| Number and Number
Systems |
- Identify and generate
equivalent forms of whole numbers (e.g., 36, 30+6, 9X4, 46-10, number of
inches in a yard).
- Use place value concepts to
represent whole numbers and decimals using numerals, words, expanded
notation and physical models. For example:
a. Recognize 100 means "10 tens" as well as a single
entity (1 hundred) through physical models and trading games.
b. Describe the multiplicative nature of the number system (e.g.,
the structure of 3205 as 3X1000 plus 2X100 plus 5X1.
c. Model the size of 1000 in multiple ways (e.g., packaging 1000
objects into 10 boxes of 100, modeling a meter with centimeter and
decimeter strips, or gathering 1000 pop-can tabs.
d. Explain the concept of tenths and hundredths using physical
models. such as metric pieces, base ten blocks, decimal squares or money.
- Use mathematical language and
symbols to compare and order (e.g., less than, greater than, at most, at
least, <, >, =).
- Count money and make change using
coins and paper bills to ten dollars.
- Represent fractions and mixed
numbers using words, numerals and physical models.
- Compare and order commonly used
fractions and mixed numbers using number lines, models (such as fraction
circles or bars), points of reference (such as more or less than 1/2), and
equivalent forms using physical or visual models.
- Recognize and use decimal and
fraction concepts and notations as related ways of representing parts of a
whole or a set (e.g., 3 of 10 marbles are red can also be described as
3/10 and 3 tenths are red).
|
| Meaning of Operations |
- Model, represent and
explain multiplication (e.g., repeated addition, skip counting,
rectangular arrays and area model). For example:
a. Use conventional mathematical symbols to write equations for word
problems involving multiplication.
b. Understand that, unlike addition and subtraction, the factors in
multiplication and division may have different units (e.g., 3 boxes or 5
cookies each).
- Model, represent and explain
division (e.g., sharing equally, repeated subtraction, rectangular arrays
and area model. For example:
a. Translate contextual situations involving division into
conventional mathematical symbols.
b. Explain how a remainder may impact an answer in a real-world
situation (e.g., 14 cookies being shared by 4 children).
- Explain and use relationships
between operations, such as:
a. relate addition and subtraction as inverse operations;
b. relate multiplication and division as inverse operations;
c. relate addition to multiplication (repeated addition);
d. relate subtraction to division (repeated subtraction).
|
| Computation and
Estimation |
- Model and use the
commutative and associative properties for addition and multiplication.
- Add and subtract whole numbers with
and without regrouping.
- Demonstrate fluency in
multiplication facts through 10 and corresponding division facts.
- Multiply and divide 2- and 3-digit
numbers by a single-digit number, without remainders for division.
- Evaluate the reasonableness of
computations based upon operations and the number involved (e.g.,
considering relative size, place value and estimates.
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