In first grade Mathematics, students learn concepts based on the following Strands:
Number Concepts, Theory, Sense
- Read, write, compare, and order numbers to millions.
- EXT: Find different names, based on place value, for the same number.
- Recognize and use commutative (order) and associative (grouping) properties of addition and subtraction.
- Explain rounding and devise a rule for rounding whole numbers, decimals, and fractions. Use the rule to round up to hundred thousands and decimals to hundredths.
- Recognize estimation strategies (rounding, front end, compatible numbers, or using a referent) as they are applied naturally in problem-solving settings.
- Review multiplication facts, identifying the difficult ones not yet known. Develop strategies and learn the remaining multiplication facts.
- Recognize factors and products in multiplication sentences and explain their relationship and the relationship between multiplication and division.
- Demonstrate division, with and without remainders, using concrete materials in a problem solving setting. Decide the significance of any remainders.
- Estimate and identify fractional parts of figures or groups.
- Read, write, and compare fractions and mixed numbers.
- EXT: Order fractions and mixed numbers.
- Find equivalent fractions using models, paper folding, or graphics.
- EXT: Change mixed numbers to fractions greater than one by drawing representative models.
- Read, write, order, and compare tenths and hundredths using money as the model, and explain that hundredths includes tenths and hundredths. Continue the pattern to include thousandths.
- Explain and write ratios.
- EXT: Make circle graphs using simple percents and ratios.
- Demonstrate that decimals and fractions are names for the same number.
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Operations
- Estimate, add, and subtract 4-digit numbers to solve problems including subtracting money amounts and subtracting across zeroes.
- EXT: Add and subtract larger numbers.
- Estimate products. Multiply one digit numbers by 2- or 3-digit numbers and mentally by multiples of 10.
- Illustrate multiplication of 2-digit numbers by 2-digit numbers using models. Multiply 2-digit by 2-digit numbers. Recognize the regrouping pattern continues to hundreds times tens.
- Estimate quotients by using compatible numbers. Illustrate division of 2-digit and 3-digit numbers by 1-digit divisors using models. Find the quotient.
- EXT: Estimate quotients. Divide by multiples of 10.
- Estimate, add, and subtract fractions with like denominators. Add and subtract fractions with unlike denominators using models.
- Estimate, add, and subtract mixed numbers with like denominators.
- EXT: Add and subtract mixed numbers with unlike denominators using models.
- Estimate, add, and subtract decimals to hundredths by using models.
- Estimate and multiply 2-digit decimal numbers by 1-digit whole numbers, referring to money.
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Measurement
- Estimate lengths and measure to the nearest fourth inch and nearest millimeter.
- EXT: Investigate linear measures to 1/8 inch.
- Find the perimeter of a polygon by measuring the distance around its edge.
- EXT: Investigate perimeter of pentominoes; explain the findings.
- Find the area of regular and irregular polygons by covering and counting squares.
- EXT: Find the area of the faces of of cubes and rectangular prisms; combine to find surface area.
- Determine the volume of a rectangular prism by counting the number of cubes contained in it.
- EXT: Investigate contexts in which volume is measured using a variety of boxes and materials (e.g., popcorn, cubes, marbles, beans).
- Classify angles as less than, equal to, or greater than a right angle.
- Measure weight using ounces, pounds, grams, and kilograms; measure capacity using pints, cups, quarts, gallons, liters, and milliliters.
- Estimate and measure temperature in degrees Fahrenheit or degrees Celsius.
- Count coins and bills up to $20. Make change by counting on.
- EXT: Use amounts greater than $20.
- Read analog and digital clocks; read and write calendar dates.
- EXT: Determine elapsed time in hours and minutes. Determine elapsed time in days, weeks, and months.
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Geometry
- Identify and draw points, lines, line segments, rays, angles, parallel lines, perpendicular lines, and intersecting lines.
- Draw lines of symmetry in plane shapes and pictures.
- Identify and sort geometric shapes including triangles, quadrilaterals, pentagons, hexagons, octagons, and circles.
- Recognize congruent shapes including triangles.
- Make models of cubes and rectangular prisms.
- Investigate moving figures using slides, flips, and rotations.
- EXT: Build tessellations with congruent shapes using slides, flips, and rotations.
- Locate points on a grid using ordered pairs; name the coordinates of a given point.
- EXT: Create a design on grid paper and list the coordinate pairs in the order necessary to reproduce it.
- Construct similar geometric figures using squared paper, geoboards, and/or dot paper.
- EXT: Enlarge a design or picture using knowledge of similar figures and grid paper with different scales.
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Data Analysis/Statistics/Probability
- Collect, organize, and display survey data on line graphs, bar graphs, and pictographs.
- Explain the concept of average using concrete models.
- EXT: Find and record averages.
- Recognize that mean, median, mode, and range are different ways to describe the same data.
- Read and interpret circle graphs.
- EXT: Compare to data organized in other ways.
- Discuss probability including trials and outcomes (certain, impossible, probable, equally likely, and not equally likely).
- Estimate probability and write as ratios.
- Show possible outcomes for single events by making tree diagrams. Determine probability using tree diagrams.
- EXT: Create problems that can be represented by tree diagrams.
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Patterns/Functions/Algebra
- Identify and find missing addends and/or missing factors in equations.
- Multiply and divide by ten using patterns.
- Investigate patterns of multiples in a multiplication table.
- EXT: Find other patterns on a multiplication table, describing and explaining them in written form.
- Find the value of a function using positive integers as "input". (e.g., find the value (n) of the function n = x + 4 by substituting positive integers for x).
- Write a number sentence with one unknown to solve a problem (e.g., 4 + x = 9).
- Investigate counting on a calculator using the concept of a constant.
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Problem Solving/Application
- Identify and/or pose problems from everyday life and mathematical situations including problems to fit a given equation.
- Solve problems using a logical procedure (a plan).
- Identify information that is available but not needed. Identify additional information needed to solve a problem.
- Solve problems using appropriate materials and tools (e.g., calculator, grid paper, collectibles, manipulatives).
- Develop and apply operations and strategies (e.g., act it out, build a model, draw a picture or diagram, guess and check, make a chart or table, make a list, make a graph, use a pattern, use logical reasoning, solve a simpler problem, work backward) to solve a wide variety of routine and nonroutine problems.
- EXT: Generalize about information needed and process to be used to solve problems without numbers. (e.g., If I want to know how much my lunch costs for one school year, what information do I need and then what should I do?).
- Solve problems by working collaboratively with peers; entertain others' points of view.
- Share and explain (verbalize/record) thinking during and after solving a problem.
- Verify and interpret results with respect to the original problem situation.
- Investigate alternative ways of solving a problem.
- EXT: Compare and analyze solution paths (process used to solve a problem).
- Acquire confidence in using mathematics meaningfully to solve problems.
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