With this lesson, students are encouraged to investigate subtraction and gain a deeper comprehension of how addition and subtraction relate to one another. Students are going to: 
- Apply techniques for addition and subtraction. 
- Write numerical sentences or equations to illustrate what they are thinking. 
- Investigate various operations to plan and attain the target amount.

- What mathematical representations exist for relationships? 
- What are some applications for expressions, equations, and inequalities in the quantification, modeling, solving, and/or analysis of mathematical situations? 
- How can the study of mathematics aid in clear communication? 
- How are relationships in mathematical contexts described by patterns? 
- How can identifying regularity or repetition help with problem-solving efficiency? 
- How are numbers represented, compared, quantified, and modeled using mathematics?

- Subtraction: To take one quantity away from another.

- numeral cards 0–20. (M-1-3-3_Numeral Cards) 
- copies of Goal Number Recording Sheet (M-1-3-3_Goal Number Recording Sheet) 
- ten-frames or twenty-frames, one per student plus extras to have available (M-1-3-3_Twenty-Frames) 
- number line, one per student (M-1-3-2_Number Line) 
- Classroom manipulatives such as connecting cubes, snap cubes, small blocks, base-ten blocks, chips, etc. should be available for students to use if they so choose.

- Students mastery of certain strategies and areas in which they still need more support will be identified with the help of observations made during work time. 
- After the lesson, have students share their tactics and the points they received for each Think-Pair-Share activity.

Explicit instruction, modeling, scaffolding, and active engagement
W: Give students the twenty-frames as a tool to improve their thinking. 
H: Instruct students to attempt to reach their target number of 7 by using the numbers 4, 5, 3, and 0. After they've experimented in various ways, inform them that you now want them to try using as many of the four provided numbers as they can to reach the target of 7. 
E: Give each group of four or five students one deck of cards. Give them four cards to draw, and then instruct them to draw a fifth card, which will be their target number. 
R: Ask students to describe the methods and approaches they would use to get to the target number. Remind them that since the cards represent their points, they should use as many of them as they can. On the recording sheet, they will write the formula for their plan. 
E: Ask students to share their work in pairs and provide an explanation of how they arrived at their goal numbers. 
T: Give students cards with the numbers 0–10, 0–50, or 0–100 to change the numbers. 
O: In this lesson, the use of addition and subtraction in the same equations is introduced. 

"Ten-frames and number lines have been our go-to tools for solving addition and subtraction problems. Today, we're going to play a game called Goal Number using our knowledge of addition and subtraction."

Show a twenty-frame (M-1-3-3_Twenty-Frames). Instruct students who haven't used a twenty-frame recently to spend a few minutes observing how the numbers are arranged. They ought to observe that two ten-frames are used to create a twenty-frame. The darker lines, which stand for a 10 or a 5, should be visible to them.

"What do you notice about this twenty-frame tool?"

Use provocative questions like, "How many squares are on the top row? "if students aren't paying attention to what you're looking for. "To what extent does this line extend to the left? How many numbers are on the right?"

Ask students, "How many more chips would you need to make 11 if you had four on the twenty-frame?" Utilize the twenty-frame to model the topics they discuss.

Let the students know they will practice hitting a target number today. "Which numbers would you use, if you had them, to reach a goal number of seven?”

Ask students to discuss potential strategies with their groups of four or five to reach the target number.

"If using as many numbers or cards as possible is the objective, discuss with your group the best approach that will work." (Possible strategies include combining addition and subtraction, starting with the smallest numbers, etc.)

Encourage groups to present their strategies after a short while. Capture them on a larger copy of the M-1-3-3_Goal Number Recording Sheet.

"You will play the Goal Number game in pairs for several rounds today. You will write down the final equation to determine the tactics you use and the points you receive."

Assign one partner to obtain the M-1-3-3_Numeral Cards and the other to the M-1-3-3_Goal Number Recording Sheet. Together, the partners should locate a suitable location for play. Make sure you have enough time to speak with each partner pair at least once or give the students enough time to play multiple rounds.

As the allotted time has elapsed, assemble the pupils and ask them to disclose the total points they have earned from the rounds they have participated in. Discuss the strategies students used to get the most points. Discuss which numbers were the most difficult to achieve and why they believe that was the case.

Make a poster for the class that highlights the game's "high points"—optional.

Extension:

Expansion: Modify the Goal Numbers to accommodate your students' needs. Count cards with up to 50 or 100 digits for advanced students.

Workstation or Small Group: Provide number lines (M-1-3-2_Number Line) to students who struggle with mental strategies or twenty-frames. After having students circle the goal number on the number line, have them try different approaches to achieving that goal number using the numeral cards.