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Counting Houses TaskMary, Nick, and Jean are collecting donations to support homeless people. Each student starts on a different path. The houses are side-by-side. Which student will visit the most houses and how do you know? Write an equation that describes each part of the students’ paths and explain which student visited the most houses and how you know.
Mary claims she sees a pattern in the Counting Houses Task that she can use to solve the tasks below.
9 + 8 = ___ 9 + 7 = ___ 9 + 6 = ___
8 + 9 = ___ 7 + 9 = ___ 6 + 9 = ___
10 + 7 = ___ 10 + __ = 16 10 + __ = 15
What pattern do you see? ____________________________________________
• Will first grade students have opportunities to use the standards within the domain of Operations and Algebraic Thinking?
• What kind of student engagement will be possible with each task?
• Which Standards for Mathematical Practice will students have opportunities to use?
Common Core State Standards for Mathematics: Grade 1Operations and Algebraic Thinking 1.OA
Represent and solve problems involving addition and subtraction.
1.OA.A.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
1.OA.A.2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
Common Core State Standards, 2010, p. 15, NGA Center/CCSSO
Common Core State Standards for Mathematics: Grade 1Operations and Algebraic Thinking 1.OA
Understand and apply properties of operations and the relationship between addition and subtraction.
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.)
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.
Common Core State Standards, 2010, p. 15, NGA Center/CCSSO
Common Core State Standards for Mathematics: Grade 1Operations and Algebraic Thinking 1.OA
Add and subtract within 20.
1.OA.C.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).
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).
Common Core State Standards, 2010, p. 15, NGA Center/CCSSO
Common Core State Standards for Mathematics: Grade 1
Operations and Algebraic Thinking 1.OA
Work with addition and subtraction equations.
1.OA.D.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.
1.OA.D.8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = ? – 3, 6 + 6 = ?.
Common Core State Standards, 2010, p. 15, NGA Center/CCSSO
The CCSS for Mathematical Practice
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Common Core State Standards, 2010, p. 6-8, NGA Center/CCSSO
Research has identified characteristics related to each of the categories on the Mathematical Task Analysis Guide (TAG).
How do the characteristics that we identified when discussing the Counting Houses Task relate to those on the TAG? Which characteristics describe the Nine Plus a Number Task?
Tell if the scale will balance or tilt. If the scale does not balance, write which side will tilt down and why and indicate what would have to change to make the scale balance.
Addition Task DManipulatives/Tools available: Counters, cubes, grid paper, base ten blocks
Write a word problem for the number sentence.
8 + 6 = ___
Ask a question with your story problem so we know what we are supposed to figure out.
Write a word problem for the number sentence.
14 – 5 = ___
Ask a question with your story problem so we know what we are supposed to figure out.
Compare the two word problems. How do they differ from each other?
Subtraction Task EManipulatives/Tools available: base ten blocks
Solve this problem in two different ways: 32 - 17
After each way, write about how you did it. Be sure to include:• what materials, if any, you used to solve this problem;• how you solved it; and• an explanation of your thinking as you solved it.
First Way:
Second Way:
Adapted from Investigations in Number, Data, and Space, Dale Seymour, Menlo Park, CA, 1998.