Skills:
Solving problems using logic
Teaching Logic, Anyone?
Using visual reasoning,
mathematical language, and
number concepts
Students use logic, visual reasoning, and number
concepts to work with Venn diagrams.
Tasks
Tier 1
Differentiated Activities for Teaching Key Math Skills: Grades 2-3 © Lee & Miller, Scholastic Teaching Resources
Below Level
Tier 2
On Level
Tier 3
Above Level
Identify the location of numbers in a Venn diagram.
X
X
X
Answer questions about Venn diagrams.
X
X
X
Complete a new Venn diagram using given rules.
X
X
X
Apply mathematical terms to solve problems.
X
X
X
X
X
Use number concepts to solve problems.
Formulate questions about Venn diagrams.
X
Getting Started
See the tips below for introducing the lesson. Make copies of the student data sheet (page 64) and the
appropriate leveled activity sheet for each group of learners (pages 65–67).
Access prior knowledge by explaining that logic is organized thinking using exact language, orderly
reasoning, and facts. Use the language of logic, focusing on and/or. For example: Who is a boy and 8 years old?
Compare with: Who is a boy or 8 years old? Review Venn diagrams, positional words (outside, inside, within), and
plane figures.
Tier 1
• Use the Diagram: Point out
that detectives use logic to solve
mysteries and scientists use it to
figure out how and why things
work. To focus on parts of the
Venn diagram, have students
outline each shape using different
colored highlighters. Also have
students block off parts of
the diagram with paper strips.
Then pose questions to check
comprehension and model
answering. For example: I see
a 10 inside 2 shapes. Who can
trace one of the shapes? Who can
outline the other? Who can point to
where those shapes overlap?
• Finish the Venn Diagram: Have
pairs complete this activity. As
needed, review odd and even
numbers.
• Look Back: Assemble the group
to answer and discuss these
questions together.
Tier 2
• Use the Diagram:
Discuss the data sheet
before students begin
the activity sheet. Invite
students to work in
pairs. Provide different
colored highlighters for
students to outline each
shape in a distinct color.
• Finish the Venn
Diagram: As needed,
review the concepts of
odd and even and the
mathematical terms
sum, product, and
multiple.
• Look Back: Assemble
the group to answer
and discuss the
questions together. Ask:
Why is it possible to
have different correct
answers for item 10?
Tier 3
• Use the Diagram: Talk about the
data sheet together, and ask about
the position of numbers in the Venn
diagram. Invite children to explain how
they know to focus on a certain area
and ignore another. Have students
work in pairs to answer items 1–6.
Remind partners to read each
statement carefully to check that they
have followed its clues precisely.
• Finish the Venn Diagram: Review
the mathematical terms: odd and
even; sum; multiple; product. Tell
children that different solutions are
correct. After they finish, compare and
contrast completed diagrams, looking
for similarities and differences as they
adhere to the given rules.
• Look Back: Have children use
questions 1–6 to generate their own
logic problems for the Venn diagram.
Assemble the group to pose and
solve each other’s items.
63
Name
Skills:
Date
Solving problems using logic
Logic, Anyone?
Using visual reasoning,
mathematical language, and
number concepts
Data Sheet
Look at the figure below. It has a circle, a square, and a
triangle. The three shapes overlap. Some numbers are inside
Differentiated Activities for Teaching Key Math Skills: Grades 2-3 © Lee & Miller, Scholastic Teaching Resources
only one shape. Some numbers are inside two shapes at the
same time. Some are inside all three shapes at the same time.
Logic is
careful reasoning.
Logic can help you
find a clear and
correct answer.
Some numbers aren’t inside any of the shapes.
8
6
1
7
9
2
3
10
4
64
5
Name
Logic, Anyone?
Date
Activity Sheet
Use the Diagram Answer each logic question.
1.
Which two numbers are not inside any shape?
