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Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Automaticity
- Equation
- Expression
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
The purpose of this benchmark is to build students’ automaticity with addition facts with sums to 20 and related subtraction facts. Students in grade 1 worked to recall sums within 10 and the related subtraction facts. In grade 3, students will compose and decompose four-digit numbers in multiple ways, as well as fluently adding and subtracting multi-digit whole numbers.- Instruction focuses on the fact that automaticity is usually the result of repetition and practice.
- Instruction of this benchmark should not be in isolation from other benchmarks that emphasize understanding.
- Instruction should not focus on speed in the classroom.
- Instruction may initially include explicit strategies such as doubles, doubles plus one, making a ten and fact families.
- The correct way to assess automaticity is to observe students within the instructional setting as they complete problems that involve addition and subtraction. Even though such problems can typically be done without automaticity they will be done with less effort with automaticity.
Common Misconceptions or Errors
- Students may rely heavily on visual representation or manipulatives.
Strategies to Support Tiered Instruction
- Teacher provides the addition expression 8 + 6 and has students provide the sum. Once they have given the correct sum of 14, teacher asks “Is there another fact with the same sum?” If students are able to provide another addition expression, teacher asks them to find another one and repeats with subtraction expression, 17 – 9. Students should provide the difference of 8. Students may need to use a manipulative to assist in determine the difference. Once students have given the correct difference, teacher asks “Can you give me a related subtraction equation?”
- Example:
- Teacher co-creates a real-world scenario using a set of given numbers: 6, 7, and 13. Once students have helped to develop an appropriate real-world scenario, teacher discusses what might happen with the problem if the scenario is changed to the inverse operation. The teacher may find that students are not creating a true equation from the scenario they shared. Consider discussing how the numbers are related and how they are affected when the inverse operation is used.
- Teacher provides manipulatives like two color counters and asks students to create a representation of 12. Depending on how they represent the number six, the teacher has them separate the counters into two addends. They may have 12 red counters and 0 yellow showing. The equation is 12 + 0 = 12. The teacher asks them how they could create a different representation, but with the same sum. Manipulation of the counters is continued until students can identify all sets of two addends that equal 12. Students represent their model with an equation.
- Teacher provides a real-world problem using numbers up to 20.
- For example, Gavin has 14 toy cars. His brother takes 6 of his toy cars. How many toy cars does he have now? Students use a manipulative to helps solve the problem. The teacher acts out the scenario with the students, then represents the problem in an equation.
- Once students create their models, teacher asks them to draw the models on paper, bridging students between concrete manipulatives and drawings. Students should always write the equation to represent any of their models to help move the student towards abstract thinking.
Instructional Tasks
Instructional Task 1 (MTR.3.1)
Using any number between 11-20 as the target number, provide students with digit cards 1-9.- Part A. Have students select a digit card to recall the missing addend needed to make the target number.
- Part B. Work mentally to create an equation that is equal to the target number.
Instructional Task 2 (MTR.5.1)
Create two addition equations and two related subtraction equations using only the digits 1, 4, 7, and 3. (Digits can be combined and used more than once.)
Instructional Items
Instructional Item 1
What subtraction equation can be used to determine the value of 5+13?
a. 19-5 =14
b. 18–5=13
c. 12–8=4
d. 13–5=8
Instructional Item 2
a. 8 + 12b. 15 + 4c. 11 + 9d. 6 + 13e. 3 + 7f. 14+4g. 10+10
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
Related Courses
Related Access Points
Related Resources
Formative Assessments
Lesson Plans
Perspectives Video: Experts
Student Center Activities
Worksheets
STEM Lessons - Model Eliciting Activity
In this Model Eliciting Activity, MEA, The Give A Cheer Yearbook Committee needs the students' assistance to determine the best company to purchase the school yearbooks. Students will need to consider the cost, tax, and delivery time in their decision. In a “twist,” students are given additional information about shipping cost and are asked to determine if their procedure for ranking should change.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx
MFAS Formative Assessments
Students are asked to solve six addition within 20 problems and to explain their strategies for solving each problem.
Students are asked to solve six subtraction within 20 problems and to explain their strategies for solving each problem.
Students are assessed on their fluency with addition facts within 20.
Student Resources
Worksheet
Parent Resources
Perspectives Video: Expert
Explore ways students may solve addition problems within 100 and how to support their understanding in this video.
FCR-STEM’s Count Us In! initiative is designed to support out-of-school providers and parents in fostering math success and enjoyment among K-5 children.
Type: Perspectives Video: Expert
Student Center Activities
In this game, students develop fluency with addition or multiplication facts and strengthen number sense through fast-paced problem-solving.
FCR-STEM’s Count Us In! initiative is designed to support out-of-school providers and parents in fostering math success and enjoyment among K-5 children.
Type: Student Center Activity
In this game, students bop balloons into the correct basket by solving math facts and matching them to their answers to strengthen fluency through movement-based play.
FCR-STEM’s Count Us In! initiative is designed to support out-of-school providers and parents in fostering math success and enjoyment among K-5 children.
Type: Student Center Activity
Worksheets
Addition Flash Cards Single Digit Numbers Answers to 20
Type: Worksheet
Addition Flash Cards Two Digit Answers from 10 to 20
Type: Worksheet
Subtraction Flash Cards Related to Addition with Single Digit Numbers with Answers to 20
Type: Worksheet
