whole: Whole Unknown Cards Cut along dotted lines.
*Problem A
The zoo has 5 brown snakes and 4 black snakes. How many
brown and black snakes are at the zoo?
*Problem B
Two polar bears and 3 brown bears are napping on the rocks.
How many bears are napping on the rocks?
*Problem C
There are 6 birds and 2 squirrels in a tree. How many animals
are in the tree?
*Problem D
There are 6 adult sea lions and 1 baby sea lion swimming in the
water. How many sea lions are swimming in the water?
Problem E
Eight big tigers and 4 small tigers are napping on the grass. How
many tigers are napping on the grass?
Problem F
There are 9 monkeys in the tree and 7 monkeys by the water.
How many monkeys are there altogether?
*Kindergarten (quantities up to 10)
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Activity 2: Using a Part-Part-Whole Mat
Materials:
Part-Part-Whole: Whole Unknown Cards (*Kindergarten Appropriate)
Part-Part-Whole: Part Unknown Cards Grade 1
Part-Part-Whole Mat
Counters
1. Display and read one problem aloud.
Questions:
What do you know?
What do you need to know?
Is there an action in this problem? How do you know?
Do we know the total number of ______? Do we know the parts of the set of ______?
How many ______ are in one part?
How many ______ are in the other part?
How many ______ are in the whole?
2. Prompt the students to use counters to represent the given part(s) and/or whole on the
Part-Part-Whole Mat.
How did you know the number of counters needed to represent the situation?
3. Ask, “How can we determine the number of ______?”
4. Prompt students to use the Part-Part-Whole Mat and counters to solve the problem.
5. Repeat steps 1-4 for the remaining problems.
Look/listen for:
Understanding the parts and the whole in a word problem
Using strategies to solve the part-part-whole word problem
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Part-Part-Whole Mat
Whole
Part
Part
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
4-2-1 Addition and Subtraction Materials:
4-2-1: Solving Addition and Subtraction Problems Kindergarten
4-2-1: Solving Addition and Subtraction Problems First Grade
1. Prompt students to make a group of four.
2. Display and read the problem aloud.
3. Prompt students to work together to solve the problem.
4. Prompt students to split into two groups of two.
5. Display and read the problem aloud.
6. Prompt students to work together to solve the problem.
7. Prompt students to work alone for the next problem.
8. Display and read the problem aloud.
Question:
Were the objects in the problem being joined together or separated? How do you know?
Look/listen for:
Modeling the action of joining sets of objects or separating sets of sets from a set of objects
Understanding of the parts and the whole in a word problem
Modeling the comparison of two sets with the difference unknown
Strategies to determine the unknown in a word problem
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
4-2-1: Solving Addition and Subtraction Problems Kindergarten
Group of 4
Carter had 7 gumballs. Jason gave him 4 more gumballs. How many gumballs does Carter have now?
Group of 2
Mr. Hudson has 10 stickers. He gave 5 stickers to Miguel. How many stickers does Mr. Hudson have now?
On My Own!
Molly has 6 pink gumballs and 3 white gumballs. How many gumballs does Molly have in all?