Differentiated Activities for Teaching Key Math Skills: Grades 2-3 © Lee & Miller, Scholastic Teaching Resources
2. Which number is inside all three shapes?
3. Which number is inside the square only?
4. Which number is inside the triangle only?
5. Which two numbers are inside the circle only?
6. Which two numbers are in both the square and triangle?
7. Which two numbers are in both the circle and square?
8. Which two numbers are in both the circle and triangle?
Finish the Venn Diagram
Use the rules given below. Write:
A
B
44 1 in Circle A only.
44 2 in Circle B only.
44 3 in both circles at once.
44 4 in both circles at once.
44 5 outside both circles.
44 an even number between 6 and 10 in Circle B only.
44 an odd number between 6 and 10 in both circles at once.
Look Back Answer these questions about your Venn diagram.
9. Which circle has more odd numbers in it than the other?
10. Which numbers between 6 and 10 were not used?
65
Name
Logic, Anyone?
Date
Activity Sheet
Use the Diagram Answer each logic question.
1.
Which numbers are not inside any shape?
Differentiated Activities for Teaching Key Math Skills: Grades 2-3 © Lee & Miller, Scholastic Teaching Resources
2. Which numbers are inside the circle only?
3. Which number is inside the square only?
4. Which number is inside the triangle only?
5. Which number is in all three shapes?
6. Which numbers are in the square and triangle?
7. What addition problem and solution can you make with the numbers in
both the circle and square?
Finish the Venn Diagram
Use the rules given below. Write:
44 1 only in Circle A.
A
44 2 only in Circle B.
44 9 outside the circles.
44 an odd number between 2 and 6 in
both circles at once.
44 an even number between 5 and 8 in
both circles at once.
44 a multiple of 10 in Circle B only.
44 the product of any number and 0 in both circles at once.
Look Back Answer these questions about your Venn diagram.
8. Which circle has more numbers in it?
9. What is the sum of all numbers inside the circles?
66
B
Name
Logic, Anyone?
Date
Activity Sheet
Use the Diagram Answer each logic question.
1.
Which numbers are not inside any shape?
Differentiated Activities for Teaching Key Math Skills: Grades 2-3 © Lee & Miller, Scholastic Teaching Resources
2. Which number is in all three shapes?
3. Which numbers are in the circle only?
In the square only?
In the triangle only?
4. What is the sum of numbers in both the square and triangle?
5. What is the sum of numbers in both the circle and square?
6. What is the product of numbers in both the circle and triangle?
A
Finish the Venn Diagram
Use the rules given below. Write:
44 9 outside the circles.
44 1 in Circle A only.
44 an odd number between 2 and 6 in
B
C
all three circles at once.
44 a multiple of 10 in Circle C only.
44 the sum of 0 and 7 in Circles A and B only.
44 the product of any number and 0 in
Circles B and C only.
Look Back
Write a question about your Venn diagram.
67
Answer Key
Logic, Anyone?
Differentiated Activities for Teaching Key Math Skills: Grades 2-3 © Lee & Miller, Scholastic Teaching Resources
Tier 1, page 65: Use the Diagram:
1. 4, 8 2. 2
3. 6 4. 3
5. 7, 9 6. 2, 5
7. 1, 2 8. 2, 10
Finish the Venn Diagram: Sample at right:
Look Back: 9. A 10. Answers will vary.
Tier 2, page 66: Use the Diagram:
1. 4, 8 2. 7, 9
3. 6 4. 3
5. 2 6. 2, 5
7. 1 + 2 = 3
Finish the Diagram: Sample at right:
Look Back: 8. B 9. Answers will vary.
80
A
B
7
1
3
4
2
6
5
9
A
B
o
1
3
6
2
10
Tier 3, page 67: Use the Diagram:
1. 4, 8 2. 2
3. 7, 9; 6; 3 4. 2 + 5 = 7
5. 1 + 2 = 3 6. 2 × 10 = 20;
Finish the Diagram: Sample at right:
Look Back: Answers will vary.
A
9
B
1
C
7
3
0
10