Elementary Mathematics K-5 Essential Standards
- count to tell the number of objects.
- compare numbers to 10.
- understand addition means putting together and subtraction means taking apart.
- show and solve problems involving addition and subtraction, using, math mountains, equations, and/or drawings.
- decide correctly when to use addition and when to use subtraction when solving math word problems.
- add and subtract within 20.
- count to 120.
- tell time to the hour and half hour using analog and digital clocks.
- add and subtract 2-digit numbers, without regrouping.
- use paper clips, cubes, etc., to measure the length of objects.
- describe what makes a square a square, a circle a circle, etc.
- tell the differences between shapes.
- create shapes.
- measure with centimeters and inches.
- tell time on digital and analog clocks.
- add and subtract 3 digit numbers.
- draw equal shares.
- recognize and draw 3 dimensional shapes.
- find the value of a collection of dollar bills, quarters, dimes, nickels, and pennies.
- solve second grade word problems.
- represent and solve problems involving multiplication and division.
- use place value understanding and properties of operations to perform multi-digit arithmetic.
- develop an understanding of fractions as numbers.
- represent and interpret data.
- solve problems involving estimation and measurement.
- fluently add and subtract multi-digit whole numbers.
- represent and solve problems involving multiplication of 2-digit x 2-digit and 1-digit x 3-digit numbers.
- represent and solve problems involving division of up to 4-digit quotients and single digit divisors.
- use the order of operations to solve equations (exponents not introduced yet).
- fluently add and subtract fractions with like denominators.
- fluently multiply fractions by a whole number.
- read, write and compare decimals to the hundredths place.
- understand the concept of angles and measure angles.
- understand the place value system and be able to perform operations on multi-digit whole numbers and decimals to the hundredths place.
- multiply with whole numbers, decimals and fractions.
- divide with whole numbers, decimals and fractions.
- add and subtract using decimals and fractions.
Grades 4K - 5
Math Expressions
Math Expressions is a Houghton Mifflin Harcourt curriculum based on the Children's Math Worlds Research Project. The researchers in this project carried out ten years of research, working with teachers, students, parents and administrators to identify learning approaches accessible to all children. This program is a blend of traditional practices and new, more innovative ways of teaching students.
The units for grades kindergarten and first grade consist of completely integrated units. Units in grades 2-5 employ longer units that focus on computations, algebra and data. Each is then followed by a mini-unit that focuses on geometry or measurement and uses previously learned mathematics. Word problems are continually intertwined with all computational learning, and students solve an ambitious and carefully chosen trajectory of word problem types across the grades.
The Children's Math World Research identified five crucial components of a classroom that develop mathematical understandings, competence and competence. These components - building concepts, math talk, student leaders, quick practice and building communities - are the basis for the way that Math Expressions is put together. It is an approach that emphasizes in-depth, sustained learning of core grade level concepts.
Key Components:
- Unit and lessons start at a student's level and continually elicit thinking.
- Visual and linguistic supports that all children understand are provided.
- Many types of math drawings are used in each math domain. They are either made by students or are researched-based visual representations to support students understanding and class discussions of mathematical thinking.
- Ongoing interaction between individual and whole-class learning is promoted.
- Differentiated instruction within whole-class activities is infused.
- Research-based models, strategies and algorithms are used to help all students.