Agenda Day -3. Do Now Gallery Walk-Progressions Let’s Go to the Videotape Reflections. Day -5 . DO NOW Solve the Problem:. Find different ways to solve this problem. A second grade class needs 5 leaves each day to feed its 2 caterpillars.
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Solve the Problem:
A secondgrade class needs 5 leaves each day to feed its 2 caterpillars.
How many leaves would the students need each day for 12 caterpillars?
A Closer Look at the Progressions
How does seeing the progression of math instruction K-12 impact your practice?
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In Kindergarten, students represented addition and subtraction situations using objects, pictures and words.
In First Grade, students use the addition symbol (+) to represent joining situations, the subtraction symbol (-) to represent separating situations, and the equal sign (=) to represent a relationship regarding quantity between one side of the equation and the other.
Students need extensive experiences with addition and subtraction situations in order to connect the experiences with symbols (+, -, =) and equations (5 = 3 + 2).
Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 AND 5 = 4 + 1)
Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 (within 10)
e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
Mrs. Smith has 4 oatmeal raisin cookies, 5 chocolate chip cookies, and 6 gingerbread cookies. How many cookies does Mrs. Smith have?
I wrote: 4 + 5 + 6 = 1.
“ I know that 4 and 6 equals 10, so the oatmeal raisin and gingerbread equals 10 cookies. Then I added the 5 chocolate chip cookies. 10 and 5 is 15. So, Mrs. Smith has 15 cookies. “
Apply properties of operations as strategies to add and subtract. (within 10)
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.)
*Students need not use formal terms for these properties.
Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8. (within 10)
1.OA.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).
When solving addition and subtraction problems to 20, First Graders often use counting strategies, such as counting all, counting on, and counting back, before fully developing the essential strategy of using 10 as a benchmark number.
Counting All: Students count all objects to determine the total amount.
Counting On & Counting Back: Students hold a “start number” in their head and count on/back from that number.
Once students have developed counting strategies to solve addition and subtraction problems, it is very important to move students toward strategies that focus on composing and decomposing numbers using ten as a benchmark number
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);
•creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
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.
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 = ?
Five cookies were on the table. I ate some cookies. Then there were 3 cookies. How many cookies did I eat?
Student A: What goes with 3 to make 5? 3 and 2 is 5. So, 2 cookies were eaten.
Student B: Fiiivee, four, three (holding up 1 finger for each count). 2 cookies were eaten (showing 2 fingers).
Student C: We ended with 3 cookies. Threeeee, four, five (holding up 1 finger for each count). 2 cookies were eaten (showing 2 fingers).
Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
2.OA.2 Fluently add and subtract within 20 using mental strategies.
By end of grade 2, know from memory all sumtwo one-digit numbers.