Grade 4: “Making 1 through 12”
Lesson:
Approx. time:
Making 1 through 12
45 minutes
A. Focus and Coherence
Students will know…
 A variety of equations can be created using at least 2
different digits.
CCSS-M Standards: 4.OA.2; 4.OA.5; 4.OA.4
SMP’s: 1, 3, 6, 7
B. Evidence of Math Practices
What will students produce when they are making sense,
persevering, attending to precision and/or modeling, in
relation to the focus of the lesson?
Students will be able to…
 Create equations for the numbers 1 through 12 by
using at least 2 digits from the numbers 3, 4, 5, and 6.
Students will make sense and persevere by:
 Re-stating the problem
 Coming up with a solution pathway before jumping in
to a solution
 Determining the reasonableness of their answer
Student prior knowledge:
 Addition, subtraction, multiplication, and division of
single digit and two-digit whole numbers.
Which math concepts will this lesson lead to?
 Order of operations
 Creating and solving algebraic equations
Students will critique the reasoning of others by:
 Listening to other students’ solutions and agreeing or
disagreeing with them
 Understanding others’ solution pathways and
problem-solving methods
Students will attend to precision by:
 Using the equal sign correctly and appropriately
 Using precise language to explain why an equation
does (or does not) work for a given number
Students will look for and make use of structure by:
 Using an equation from one number to assist in
creating subsequent equations for other numbers.
Essential Question(s)
How can there be multiple equations to create the same number?
For example, how can 11 = 3 x 5 - 4 and 11 = (6 ÷ 3) + 5 + 4
Formative Assessments
Whole-group student share out of responses.
Ticket-Out-The-Door reflection question.
Anticipated Student Preconceptions/Misconceptions
Students will be unable to come up with an entire list for creating the numbers 1 – 12.
Materials/Resources
Cut-out tiles as needed (see attached)
C. Rigor: Conceptual Understanding, Procedural Skills and Fluency, and Application
What are the learning experiences that provide for rigor? What are the learning experiences that provide for evidence of
the Math Practices? (Detailed Lesson Plan)
Warm Up
Fill in the three empty boxes with the numbers 2, 3, and 5 to make the equation true:
12
=
×
+
Lesson
Directions to Students (write on the board):
Using only the numbers 3, 4, 5, and 6, create the numbers 1 – 12 using at least 2 of the numbers. You can only use a
number once in an equation. Any mathematical operation is acceptable.
1) Have students read the prompt to themselves, then have a few students read the prompt out loud.
2) Talk about what this prompt means as a class, before students jump in to finding solutions.
3) Create a list on the board:
1=
7=
2=
8=
3=
9=
4=
10 =
5=
11 =
6=
12 =
4) Optional. Pass out the number tile cut-outs and the graphic organizer for using the cut-outs (see attached). This
may help some students manipulate equations and physically move things around. Even if students use the
manipulatives, they still need to record their work on a piece of paper.
5) Give students individual think time, and then pair-share time, to discuss how they could “make 1” using at least 2
numbers from the digits 3, 4, 5, and 6. Have a few different students share their responses and explain their
thinking.
Possible solutions:
1=6–5
1=3+4–6
= 7 – 6
6) Give students individual think time, and then pair-share time, to discuss how they could “make 2” using at least 2
numbers from the digits 3, 4, 5, and 6. Have a few different students share their responses and explain their
thinking.
Possible solutions:
2 = (6 + 4) – (5 + 3)
= 10 – 8
2 = (5×4) – (6×3)
= 20 – 18
7) Have students work in partners to create the rest of their list. On their papers, they should have all of the numbers
listed, 1 – 12, with some space in between each number to show work, if needed.
Not all students’ lists will look the same, and that’s ok. As students are working, circulate the room and monitor
their progress, assisting students with guiding questions, when needed. Be prepared to call on certain students
during the whole class share-out.
8) Whole class share-out. Have different students share their responses for each number, 3 – 12, as well as their
thinking behind their response. Some students may have something different on their list than what you put up as
the class list, and they may want to share how their way is “different.” It’s okay to put up more than 1 solution for a
given number. Students should be agreeing or disagreeing with each solution that gets put on the board, and
include arguments for those responses that they don’t agree with.
9) The whole list, 1 – 12, should be complete by the end of the class, with student agreement.
Closure –
Ticket-Out-The-Door reflection question:
What did you learn from today’s activity?
3 4 5 6 + + – –
÷ ÷ × ×
3 4 5 6 + + – –
÷ ÷ × ×
3 4 5 6 + + – –
÷ ÷ × ×
1=
2=
3=
4=
5=
6=
7=
8=
9=
10=
11=
12=