For Educators

Subtraction Strategy Spotlights

In this activity, students will demonstrate their ability to use a variety of strategies to mentally solve subtraction problems. Understanding the way these strategies work helps build students’ number sense, flexibility with numbers, and confidence in manipulating numbers in a variety of ways. Students will learn, review, and practice using four subtraction strategies before showing their strategy skills on a mini quiz.

Common Core State Standards

Mathematical Practices:

MP2	Reason abstractly and quantitatively.
MP3	Construct viable arguments and critique the reasoning of others.
MP7	Look for and make use of structure.
MP8	Look for and express regularity in repeated reasoning.

1st Grade

CCSS.Math.Content.1.OA.B.3 – Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)

CCSS.Math.Content.1.OA.B.4 – Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8.

CCSS.Math.Content.1.OA.C.5 – Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

CCSS.Math.Content.1.OA.C.6 - Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

CCSS.Math.Content.1.NBT.B.2.A – Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: 10 can be thought of as a bundle of ten ones — called a "ten."

CCSS.Math.Content.1.NBT.B.2.B – Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

CCSS.Math.Content.1.NBT.B.2.C – Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

CCSS.Math.Content.1.NBT.C.5 – Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

CCSS.Math.Content.1 NBT.C.6 – Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

2nd Grade

CCSS.Math.Content.2.OA.B.2 - Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.

CCSS.Math.Content.2.NBT.B.5 - Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

CCSS.Math.Content.2.NBT.B.7 - Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

CCSS.Math.Content.2.NBT.B.8 - Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.

CCSS.Math.Content.2.NBT.B.9 - Explain why addition and subtraction strategies work, using place value and the properties of operations.

3rd Grade

CCSS.Math.Content.3.NBT.A.2 - Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationships between addition and subtraction.

Downloads

Subtraction strategy PowerPoint

Note-taking guide

Optional assessment

Objectives:

Students will be able to use a variety of number-sense based strategies to mentally solve subtraction problems.

Students will use writing to reflect on the effectiveness and efficiency of each strategy used.

Materials:

• Building Blocks of Math series, specifically Subtraction

• Subtraction Strategy Spotlights PowerPoint Presentation

• Subtraction Strategy Spotlights Note-Taking Guide (1 per student)

• Optional Assessment: Subtraction Strategy Spotlights Mini Quiz (1 per student)

• Optional: Manipulatives (counters, beads, tokens, base ten blocks etc.)

• Optional: Blank tens frames

• Optional: Blank number lines

Differentiation Considerations:

For additional support, allow students to use manipulatives, blank tens frames, and/or blank number lines to help make the subtraction strategies more concrete and therefore easier to understand. Students can physically move manipulatives or draw jumps on number lines to demonstrate subtraction.

Addition Stratagies Highlights:

• Counting Back

• Finding Tens

• Number Lines

• Near Doubles

Procedures:

These procedures are general and can be applied to each strategy spotlighted in this activity.

Name and describe the strategy using the slides in the presentation.
Review/model your thinking aloud for both examples, highlighting the strategy and allowing time for students to process and ask relevant questions.
3Transition and provide one note-taking guide to each student. Present the first problem and provide them 1-2 minutes for students think independently and solve the problem in their guide. Next, have students spend another 1-2 minutes sharing their strategy choice and thinking with a neighbor. Finally, allow 2-3 students to share their thinking with the entire class. If possible, determine students to share ahead of time. It can be beneficial to highlight strong uses of a strategy or to address any major misconceptions here. Repeat these steps with the remaining problems on the note-taking guide.
Read the written response question aloud and provide 3-5 minutes for students to reflect and respond independently. Provide time for 2-3 students to share their thinking and encourage students to add anything interesting from their peers to their own written responses.
Summarize the activity by reviewing the strategy and readdressing any major misconceptions.
Repeat steps 1-5 for each strategy. Consider highlighting one strategy at a time (per class period, per week, etc.) and practicing related problems so students have time to practice and develop their strategic thinking.

Optional: After students have had exposure to and practice using all four strategies highlighted in this activity, consider using the optional mini quiz as a form of assessment. Here, students are provided four subtraction problems and asked to solve them using whatever strategies they would like. In addition, students must justify why they chose the strategies they did.