Early+Problem+Solving+and+Fluency

=Early problem solving leading to fluency=

[|Early Problem Solving and Fluency powerpoint] (The ideas in this presentation are from Children's Mathematics: Cognitively Guided Instruction, by Thomas Carpenter, Elizabeth Fennema, Megan Loef Franke, and Linda Levi, published by Heinemann, 1999.) [|CGI problem set] [|Classification of addition and subtraction word problems, and typical strategies], from Children's Mathematics: CGI.

Use object and finger counting or drawings to solve real world problems (situations and stories) involving putting together and taking apart for totals up to 10. Write simple addition and subtraction sentences that go along with these problems.
 * Kindergarten Problem Solving **


 * 1st Grade Problem Solving and Fluency**

** Single digit numbers ** Use a progression of strategies (direct modeling, counting strategies, derived facts and known facts) to solve real world problems involving addition and subtraction with one digit numbers; record using numbers and symbols. Add three one-digit numbers. Learn all the addition facts up to 10 + 10, and solve the related subtraction problems fluently. Understand that subtraction “undoes” addition: because 3 + 5 = 8, we know that 8 - 3 = 5 and 8 - 5 = 3. S olve simple open sentences for addition and subtraction, such as: ? + 2 = 7 and 10 - ? = 6, using knowledge of fact families.

Use strategies and number facts to solve real world problems involving addition and subtraction with numbers up to 30; record using numbers and symbols. Compute sums and differences through 30 using number facts and strategies, but no formal algorithm. Calculate mentally sums and differences involving a two-digit number and a one-digit number without regrouping, or a two-digit number and a multiple of 10.
 * With numbers to 30**

Solve simple one-step word problems using addition and subtraction of length, money and time, including “how much more/less,” without mixing units.
 * Use real-life measurement problems**


 * 2nd Grade Problem Solving and Fluency**

Use strategies and number facts to solve real world problems involving addition and subtraction with numbers up to 30. Find the distance between numbers on the number line, e.g., how far is 79 from 26? Add fluently two numbers through 99, using strategies including formal algorithms; subtract fluently two numbers through 99. Find missing values in open sentences, e.g., 42 + ? = 57; use relationship between addition and subtraction. Estimate the sum of two numbers with three digits.
 * Adding and subtracting **

Represent situations involving groups of equal size or of sharing equally (not measurement division) with objects and symbols; solve using various strategies with numbers up to 5 x 5. Understand multiplication as the result of counting the total number of objects in a set of equal groups, e.g., 3 x 5 gives the number of objects in 3 groups of 5 objects, ie., 3 x 5 = 5 + 5 + 5 = 15. Represent multiplication using area and array models. Understand division (÷) as another way of expressing multiplication, using fact families within the 5 x 5 multiplication table; understand that division “undoes” multiplication, e.g., 2 x 3 = 6 can be rewritten as 6 ÷ 2 = 3 or 6 ÷ 3 = 2.
 * Multiplication and division**