Mathematics Course: Parent Teaching Notes and Answers
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Companion to the ten-lesson Mathematics student course. Student reasoning and intermediate steps matter. Answers assume problems exactly as stated. Work by demonstrated readiness, not birthday. Keep assessment records private.
Lesson 1: Place value
- Foundations: 17=1 ten and 7 ones; 16>12
- Builders: 2,406=2,000+400+6; ascending 709,790,907; 583 rounds to 580
- Advancing: 6,052,013=6,000,000+50,000+2,000+10+3; -4>-9
Lesson 2: Addition and subtraction
- Foundations: 7+5=12; 10-6=4; 9+8=17
- Builders: 368+475=843; 904-587=317; 35-18=17
- Advancing: -7+12=5; -3-8=-11; 204.75+39.68=244.43; 1002-478=524
Lesson 3: Multiplication and division
- Foundations: 3×4=12; 12÷3=4
- Builders: 26×8=208; 144÷12=12; 375÷5=75
- Advancing: -12×7=-84; 2.4×0.6=1.44; 315÷0.9=350; 3(2x+5)=6x+15
Lesson 4: Fractions
- Foundations: One fourth is 1/4; two fourths is 2/4=1/2
- Builders: 6/8=3/4; 3/8+2/8=5/8; 3/4 of 28=21; 5/6-1/3=1/2
- Advancing: 2/3+5/8=31/24=1 7/24; 7/9 ÷ 2/3=7/6; -3/4×8/5=-6/5
Lesson 5: Decimals and money
- Foundations: 100 cents=$1, 50 cents=$0.50; 1 dollar is greater
- Builders: 6.75+3.80=10.55; 12.4-5.95=6.45; .25×60=15; $40 less 10%=$36
- Advancing: 18% of 250=45; $85 less 12%=$74.80; 3.75÷.15=25; 40 to 50 rises 25%
Lesson 6: Measurement and geometry
- Foundations: Check direct comparison and correct identification of shapes
- Builders: Rectangle perimeter 26 cm and area 36 cm²; 3 ft=36 in; triangle area 30 square units
- Advancing: Circle area approximately 28.26 cm²; box volume 120 cm³; supplement of 127° is 53°
Lesson 7: Ratios and proportion
- Foundations: 2 red to 1 blue repeated 3 times makes 6 red and 3 blue
- Builders: 12:18=2:3; 4/7=x/28 gives x=16; unit price $0.75 per pencil
- Advancing: 5/8=x/40 gives x=25; 7 cm=84 km; speed 60 mph
Lesson 8: Expressions and equations
- Foundations: 3+2=5
- Builders: x+18=47 gives x=29; 5x=65 gives x=13; 3x-7=20 gives x=9
- Advancing: 4(2x-3)+5x=13x-12; 2(x+4)=3x-1 gives x=9; -2(3²)+5=-13
Lesson 9: Data and probability
- Foundations: 3 red, 2 blue, 1 green, total 6 objects
- Builders: 5,7,7,9,12: mean 8, median 7, mode 7, range 7
- Advancing: 2,5,5,8,10: mean 6, median 5, mode 5, range 8; even result on fair die=1/2
Lesson 10: Review
- Foundations: 8+7=15; 14-6=8; 4 groups of two=8; count 16
- Builders: 245+376=621; 72÷9=8; 3/4 of 36=27; area 8×7=56
- Advancing: 4x-9=23 gives x=8; 5/6+3/4=19/12=1 7/12; 22% of 150=33; mean 4,8,10,14=9
Instruction and Review Routine
- Before instruction, check prerequisite counting, number recognition, and operations. Model a worked problem, solve a different one together, then ask for independent work.
- When a student misses a problem, ask for the process. Revisit the prerequisite, model a corrected method, then give a NEW problem rather than the same memorized item.
- Separate calculation accuracy from the explanation. Note whether the student independently chose a strategy and checked units.
- Use the official current grade-level mathematics standards for full-year planning; these ten lessons alone do not certify coverage of all standards.