Place Value, Operations, and Geometry

The year opens with place value to ten thousands, including reading and writing numbers in standard and expanded form, comparing multi-digit numbers, and rounding to the nearest ten, hundred, or thousand. Work continues with multi-digit addition and subtraction with regrouping, then multiplication through arrays, equal groups, and facts to 10 times 10, followed by division within 100 and related fact families. Fractions are studied as parts of a whole, with shading, comparison, number lines, and simple equivalents. Measurement and time cover length to the quarter-inch, liquid volume in cups, pints, and quarts, and elapsed time to the minute, while geometry addresses perimeter, area of rectangles, and quadrilaterals. The year closes with scaled bar and picture graphs plus multi-step word problems using all four operations.

Materials and booklist

• Spectrum Math Grade 3 · Spectrum (optional)A straightforward workbook you can open to the matching topic for extra practice pages whenever Nora wants more reps.
• Khan Academy Grade 3 Math · Khan Academy (optional)Short free videos and practice sets that line up with each unit; great for a quick demo or independent review.
• Household measuring tools and grid paper (optional)A ruler, measuring cups, a kitchen scale if you have one, and plain grid paper let you turn baking and horse chores into hands-on math without buying special kits.
• The Grapes of Math · Greg Tang (optional)A lively picture book of math riddles you can read aloud for fun number-sense practice any week.

1. 1. Place Value to Ten Thousands · weeks 1–4

   Nora learns to read, write, and break apart numbers up to 10,000 using place-value charts, base-ten blocks (or homemade ones from cereal), and quick games. We practice comparing and rounding so big numbers feel friendly, not scary.

   Learns to: reads and writes numbers to 10,000 in standard and expanded form · compares multi-digit numbers using greater-than and less-than symbols · rounds numbers to the nearest ten, hundred, or thousand · identifies the value of any digit in a four- or five-digit number

2. 2. Multi-Digit Addition and Subtraction · weeks 5–9

   Nora masters adding and subtracting three- and four-digit numbers with regrouping. We use number lines, place-value drawings, and real life (baking batch sizes, horse feed bags) so the steps make sense and stick.

   Learns to: adds three- and four-digit numbers with regrouping · subtracts three- and four-digit numbers with regrouping · checks subtraction answers by adding · solves one- and two-step word problems using addition or subtraction

3. 3. Multiplication Concepts and Facts · weeks 10–14

   Nora discovers multiplication as equal groups, arrays, and repeated addition. She builds fluency with facts through 10 using skip-counting, games, and horse-related story problems (hooves, stalls, apple treats).

   Learns to: represents multiplication with arrays and equal groups · recalls multiplication facts through 10 times 10 · multiplies one-digit numbers by multiples of 10 · writes related multiplication sentences for a given array

4. 4. Division and Fact Families · weeks 15–18

   Nora learns division as sharing and as the partner of multiplication. She practices dividing within 100, connects facts into families, and solves simple story problems about sharing trail-mix bags or stall chores.

   Learns to: divides numbers within 100 with whole-number answers · writes the full fact family for a set of related numbers · solves one-step division word problems · identifies the dividend, divisor, and quotient in a division equation

5. 5. Fractions as Parts of a Whole · weeks 19–23

   Nora explores unit fractions and simple fractions using baking pans, measuring cups, and paper folding. She compares fractions, finds equivalents, and places them on a number line so parts-of-a-whole feel concrete.

   Learns to: names and shades unit fractions and simple fractions of a whole · compares two fractions with the same numerator or same denominator · locates fractions on a number line between 0 and 1 · recognizes and generates simple equivalent fractions

6. 6. Measurement and Time · weeks 24–27

   Nora measures length in inches and feet, mass in ounces and pounds, and liquid volume in cups, pints, and quarts (perfect for baking). She also tells time to the minute and calculates elapsed time for horse-show schedules or cookie baking.

   Learns to: measures length to the nearest half-inch and quarter-inch · estimates and measures liquid volume using cups, pints, and quarts · tells and writes time to the nearest minute on analog clocks · solves word problems involving elapsed time within an hour

7. 7. Area, Perimeter, and Shapes · weeks 28–31

   Nora finds the perimeter and area of rectangles using grid paper, tile squares, and real objects (stall mats, cookie sheets). She classifies shapes by sides and angles and builds simple figures.

   Learns to: calculates the perimeter of rectangles and other polygons · finds the area of rectangles by counting square units or multiplying side lengths · distinguishes between area and perimeter in word problems · identifies and draws quadrilaterals including rectangles, squares, and rhombuses

8. 8. Data, Graphs, and Problem-Solving · weeks 32–36

   Nora collects simple data (favorite horse breeds, cookie preferences), makes bar graphs and picture graphs, and solves multi-step word problems that pull together the year’s skills. This unit wraps up with confidence-building mixed practice.

   Learns to: creates and reads scaled bar graphs and picture graphs · solves one- and two-step word problems using data from a graph · solves multi-step word problems using any of the four operations · explains the steps used to solve a multi-step problem in writing