Day of the Week worksheet

1. Day of the week: Monday

1. Use month m = 4 and year 2026, then split the year into its century (J) and last two digits (K). Only January and February move to the year before

   $\text{q, m, K, J}$$=\text{27, 4, 26, 20}$

2. Add up how far the day, month, year and century each push the weekday along

   $27+13+26+6+5+100$$=177$

3. Divide by 7 and keep the remainder, since the days repeat every week: 0 is Saturday, 1 Sunday, up to 6 for Friday

   $177\text{mod 7}$$=2$

4. Match the remainder to its weekday

   $\text{h =}2$$=\text{Monday}$

2. Day of the week: Friday

1. Use month m = 12 and year 2024, then split the year into its century (J) and last two digits (K). Only January and February move to the year before

   $\text{q, m, K, J}$$=\text{13, 12, 24, 20}$

2. Add up how far the day, month, year and century each push the weekday along

   $13+33+24+6+5+100$$=181$

3. Divide by 7 and keep the remainder, since the days repeat every week: 0 is Saturday, 1 Sunday, up to 6 for Friday

   $181\text{mod 7}$$=6$

4. Match the remainder to its weekday

   $\text{h =}6$$=\text{Friday}$

3. Day of the week: Friday

1. In Zeller's method, February counts as month 14 of the year before (2025), so the leap day falls at the end of the counting year

   $\text{q, m, K, J}$$=\text{6, 14, 25, 20}$

2. Add up how far the day, month, year and century each push the weekday along

   $6+39+25+6+5+100$$=181$

3. Divide by 7 and keep the remainder, since the days repeat every week: 0 is Saturday, 1 Sunday, up to 6 for Friday

   $181\text{mod 7}$$=6$

4. Match the remainder to its weekday

   $\text{h =}6$$=\text{Friday}$

4. Day of the week: Thursday

1. In Zeller's method, February counts as month 14 of the year before (2026), so the leap day falls at the end of the counting year

   $\text{q, m, K, J}$$=\text{4, 14, 26, 20}$

2. Add up how far the day, month, year and century each push the weekday along

   $4+39+26+6+5+100$$=180$

3. Divide by 7 and keep the remainder, since the days repeat every week: 0 is Saturday, 1 Sunday, up to 6 for Friday

   $180\text{mod 7}$$=5$

4. Match the remainder to its weekday

   $\text{h =}5$$=\text{Thursday}$

5. Day of the week: Monday

1. In Zeller's method, January counts as month 13 of the year before (2026), so the leap day falls at the end of the counting year

   $\text{q, m, K, J}$$=\text{25, 13, 26, 20}$

2. Add up how far the day, month, year and century each push the weekday along

   $25+36+26+6+5+100$$=198$

3. Divide by 7 and keep the remainder, since the days repeat every week: 0 is Saturday, 1 Sunday, up to 6 for Friday

   $198\text{mod 7}$$=2$

4. Match the remainder to its weekday

   $\text{h =}2$$=\text{Monday}$

6. Day of the week: Thursday

1. Use month m = 7 and year 2025, then split the year into its century (J) and last two digits (K). Only January and February move to the year before

   $\text{q, m, K, J}$$=\text{24, 7, 25, 20}$

2. Add up how far the day, month, year and century each push the weekday along

   $24+20+25+6+5+100$$=180$

3. Divide by 7 and keep the remainder, since the days repeat every week: 0 is Saturday, 1 Sunday, up to 6 for Friday

   $180\text{mod 7}$$=5$

4. Match the remainder to its weekday

   $\text{h =}5$$=\text{Thursday}$

7. Day of the week: Wednesday

1. Use month m = 4 and year 2026, then split the year into its century (J) and last two digits (K). Only January and February move to the year before

   $\text{q, m, K, J}$$=\text{15, 4, 26, 20}$

2. Add up how far the day, month, year and century each push the weekday along

   $15+13+26+6+5+100$$=165$

3. Divide by 7 and keep the remainder, since the days repeat every week: 0 is Saturday, 1 Sunday, up to 6 for Friday

   $165\text{mod 7}$$=4$

4. Match the remainder to its weekday

   $\text{h =}4$$=\text{Wednesday}$

8. Day of the week: Saturday

1. Use month m = 7 and year 2026, then split the year into its century (J) and last two digits (K). Only January and February move to the year before

   $\text{q, m, K, J}$$=\text{11, 7, 26, 20}$

2. Add up how far the day, month, year and century each push the weekday along

   $11+20+26+6+5+100$$=168$

3. Divide by 7 and keep the remainder, since the days repeat every week: 0 is Saturday, 1 Sunday, up to 6 for Friday

   $168\text{mod 7}$$=0$

4. Match the remainder to its weekday

   $\text{h =}0$$=\text{Saturday}$

9. Day of the week: Monday

1. Use month m = 11 and year 2025, then split the year into its century (J) and last two digits (K). Only January and February move to the year before

   $\text{q, m, K, J}$$=\text{17, 11, 25, 20}$

2. Add up how far the day, month, year and century each push the weekday along

   $17+31+25+6+5+100$$=184$

3. Divide by 7 and keep the remainder, since the days repeat every week: 0 is Saturday, 1 Sunday, up to 6 for Friday

   $184\text{mod 7}$$=2$

4. Match the remainder to its weekday

   $\text{h =}2$$=\text{Monday}$

10. Day of the week: Monday

1. In Zeller's method, February counts as month 14 of the year before (2026), so the leap day falls at the end of the counting year

   $\text{q, m, K, J}$$=\text{15, 14, 26, 20}$

2. Add up how far the day, month, year and century each push the weekday along

   $15+39+26+6+5+100$$=191$

3. Divide by 7 and keep the remainder, since the days repeat every week: 0 is Saturday, 1 Sunday, up to 6 for Friday

   $191\text{mod 7}$$=2$

4. Match the remainder to its weekday

   $\text{h =}2$$=\text{Monday}$